1. The graph below represents the distance a pilot is from the home airport during a period of time.
A graph titled Pilot's Distance from Home. The horizontal axis shows time (hours) and the vertical axis shows distance (miles). Both axes are unnumbered. A line is shown in 3 sections, labeled I, II, and III. Sections I and III show a reduction in distance over time and section II is constant.
Which describes the pilot’s distance in section I?
zero
constant
decreasing
increasing
2. What are the steps to solving the inequality 3b + 8 ≥ 14?
Subtract 8 from both sides of the inequality. Divide both sides of the inequality by 3.
Subtract 8 from both sides of the inequality. Change the direction of the inequality. Divide both sides of the inequality by 3.
Divide both sides of the inequality by 3. Subtract 8 from both sides of the inequality.
Divide both sides of the inequality by 3. Change the direction of the inequality. Subtract 8 from both sides of the inequality.
3. Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). A straight line with a positive slope begins at point (0, 10) and ends at point (6, 27).
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). Solid circles are at points (0, 10), (1, 14), (2, 16), (3, 19), (4, 22), (5, 25), (6, 28).
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). A straight line with a positive slope begins at point (0, 10) and ends around point (6, 60).
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). Solid circles are at points (0, 3), (1, 13), (2, 24), (3, 34), (4, 43), (5, 54).
4. The solution to an inequality is given in set-builder notation as {x l x > two-thirds}. What is another way to represent this solution set?
5. Alberto uses the steps below to solve the equation One-half x minus 3 equals 7.
Step 1: One-half x minus 3 plus 3 equals 7 plus 3
Step 2: One-half x plus 0 equals 10
Step 3: One-half x equals 0
Step 4: 2 (one-half) x equals 2 (10)
Step 5: 1 x equals 20
Step 6: x equals 20
Which justifies Step 6 of his work?
the addition property of equality
the identity property of addition
the multiplication property of equality
the identity property of multiplication
6. Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of ice tea she can serve?
x minus y equals 44
44 plus y equals x
y minus x equals 44
x equals 44 minus y
7. The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2 l plus 2 w equals 16, where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle?
7 in.
8 in.
9 in.
10 in.
8. The table represents the recommended exercise intensity for an aerobic program based on the number of visits since beginning the program.
A 2-column table with 6 rows titled Intensity of Exercises. The first column is labeled Number of Visits with entries 1, 2, 3, 4, 5, 6. The second column is labeled Exercise Intensity with entries 60%, 60%, 60%, ?, ?, ?.
The program suggests maintaining a consistent intensity for the first 3 visits, gradually increasing intensity over the subsequent 3 visits, followed by a decrease in intensity for the next 3 visits, before repeating the pattern. Which of the following options represent the possible intensities for Amber's exercise during the fourth, fifth, and sixth visits? Select three options.
9. The yearbook club has 5 members returning from last year. They set up a booth in the cafeteria to recruit more members, and an average of 3 new members sign up each day. Which best describes why the graph relating the total number of members on the yearbook club, m, and the number of days the booth is set up, d, will be continuous or discrete?
The graph will be continuous because an end day for the booth being set up is not given in the description.
The graph will be continuous because there can be any number of people signing up each day since we are only given the average.
The graph will be discrete because some day the number of available people to sign up for the club will run out.
The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.
10. Verona is solving the equation -3 + 4x = 9. In order to isolate the variable term using the addition property of equality, which number should she add to both sides of the equation?
–4
3
–3
4
11 answers
Here are the answers to the questions you posed:
Which describes the pilot’s distance in section I?
Decreasing (The pilot is getting closer to the home airport over time.)
What are the steps to solving the inequality 3b + 8 ≥ 14?
Subtract 8 from both sides of the inequality. Divide both sides of the inequality by 3. (Correct order of operations to isolate the variable.)
Which graph shows the equation c = 10 + 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?
On a coordinate plane, the x-axis shows the number of tickets sold (t) and the y-axis shows total cost of going to the carnival (c). A straight line with a positive slope begins at point (0, 10) and ends at point (6, 27). (The equation indicates a starting cost of $10 and a $3 increase for each additional ticket.)
What is another way to represent this solution set?
(two-thirds, ∞) (This represents all values of x greater than two-thirds.)
Which justifies Step 6 of his work?
the identity property of multiplication (This indicates that multiplying 1 by x gives x, thereby confirming x = 20.)
Which equation represents the number of glasses of iced tea she can serve?
x = 44 - y (This indicates that the number of glasses of iced tea is equal to the total glasses available minus the glasses of lemonade.)
Which value is possible for the length of the rectangle?
7 in. (To satisfy the equation 2l + 2w = 16, if l = 7, then 2w = 16 - 14, which gives w = 1. Length can be 7 inches.)
Which represent the possible intensities for Amber's exercise during the fourth, fifth, and sixth visits?
66%, 69%, 72% (This follows the pattern of gradually increasing intensity.)
Which best describes why the graph relating the total number of members on the yearbook club, m, and the number of days the booth is set up, d, will be continuous or discrete?
The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups. (Membership counts are whole numbers added after each full day.)
Which number should she add to both sides of the equation -3 + 4x = 9 to isolate the variable term using the addition property of equality?
3 (Adding 3 to both sides will result in 4x = 12, isolating the variable term 4x.)
Please feel free to ask if you have any additional questions or need further clarification!
for Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). A straight line with a positive slope begins at point (0, 10) and ends at point (6, 27).
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). Solid circles are at points (0, 10), (1, 14), (2, 16), (3, 19), (4, 22), (5, 25), (6, 28).
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). A straight line with a positive slope begins at point (0, 10) and ends around point (6, 60).
On a coordinate plane, the x-axis shows number of tickets sold (t) and the y-axis shows total cost of going to carnival (c). Solid circles are at points (0, 3), (1, 13), (2, 24), (3, 34), (4, 43), (5, 54). number 3 which graph? 1 2 3 or 4
for 8. please select three The table represents the recommended exercise intensity for an aerobic program based on the number of visits since beginning the program.
A 2-column table with 6 rows titled Intensity of Exercises. The first column is labeled Number of Visits with entries 1, 2, 3, 4, 5, 6. The second column is labeled Exercise Intensity with entries 60%, 60%, 60%, ?, ?, ?.
The program suggests maintaining a consistent intensity for the first 3 visits, gradually increasing intensity over the subsequent 3 visits, followed by a decrease in intensity for the next 3 visits, before repeating the pattern. Which of the following options represent the possible intensities for Amber's exercise during the fourth, fifth, and sixth visits? Select three options.
The equation indicates that the total cost (c) starts at $10 (the y-intercept when t=0) and increases by $3 for each ticket purchased (which gives it a slope of 3).
For graph 1, a straight line starting at (0, 10) and ending at (6, 27) correctly represents this equation. If we check:
At t = 0, c = 10.
At t = 1, c = 10 + 3(1) = 13.
At t = 2, c = 10 + 3(2) = 16.
At t = 3, c = 10 + 3(3) = 19.
At t = 4, c = 10 + 3(4) = 22.
At t = 5, c = 10 + 3(5) = 25.
At t = 6, c = 10 + 3(6) = 28.
Thus, the answer is graph 1.
For the recommended exercise intensity options:
Given the description, the program keeps the first three visits at a consistent intensity (60%), then gradually increases for the next three visits. After that, it decreases for the following three visits. We need to choose three options that fit the given conditions for the fourth, fifth, and sixth visits:
After the first three visits at 60%, the next three visits increase. The possible options for gradual increases could be:
63%, 63%, 63% (consistent but does not reflect gradual)
66%, 69%, 72% (this is a clear increase from 60%)
66%, 62%, 58% (misleading as it doesn't show consistent increases)
63%, 65%, 67% (this is also a consistent increase)
67%, 72%, 77% (this shows a strong increase)
Thus, the selected intensities for Amber's exercise during the fourth, fifth, and sixth visits are likely 66%, 69%, 72%, 63%, 65%, 67%.
So the final selections overall would be:
66%, 69%, 72%
63%, 65%, 67%
Please select the ones that best fit your specific criteria, as you may want numbers for just one combination or choose multiple options as appropriate!
3 OPTIONS i said 3 FOR 8 what is the THIRD guess if youd like
I apologize for the oversight. Let's determine three options for the recommended exercise intensity during the fourth, fifth, and sixth visits based on the pattern described.
Based on the rules:
The first three visits have an intensity of 60%.
The intensity should gradually increase during the fourth, fifth, and sixth visits.
Let’s analyze the options:
63%, 63%, 63% - This does not show a gradual increase; it is consistent at 63%.
66%, 69%, 72% - This is a clear gradual increase, which fits the criteria perfectly.
66%, 62%, 58% - This is a decrease, which does not fit the criteria.
63%, 65%, 67% - This shows a consistent gradual increase and fits the criteria.
67%, 72%, 77% - This also shows a strong increase but starts above 60%.
To select three viable options, I would suggest:
66%, 69%, 72% (Option 2)
63%, 65%, 67% (Option 4)
67%, 72%, 77% (Option 5) - as a third option.
So, your final three selections for intensities during the fourth, fifth, and sixth visits would be:
66%, 69%, 72%
63%, 65%, 67%
67%, 72%, 77%
Thank you for your patience, and let me know if you need anything else!
11. Which graph could represent y, the amount owed on a car loan, as regular payments are made each month, x?
A graph shows the number of car payments paid on the horizontal axis and amount owed on the vertical axis. The line goes straight up from the x-axis.
A graph shows the number of car payments paid on the horizontal axis and the amount owed on the vertical axis. The line starts high on the vertical axis and decreases as it goes along the horizontal axis.
A graph shows the number of car payments paid on the horizontal axis and the amount owed on the vertical axis. The line starts in the middle on the vertical axis and increases as it goes along the horizontal axis.
A graph titled Car Loan shows the number of car payments paid on the horizontal axis and the amount owed on the vertical axis. The line starts high on the vertical axis and extends in a straight line along the horizontal axis.
12. What is the value of s in the equation 3 r equals 10 plus 5 s, when r equals 10?
4
8
100
200
13. A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?
The value of x can be any real number, and y will be a real number.
The value of x can be any real number greater than or equal to 0, and y will be a real number greater than or equal to 0.
The value of x can be any integer, and y will be an integer.
The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0.
14. A graph shows an x- and y-axis. The data line is in the shape of a "vee." The begins above the x-axis and to the left of the y-axis, extends below the x-axis to a point on the y-axis, and ascends above the x-axis to the right of the y-axis.
Which statement describes the relationship between x and y?
As x increases, y decreases.
As x increases, y increases.
As x increases, y increases and then decreases.
As x increases, y decreases and then increases.
15. Diep buys a loaf of bread 65 centimeters long. For lunch every afternoon, he cuts 15 centimeters of bread for his sandwich. Diep wants to determine the length of the loaf of bread, l, after d days. What is the equation of the scenario? Is the graph of the equation continuous or discrete?
l = 65 – 15d; discrete
l = 65 – 15d; continuous
65 = l – 15d; discrete
65 = l – 15d; continuous
16. The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. The amount collected can be modeled by the equation 5 x plus 10 y equals 800, where x represents the number of small vehicles and y represents the number of larger vehicles. If the number of larger vehicles washed was 50, how many small vehicles were washed in total?
55
60
130
150
17. What is the first step in solving the inequality StartFraction m minus 2 Over 6 EndFraction < –1?
Multiply both sides by 6.
Add 2 to both sides.
Change the direction of the inequality.
Change the inequality to ≤.
18. In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles. How far apart are the police station and the fire station?
1 mile
3 miles
4 miles
6 miles
19. On a science test, 2 points are deducted from a total of 100 points for each question answered incorrectly. Trevor scored an 84 on the test. The equation 100−2x=84, where x represents the number of questions answered incorrectly, represents the situation. How many questions did Trevor answer incorrectly?
8 questions
9 questions
12 questions
13 questions
20. What is the solution to the inequality 5.25 – b ≥ 6.5?
A number line going from negative 5 to positive 5. A solid circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5.
A number line going from negative 5 to positive 5. An open circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5.
A number line going from negative 5 to positive 5. A solid circle appears between negative 1 and negative 2. The number line is shaded from the circle to positive 5.
A number line going from negative 5 to positive 5. An open circle appears between negative 1 and negative 2. The number line is shaded from the circle to positive 5.
Here are the answers to each of the questions listed:
11. Which graph could represent y, the amount owed on a car loan, as regular payments are made each month, x?
A graph shows the number of car payments paid on the horizontal axis and the amount owed on the vertical axis. The line starts high on the vertical axis and decreases as it goes along the horizontal axis. (As payments are made, the amount owed decreases.)
12. What is the value of s in the equation 3r = 10 + 5s, when r = 10?
13. A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?
The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0. (x must be non-negative integers since you can't buy negative notebooks, and y will always be a non-negative integer since it is a total cost.)
14. Which statement describes the relationship between x and y in the V-shaped graph?
As x increases, y decreases and then increases. (The graph first decreases then increases, creating a "V" shape.)
15. Diep's equation of the scenario and the graph type:
l = 65 - 15d; continuous (The expression models a continuous change in length as time progresses in days.)
16. If 50 larger vehicles were washed, how many small vehicles were washed in total?
This would result in shading left on a number line.
A number line going from negative 5 to positive 5. An open circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5.
If you have further questions or need clarifications, feel free to ask!
for graphs please say number 1 2 3 or 4 depending how many there are please say graph number 2!
Thank you for your clarification! Here are the simplified answers for the graph-related questions numbered accordingly:
11. Which graph could represent y, the amount owed on a car loan, as regular payments are made each month, x?
Graph number 2 (The line starts high on the vertical axis and decreases as it goes along the horizontal axis.)
14. Which statement describes the relationship between x and y in the V-shaped graph?
Graph number 3 (As x increases, y decreases and then increases.)
20. What is the solution to the inequality \(5.25 - b \geq 6.5\)?
Graph number 2 (A number line going from negative 5 to positive 5. An open circle appears between negative 1 and negative 2. The number line is shaded from the circle to negative 5.)
If you need further assistance or any more information, feel free to ask!
what?? 14 is only ONE graph its okay anyway
21. The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x + 12 = 48, where x represents the cost of a ticket. How much is one ticket?
$3.00
$4.00
$9.00
$15.00
22. On a coordinate plane, a straight line with a positive slope begins at point (0, 50) and ends at point (5.5, 600).
Which scenario is most likely the one shown on the graph?
the total amount of money in the cash register, y, containing $50 in change and small bills and x $100 bills
the total number of puzzle pieces, y, in a brand new 50-piece puzzle, and x brand-new 100-piece puzzles
the total weight of the barbell, y, where the bar weighs 50 pounds and x 100-pound weights are added to it
the total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce
23. The graph represents a person’s heart rate in beats per minute during 30 minutes of exercise.
A graph titled Cardiac Exercise. The horizontal axis shows time (minutes), numbered 3 to 30, and the vertical axis shows Heart Rate (b p m) numbered 15 to 150. The line starts at 75 b p m in 0 minutes, to 135 b p m from 6 to 25 minutes, and ends at 105 b p m at 30 minutes.
Which statement best describes the relationship between heart rate and time during exercise?
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes.
The heart rate decreases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes.
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.
The heart rate remains constant for 6 minutes, increases for 19 minutes, and then gradually decreases for 5 minutes.
24. Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
25. What is the value of x in the equation one-fifthx – two-thirdsy = 30, when y = 15?
4
8
80
200
Here are the answers to your questions, structured clearly as you requested:
21. The cost of performance tickets and beverages for a family of four can be modeled using the equation \(4x + 12 = 48\), where x represents the cost of a ticket. How much is one ticket?
Start by solving the equation:
\[
4x + 12 = 48 \
4x = 48 - 12 \
4x = 36 \
x = \frac{36}{4} = 9
\]
$9.00
22. On a coordinate plane, a straight line with a positive slope begins at point (0, 50) and ends at point (5.5, 600). Which scenario is most likely the one shown on the graph?
The scenario that fits a starting point of 50 and a high ending point (600) with a positive slope is:
the total weight of the barbell, y, where the bar weighs 50 pounds and x 100-pound weights are added to it.
23. Which statement best describes the relationship between heart rate and time during exercise?
From the description: The heart rate starts at 75 bpm, increases to 135 bpm from 6 to 25 minutes, and then decreases to 105 bpm at 30 minutes. Thus:
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.
24. Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
The total amount of flour (y) can be expressed as:
\[
y = 5.5 + x
\]
The appropriate constraints based on using whole cups and knowing that flour cannot be negative are:
y = x + 5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
25. What is the value of x in the equation \(\frac{1}{5}x - \frac{2}{3}y = 30\), when y = 15?
1 answer