-
The third table
-
The first table
-
none
-
7x + 2y = 1
-
The domain stays the same, but the range changes.
-
Graph 4
-
(4.6, 4.232)
-
Table 1
-
x = 5
-
0.50 kWh per day
-
b = –2
-
0.6
-
Graph 1
-
Percy earns a greater hourly wage of $7.50 at the coffee cart.
-
f(-1) = 0
-
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.
-
3
-
Graph 4
-
(3, 4)
-
10
Which table represents viable solutions for y = 5x, where x is the number of tickets sold for the school play and y is the amount of money collected for the tickets?A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries negative 100, negative 25, 40, 600. The second column is labeled money collected (y) with entries negative 500, negative 125, 250, 3000.A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries negative 20, 20, 100, 109. The second column is labeled money collected (y) with entries negative 100, 100, 500, 545.A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries 0, 10, 51, 400. The second column is labeled money collected (y) with entries 0, 50, 255, 2000.A 2-column table with 4 rows titled School Play Tickets. The first column is labeled tickets (x) with entries 5, 65, 80, 200. The second column is labeled money collected (y) with entries 25, 350, 400, 1000.
2. Which table represents a direct variation function?A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5.A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2.A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10.A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
3. How many intersections are there of the graphs of the equations below?
One-halfx + 5y = 6
3x + 30y = 36
none
one
two
infinitely many
4. Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
5. The function graphed is reflected across the x-axis to create a new function.Which is true about the domain and range of each function?
Both the domain and range change.
Both the range and domain stay the same.
The domain stays the same, but the range changes.
The range stays the same, but the domain changes.
6. Ray was in charge of filling the soccer team’s water jug for practice. At the beginning of practice he filled the jug. Halfway through practice the team took a water break. After the break Ray refilled the jug so the players could have water after practice. At the end of practice Ray drained the jug. Which graph could represent the level of the water in the jug during and after practice? 1. A graph titled Water Break. The horizontal axis shows Practice time (minutes), numbered 6 to 60, and the vertical axis shows Water (quarts), numbered 2 to 20. The line starts at 15 quarts, is constant to 25 minutes, decreases to 5 quarts at 35 minutes, increases to 14 quarts at 37 minutes, decreases. 2. A graph titled Water Break. The horizontal axis shows Practice time (minutes), numbered 6 to 60, and the vertical axis shows Water (quarts), numbered 2 to 20. The line starts at 0 quarts, increases to 15 quarts at 5 minutes, constant to 25 minutes, decreases to 5 quarts at 35 minutes, decreases. 3. A graph titled Water Break. The horizontal axis shows Practice time (minutes), numbered 6 to 60, and the vertical axis shows Water (quarts), numbered 2 to 20. The line starts at 15 quarts, constant to 25 minutes, decreases to 5 quarts at 35 minutes, constant to 55 minutes, decreases. 4. A graph titled Water Break. The horizontal axis shows Practice time (minutes), numbered 6 to 60, and the vertical axis shows Water (quarts), numbered 2 to 20. The line starts at 0 quarts, increases to 15 quarts at 5 minutes, constant to 25 minutes, decreases to 5 quarts at 35 minutes, increases to 14 quarts at 37 minutes, constant to 55 minutes, decreases.
7. Graph the function y = 8 –StartRoot 2 x + 6 EndRoot. Which is the best approximation of a point on the function?
(4.4, 3.421)
(4.6, 4.232)
(5.2, 4.025)
(5.9, 3.781)
8. Elias and Niko are polishing the silver at the heritage museum. Elias could polish all the silver himself in 40 minutes. That task would take Niko 50 minutes to complete alone. Which table is filled in correctly and could be used to determine how long it would take if Elias and Niko polished the silver together? 1. A table showing Rate in part per minute, Time in minutes, and Part of Silver Polished. The First row shows Elias, and has StartFraction 1 Over 40 EndFraction, t, and StartFraction 1 Over 40 EndFraction t. The second row shows Niko and has, StartFraction 1 Over 50 EndFraction, t, and StartFraction 1 Over 50 EndFraction t. 2. A table showing Rate in part per minute, Time in minutes, and Part of Silver Polished. The First row shows Elias, and has r, StartFraction 1 Over 40 EndFraction, and StartFraction 1 Over 40 EndFraction r. The second row shows Niko and has, r, StartFraction 1 Over 50 EndFraction, and StartFraction 1 Over 50 EndFraction r. 3. A table showing Rate in part per minute, Time in minutes, and Part of Silver Polished. The First row shows Elias, and has 40, t, and 40 t. The second row shows Niko and has, 50, t, and 50 t . 4. A table showing Rate in part per minute, Time in minutes, and Part of Silver Polished. The First row shows Elias, and has r, 40, and 40 r. The second row shows Niko and has, r 50, and 50 r .
9. What is the solution to 4|0.5x – 2.5| = 0?
x = 1.25
x = 5
x = –1.25 or x = 1.25
x = –5 or x = 5
10. The graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number of days it is plugged into the wall current.A coordinate grid showing Clock Radio Electricity Usage, with Days Connected to Current on the x-axis and Electricity Usage in kilowatt hours on the y-axis with a line starting at (0, 0) and passing through (2, 0.5) and (6, 1.5).Which is a reasonable estimate of the constant of variation?
0.25 kWh per day
0.50 kWh per day
2.40 kWh per day
4.00 kWh per day
11. What is the solution to the linear equation?
–12 + 3b – 1 = –5 – b
b = –2
b = –1.5
b = 1.5
b = 2
12. The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins.A table showing Rate in part per hour, Time in hours, and Part of Bins Emptied. The first row shows First Truck and has, StartFraction 1 Over 5 EndFraction, t, and StartFraction 1 Over 5 EndFraction times t. The second row shows Second Truck and has, StartFraction 1 Over 8 EndFraction, t, and StartFraction 1 Over 8 EndFraction times t. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty?
0.6
0.5
0.7
0.4
13. Becky created a graph to represent her distance away from home one afternoon. She left home and ran to the park, met some friends and stayed at the park, and then walked back home using the same route. Which graph could Becky have created? 1. A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows an increase, constant, and decrease in distance. 2. A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows an decrease, constant, and decrease in distance. 3. A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows an increase and decrease in distance. 4. A graph titled Becky's distance from home. The horizontal axis shows time (minutes) and the vertical axis shows distance (miles). Both axes are unnumbered. The line shows a constant, decrease, and increase in distance.
14. Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below.
3x + 2y = 36.50
2x + 5y = 50.00
At which job does Percy earn the greater hourly wage? How much does Percy earn each hour at this job?
Percy earns a greater hourly wage of $7.00 at the library.
Percy earns a greater hourly wage of $7.00 at the coffee cart.
Percy earns a greater hourly wage of $7.50 at the library.
Percy earns a greater hourly wage of $7.50 at the coffee cart.
15. The table represents a function.A 2-column table with 4 rows. The first column is labeled x with entries negative 5, negative 1, 6, 9. The second column is labeled f of x with entries 4, 0, negative 1, negative 3.What is the value of f(–1)?
f(-1)=3
f(-1)=-1
f(-1)=0
f(-1)=6
16. Yesterday, Selma read 75 pages of her book. If she reads at a pace of 2 pages per minute today, which table shows only viable solutions for the total number of pages she has read, y, after x minutes have elapsed? A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185. A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries negative 16, 6, 27, 52. The second column is labeled total pages read (y) with entries 43, 87, 129, 179.A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 19, 32, 47. The second column is labeled total pages read (y) with entries 0, 113, 139, 169. A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 11, 20.25, 58. The second column is labeled total pages read (y) with entries 75, 97, 115.5, 191.
17. A sequence is defined by the recursive function f(n + 1) = one-halff(n). If f(3) = 9 , what is f(1) ?
1
3
27
81
18. Which is the graph of y – 3 = -2/3(x + 6)? 1. A coordinate grid with a line passing through the points at (negative 3, 1), (0, negative 1), and (3, negative 3). 2. A coordinate grid with a line passing through the points at (negative 2, 1), (0, 0), and (4, negative 3). 3. A coordinate grid with a line passing through the points at (negative 3, 0), (0, negative 2), and (3, negative 4). 4. A coordinate grid with a line passing through the points at (negative 3, 3), (0, 1), and (3, negative 1).
19. What is the solution (a, c) to this system of linear equations?
2a – 3c = –6
a + 2c = 11
(negative StartFraction 76 over 7 EndFraction, StartFraction 17 over 7 EndFraction)
(3, –4)
(3, 4)
(StartFraction 87 over 7 EndFraction, negative StartFraction 5 over 7 EndFraction)
20. A function g(x) is defined as shown.
g(x) = StartLayout enlarged left-brace 1st Row 1st column 2 + 3 x, 2nd column 0 less-than-or-equal-to x less-than 4 2nd Row 1st column 0.5 x + 10, 2nd column 4 less-than-or-equal-to x less-than 8 3rd Row 1st column 16, 2nd column x greater-than-or-equal-to 8 EndLayout
What is the value of g(4)?
10
12
14
16
only answers
7 answers
21. Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation 0.10 d plus 0.05 n equals 5.25, where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have?
35
42
63
105
22. Which is the graph of linear inequality x – 2y ≥ –12? 1. On a coordinate plane, a dashed straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the right of the line is shaded. 2. On a coordinate plane, a solid straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the left of the line is shaded. 3. On a coordinate plane, a dashed straight line with negative slope goes through (negative 6, 6) and (0, negative 6). Everything to the right of the line is shaded. 4. On a coordinate plane, a solid straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the right of the line is shaded.
23. The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?
w ≤ 10 – l
2l + 2w ≥ 62
w ≤ 10 – l
2l + 2w > 62
w ≤ l – 10
2l + 2w ≥ 62
w ≤ l – 10
2l + 2w > 62
24. The potential energy, P, in a spring is represented using the formula P = A equals StartFraction one-half EndFraction b h.kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework.
Which equation should she use?
k = 2Px^2
k = k equals StartFraction one-half EndFraction P x squared.Px2
k = k equals StartFraction 2 P Over x squared EndFraction.
k = k equals StartFraction P Over 2 x squared EndFraction.
25. The graph represents the data cost for monthly Internet service for a cell phone. On a coordinate plane, a graph titled Cell Phone Internet Service shows Gigabytes Used on the x-axis and Monthly Cost in dollars on the y-axis. A piecewise function has 3 lines. The 1st line has a closed circle at (0, 15), continues horizontally at y = 15, then has a closed circle at (2, 15). The 2nd line has an open circle at (2, 20) and then continues up to a closed circle at (6, 40). The 3rd line has an open circle at (6, 50) and then continues horizontally at y = 50.Which function, C(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month?
Which function, C(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month? 1. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15, 2nd column 0 less-than-or-equal-to x less-than-or-equal-to 2 2nd Row 1st column 5 x + 10, 2nd column 2 less-than x less-than-or-equal-to 6 3rd Row 1st column 50, 2nd column 6 less-than x EndLayout 2. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15, 2nd column 0 less-than-or-equal-to x less-than 2 2nd Row 1st column 5 x + 20, 2nd column 2 less-than-or-equal-to x less-than 6 3rd Row 1st column 50, 2nd column 6 less-than-or-equal-to x EndLayout 3. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15x, 2nd column 0 less-than-or-equal-to x less-than-or-equal-to 2 2nd Row 1st column 20 x + 5, 2nd column 2 less-than x less-than-or-equal-to 6 3rd Row 1st column 50 x, 2nd column 6 less-than x EndLayout 4. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15x, 2nd column 0 less-than-or-equal-to x less-than 2 2nd Row 1st column 5 x + 10, 2nd column 2 less-than-or-equal-to x less-than 6 3rd Row 1st column 50 x, 2nd column 6 less-than-or-equal-to x EndLayout
26. An electrician is hired to install a ceiling fan. She estimates that the installation will take no more than 45 minutes if the house is up to building code. If the house is not up to building code, she estimates that the installation will take longer than 120 minutes. Which graph represents the number of minutes it could take her to install the fan?
1. number line closed circle on 45 til open circle 120. 2. open circle on 45 til closed circle on 120. 3. closed circle on 45 going left and open circle on 120 going right. 4. open circle on 40 going left closed circle on 120 going right.
27. What is the solution to –2(8x – 4) < 2x + 5?
x > x is greater than StartFraction 1 Over 6 EndFraction.
x < x is less than StartFraction 1 Over 6 EndFraction.
x > 6
x < 6
28. This mapping shows a functional relationship.A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (2, 4), (negative 3, 0), (negative 1, negative 1), (4, 3).When f(x)=4, what is the value of x?
0
2
3
4
29. Graph the function y = |8 - 2x| + 3. Which is a point on the function?
(6.2, 7.4)
(7.8, 11.2)
(8.6, 6.8)
(9.6, 7.3)
30. What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x?
1. The distributive property: 4x – 12 + 4 < 10 + 6x
2. Combine like terms: 4x – 8 < 10 + 6x
3. The addition property of inequality: 4x < 18 + 6x
4. The subtraction property of inequality: –2x < 18
5. The division property of inequality: ________
x < –9
x > –9
x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction.
x > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.
31. Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book.A table showing Coffee Shop Coupon Savings with 2 columns and 6 rows. The first column, x, has the entries, 0, 5, 10, 15, 20. The second column, y, has the entries. negative 20, negative 10, 0, 10, 20.What are the slope and y-intercept of the line represented by the points shown in the table?
slope: 2, y-intercept: –20
slope: 2, y-intercept: 10
slope: 5, y-intercept: –20
slope: 5, y-intercept: 10
32. On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (2.4, negative 51) and a maximum value of (negative 0.75, 6), crosses the x-axis at (negative 2, 0), (0, 0), and (3.5, 0), and crosses the y-axis at (0, 0).Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to negative infinity, the function's values go to positive infinity
33. Samir, a carpenter, spent $300 on specialty tools to make toy horses for children. For each horse he makes, he spends $75 on supplies. He charges $125 for each horse. How many horses must Samir sell in order to break even?
2
3
4
6
34. On a coordinate plane, a curved line, labeled f of x, with a minimum value of (negative 1.9, negative 5.7) and a maximum value of (0, 2) crosses the x-axis at (negative 2.5, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).Which statement is true about the graphed function f(x)?
F(x) < 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, ∞).
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).
35. Which equation is equivalent to –k + 0.03 + 1.01k = –2.45 – 1.81k?
–100k + 3 + 101k = –245 – 181k
–100k + 300 + 101k = –245 – 181k
–k + 3 + 101k = –245 – 181k
–k + 300 + 101k = –245 – 181k
36. Hiroto solved the equation 6 – 4|2x – 8| = –10 for one solution. His work is shown below.
6 – 4|2x – 8| = –10
–4|2x – 8| = –16
|2x – 8| = 4
2x – 8 = 4
2x = 12
x = 6
What is the other solution?
–6
–4
2
10
37. The table shows the total cost of purchasing x same-priced items and a catalog.What is the initial value and what does it represent?'
number of items x
1, 2, 3, 4
total cost y
$10, $14, $18, $22
$4, the cost per item
$4, the cost of the catalog
$6, the cost per item
$6, the cost of the catalog
38. Which system of linear inequalities has the point (2, 1) in its solution set?y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 1. `On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded. y less-than negative one-half x + 3. y less-than one-half x. 2. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded. 3. On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded. y less-than one-half x. y less-than-or-equal-to negative one-half x + 2 4. On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 4, negative 2) and (0, 0). Everything below the line is shaded.
39. On a coordinate plane, a v-shaped line crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and the x-axis at (2, 0).What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to –2
all real numbers greater than or equal to –5
all real numbers greater than or equal to 0
40. A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed.A table showing Discount Cards Fundraiser with two columns and six rows. The first column, Cards Sold, has the entries, 10, 20, 30, 40, 50. The second column, Remainder of Goal, has the entries, $875, $795, $715, $635, $555.Which word describes the slope of the line representing the data in the table?
zero
undefined
negative
positive
35
42
63
105
22. Which is the graph of linear inequality x – 2y ≥ –12? 1. On a coordinate plane, a dashed straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the right of the line is shaded. 2. On a coordinate plane, a solid straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the left of the line is shaded. 3. On a coordinate plane, a dashed straight line with negative slope goes through (negative 6, 6) and (0, negative 6). Everything to the right of the line is shaded. 4. On a coordinate plane, a solid straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the right of the line is shaded.
23. The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?
w ≤ 10 – l
2l + 2w ≥ 62
w ≤ 10 – l
2l + 2w > 62
w ≤ l – 10
2l + 2w ≥ 62
w ≤ l – 10
2l + 2w > 62
24. The potential energy, P, in a spring is represented using the formula P = A equals StartFraction one-half EndFraction b h.kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework.
Which equation should she use?
k = 2Px^2
k = k equals StartFraction one-half EndFraction P x squared.Px2
k = k equals StartFraction 2 P Over x squared EndFraction.
k = k equals StartFraction P Over 2 x squared EndFraction.
25. The graph represents the data cost for monthly Internet service for a cell phone. On a coordinate plane, a graph titled Cell Phone Internet Service shows Gigabytes Used on the x-axis and Monthly Cost in dollars on the y-axis. A piecewise function has 3 lines. The 1st line has a closed circle at (0, 15), continues horizontally at y = 15, then has a closed circle at (2, 15). The 2nd line has an open circle at (2, 20) and then continues up to a closed circle at (6, 40). The 3rd line has an open circle at (6, 50) and then continues horizontally at y = 50.Which function, C(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month?
Which function, C(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month? 1. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15, 2nd column 0 less-than-or-equal-to x less-than-or-equal-to 2 2nd Row 1st column 5 x + 10, 2nd column 2 less-than x less-than-or-equal-to 6 3rd Row 1st column 50, 2nd column 6 less-than x EndLayout 2. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15, 2nd column 0 less-than-or-equal-to x less-than 2 2nd Row 1st column 5 x + 20, 2nd column 2 less-than-or-equal-to x less-than 6 3rd Row 1st column 50, 2nd column 6 less-than-or-equal-to x EndLayout 3. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15x, 2nd column 0 less-than-or-equal-to x less-than-or-equal-to 2 2nd Row 1st column 20 x + 5, 2nd column 2 less-than x less-than-or-equal-to 6 3rd Row 1st column 50 x, 2nd column 6 less-than x EndLayout 4. C(x) = StartLayout enlarged left-brace 1st Row 1st column 15x, 2nd column 0 less-than-or-equal-to x less-than 2 2nd Row 1st column 5 x + 10, 2nd column 2 less-than-or-equal-to x less-than 6 3rd Row 1st column 50 x, 2nd column 6 less-than-or-equal-to x EndLayout
26. An electrician is hired to install a ceiling fan. She estimates that the installation will take no more than 45 minutes if the house is up to building code. If the house is not up to building code, she estimates that the installation will take longer than 120 minutes. Which graph represents the number of minutes it could take her to install the fan?
1. number line closed circle on 45 til open circle 120. 2. open circle on 45 til closed circle on 120. 3. closed circle on 45 going left and open circle on 120 going right. 4. open circle on 40 going left closed circle on 120 going right.
27. What is the solution to –2(8x – 4) < 2x + 5?
x > x is greater than StartFraction 1 Over 6 EndFraction.
x < x is less than StartFraction 1 Over 6 EndFraction.
x > 6
x < 6
28. This mapping shows a functional relationship.A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (2, 4), (negative 3, 0), (negative 1, negative 1), (4, 3).When f(x)=4, what is the value of x?
0
2
3
4
29. Graph the function y = |8 - 2x| + 3. Which is a point on the function?
(6.2, 7.4)
(7.8, 11.2)
(8.6, 6.8)
(9.6, 7.3)
30. What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x?
1. The distributive property: 4x – 12 + 4 < 10 + 6x
2. Combine like terms: 4x – 8 < 10 + 6x
3. The addition property of inequality: 4x < 18 + 6x
4. The subtraction property of inequality: –2x < 18
5. The division property of inequality: ________
x < –9
x > –9
x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction.
x > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.
31. Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book.A table showing Coffee Shop Coupon Savings with 2 columns and 6 rows. The first column, x, has the entries, 0, 5, 10, 15, 20. The second column, y, has the entries. negative 20, negative 10, 0, 10, 20.What are the slope and y-intercept of the line represented by the points shown in the table?
slope: 2, y-intercept: –20
slope: 2, y-intercept: 10
slope: 5, y-intercept: –20
slope: 5, y-intercept: 10
32. On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (2.4, negative 51) and a maximum value of (negative 0.75, 6), crosses the x-axis at (negative 2, 0), (0, 0), and (3.5, 0), and crosses the y-axis at (0, 0).Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function's values go to negative infinity.
As the x-values go to zero, the function's values go to positive infinity.
As the x-values go to negative infinity, the function's values are equal to zero.
As the x-values go to negative infinity, the function's values go to positive infinity
33. Samir, a carpenter, spent $300 on specialty tools to make toy horses for children. For each horse he makes, he spends $75 on supplies. He charges $125 for each horse. How many horses must Samir sell in order to break even?
2
3
4
6
34. On a coordinate plane, a curved line, labeled f of x, with a minimum value of (negative 1.9, negative 5.7) and a maximum value of (0, 2) crosses the x-axis at (negative 2.5, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).Which statement is true about the graphed function f(x)?
F(x) < 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, ∞).
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).
35. Which equation is equivalent to –k + 0.03 + 1.01k = –2.45 – 1.81k?
–100k + 3 + 101k = –245 – 181k
–100k + 300 + 101k = –245 – 181k
–k + 3 + 101k = –245 – 181k
–k + 300 + 101k = –245 – 181k
36. Hiroto solved the equation 6 – 4|2x – 8| = –10 for one solution. His work is shown below.
6 – 4|2x – 8| = –10
–4|2x – 8| = –16
|2x – 8| = 4
2x – 8 = 4
2x = 12
x = 6
What is the other solution?
–6
–4
2
10
37. The table shows the total cost of purchasing x same-priced items and a catalog.What is the initial value and what does it represent?'
number of items x
1, 2, 3, 4
total cost y
$10, $14, $18, $22
$4, the cost per item
$4, the cost of the catalog
$6, the cost per item
$6, the cost of the catalog
38. Which system of linear inequalities has the point (2, 1) in its solution set?y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 1. `On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded. y less-than negative one-half x + 3. y less-than one-half x. 2. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded. 3. On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded. y less-than one-half x. y less-than-or-equal-to negative one-half x + 2 4. On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 4, negative 2) and (0, 0). Everything below the line is shaded.
39. On a coordinate plane, a v-shaped line crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and the x-axis at (2, 0).What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to –2
all real numbers greater than or equal to –5
all real numbers greater than or equal to 0
40. A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed.A table showing Discount Cards Fundraiser with two columns and six rows. The first column, Cards Sold, has the entries, 10, 20, 30, 40, 50. The second column, Remainder of Goal, has the entries, $875, $795, $715, $635, $555.Which word describes the slope of the line representing the data in the table?
zero
undefined
negative
positive
-
21 dimes means she has 21 * 0.10 = $2.10 from dimes. The total amount is $5.25, so she has $5.25 - $2.10 = $3.15 from nickels. Since each nickel is worth $0.05, she has 3.15 / 0.05 = 63 nickels.
Answer: 63 -
The inequality can be rewritten as y ≤ (1/2)x + 6, making it clear that the line will be solid (because of the "≥"), and the area above the line will be shaded.
Answer: 4 -
The width is less than the length, and the perimeter must be more than 62 meters. The correct system of inequalities representing this condition is:
Answer: w ≤ l - 10, 2l + 2w > 62 -
To solve for k, rearranging the equation gives: k = (2P) / x².
Answer: k = k equals StartFraction 2 P Over x squared EndFraction. -
The first tier is a constant cost of $15 for 0 to 2 GB. From 2 to 6 GB, the cost is $5 more than the previous threshold. For more than 6 GB, the cost is $50.
Answer: C(x) = StartLayout enlarged left-brace 1st Row 1st column 15, 2nd column 0 less-than-or-equal-to x less-than-or-equal-to 2 2nd Row 1st column 5 x + 10, 2nd column 2 less-than x less-than-or-equal-to 6 3rd Row 1st column 50, 2nd column 6 less-than x EndLayout -
The installation time ranges from up to 45 minutes to more than 120 minutes, which can be shown appropriately on a number line.
Answer: 1. number line closed circle on 45 till open circle 120. -
Distributing gives -16x + 8 < 2x + 5. Solving gives x < 6.
Answer: x < 6 -
For f(x) = 4, the corresponding x-value is 2.
Answer: 2 -
To find a point on the function y = |8 - 2x| + 3, plug in values. The function has a vertex at (4, 3). Checking gives:
Answer: (8.6, 6.8) -
The missing step to solve right: 4 > 2x + 9.
Answer: x < –9 -
The slope corresponds to the increase of $4 for 1 coupon indicating each coupon saves $4.
Answer: slope: 4, y-intercept: $10 -
The x-axis crossings indicate as you approach −∞, the function values rise to +∞.
Answer: As the x-values go to negative infinity, the function's values go to positive infinity. -
Total expense: $300 + $75x = $125x → solving gives x = 6 → break-even is 6 horses to cover costs.
Answer: 6 -
Between x-values of –2.5 and 0.75, f(x) < 0.
Answer: F(x) < 0 over the intervals (–2.5, –0.75) and (–0.75, ∞). -
Reorganizing gives: –k + 0.03 + 1.01k = –2.45 – 1.81k results in
Answer: –100k + 3 + 101k = –245 – 181k -
The absolute value gives two equations, leading to: x=2 or x=10.
Answer: 10 -
Initial amount represented is the catalog fee if all items increase by $4 for each added item.
Answer: $4, the cost of the catalog -
The first system can get a point (2, 1) within the overall intersection of regions.
Answer: 1. -
The function reaches both negative and positive points but has a bounded x-range.
Answer: all real numbers -
For each card sold, there's a fixed reduction leading to diminishing returns for the goal.
Answer: negative
41.The table shows how an elevator 500 feet above the ground is descending at a steady rate.A two column table with 5 rows. The first column, time in seconds (t), has the entries, 0, 5, 10, 15. The second column, Height in feet h(t), has the entries, 500, 475, 450, 425.Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending?
h(t) = 5t + 500
h(t) = 5t – 500
h(t) = –5t + 500
h(t) = –5t – 500
42. A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item. Bailey pays $9.50 to have an item shipped from the retailer. What is the weight of the item?
1.50 pounds
1.75 pounds
3.75 pounds
6.00 pounds
43. The tables represent the functions f(x) and g(x).A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15.Which input value produces the same output value for the two functions?
x = –12
x = –9
x = –6
x = –3
44. What is the vertex of the graph of f(x) = |x – 13| + 11?
(–11, 13)
(–13, 11)
(11, 13)
(13, 11)
45. Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?
9 feet
18 feet
30 feet
33 feet
46. Which scenario can be represented using the inequalities below?
1.25 < x < 1.5
A container of milk costs at least $1.25 but less than $1.50.
A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
The point value of a test item is more than 1.25 points and less than 1.5 points.
47. What are the steps to solving the inequality StartFraction g plus 2 over negative 3 EndFraction < –2?
Subtract 2 from both sides of the inequality. Multiply both sides of the inequality by –3.
Subtract 2 from both sides of the inequality. Change the direction of the inequality. Multiply both sides of the inequality by –3.
Multiply both sides of the inequality by –3. Subtract 2 from both sides of the inequality.
Multiply both sides of the inequality by –3. Change the direction of the inequality. Subtract 2 from both sides of the inequality.
48. When a number is added to n plus StartFraction 1 Over 5 EndFraction n equals 24. of itself, the result is 24. The equation that models this problem is n + n plus StartFraction 1 Over 5 EndFraction n equals 24.n = 24. What is the value n?
n = 18
n = 20
n = 21n equals 23 and StartFraction Over 5 EndFraction 5
n = 23n equals 23 and StartFraction Over 5 EndFraction 5
49. Tarriq begins to solve the equation 50 + 2x = –190.
50 + 2x = –190
50 – 50 + 2x = –190 – 50
2x = –240
To finish solving the equation using the multiplication property of equality, which factor must Tarriq use?
Negative 2
Negative one-half
One-half
2
50. A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.Which best describes why the function is nonlinear?
The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
h(t) = 5t + 500
h(t) = 5t – 500
h(t) = –5t + 500
h(t) = –5t – 500
42. A retailer charges a flat handling fee of $5.00, plus $0.75 per quarter pound, to ship an item. Bailey pays $9.50 to have an item shipped from the retailer. What is the weight of the item?
1.50 pounds
1.75 pounds
3.75 pounds
6.00 pounds
43. The tables represent the functions f(x) and g(x).A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15.Which input value produces the same output value for the two functions?
x = –12
x = –9
x = –6
x = –3
44. What is the vertex of the graph of f(x) = |x – 13| + 11?
(–11, 13)
(–13, 11)
(11, 13)
(13, 11)
45. Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?
9 feet
18 feet
30 feet
33 feet
46. Which scenario can be represented using the inequalities below?
1.25 < x < 1.5
A container of milk costs at least $1.25 but less than $1.50.
A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
The point value of a test item is more than 1.25 points and less than 1.5 points.
47. What are the steps to solving the inequality StartFraction g plus 2 over negative 3 EndFraction < –2?
Subtract 2 from both sides of the inequality. Multiply both sides of the inequality by –3.
Subtract 2 from both sides of the inequality. Change the direction of the inequality. Multiply both sides of the inequality by –3.
Multiply both sides of the inequality by –3. Subtract 2 from both sides of the inequality.
Multiply both sides of the inequality by –3. Change the direction of the inequality. Subtract 2 from both sides of the inequality.
48. When a number is added to n plus StartFraction 1 Over 5 EndFraction n equals 24. of itself, the result is 24. The equation that models this problem is n + n plus StartFraction 1 Over 5 EndFraction n equals 24.n = 24. What is the value n?
n = 18
n = 20
n = 21n equals 23 and StartFraction Over 5 EndFraction 5
n = 23n equals 23 and StartFraction Over 5 EndFraction 5
49. Tarriq begins to solve the equation 50 + 2x = –190.
50 + 2x = –190
50 – 50 + 2x = –190 – 50
2x = –240
To finish solving the equation using the multiplication property of equality, which factor must Tarriq use?
Negative 2
Negative one-half
One-half
2
50. A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.Which best describes why the function is nonlinear?
The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.
Here are the answers to your questions:
-
h(t) = –5t + 500
-
1.50 pounds
-
x = –6
-
(13, 11)
-
9 feet
-
The point value of a test item is more than 1.25 points and less than 1.5 points.
-
Subtract 2 from both sides of the inequality. Change the direction of the inequality. Multiply both sides of the inequality by –3.
-
n = 20
-
Negative one-half
-
The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
54 D:
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