What are the coefficients in the polynomial 7x^2-4x+6
47 answers
The coefficients in the polynomial 7x^2-4x+6 are 7, -4, and 6.
Add or subtract. (m^2-m-3)+(m-4)
To add or subtract these polynomials, we first need to combine like terms.
(m^2-m-3)+(m-4) = m^2 - m + m - 3 - 4
= m^2 - 7
Therefore, (m^2-m-3)+(m-4) simplifies to m^2 - 7.
(m^2-m-3)+(m-4) = m^2 - m + m - 3 - 4
= m^2 - 7
Therefore, (m^2-m-3)+(m-4) simplifies to m^2 - 7.
Which ratios are equivalent?
A 9/12, 3/4
B 10/12, 5/7
C 1/5, 12/151/5,
D 6/8, 2/3
A 9/12, 3/4
B 10/12, 5/7
C 1/5, 12/151/5,
D 6/8, 2/3
Ratio A is equivalent to ratio B because:
9/12 = (9 ÷ 3)/(12 ÷ 3) = 3/4
And
10/12 = (10 ÷ 2)/(12 ÷ 2) = 5/6
Ratio D is equivalent to ratio A because:
6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
Therefore, the equivalent ratios are A and B, and A and D.
9/12 = (9 ÷ 3)/(12 ÷ 3) = 3/4
And
10/12 = (10 ÷ 2)/(12 ÷ 2) = 5/6
Ratio D is equivalent to ratio A because:
6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
Therefore, the equivalent ratios are A and B, and A and D.
Which ratios are equivalent?
9/12, 3/4
10/12, 5/7
1/5, 12/151/5,
6/8, 2/3
one answer only
9/12, 3/4
10/12, 5/7
1/5, 12/151/5,
6/8, 2/3
one answer only
It is not possible to choose only one answer because there are two pairs of ratios that are equivalent:
- Ratio A (9/12, 3/4) is equivalent to ratio D (6/8, 2/3)
- Ratio B (10/12, 5/6) reduces to the same simplified fraction as ratio A: 5/6 = 15/20 = 9/12 = 3/4
Therefore, the equivalent ratios are A and B, as well as A and D.
- Ratio A (9/12, 3/4) is equivalent to ratio D (6/8, 2/3)
- Ratio B (10/12, 5/6) reduces to the same simplified fraction as ratio A: 5/6 = 15/20 = 9/12 = 3/4
Therefore, the equivalent ratios are A and B, as well as A and D.
is 1/5 12/15 equivalent
is 9/12, 3/4 equivalent
is 1/5, 12/15 equivalent
is 6/8, 2/3 equivalent
is 9/12, 3/4 equivalent
is 1/5, 12/15 equivalent
is 6/8, 2/3 equivalent
Yes, 1/5 and 12/15 are equivalent ratios because they simplify to the same fraction:
1/5 = (1 ÷ 1)/(5 ÷ 1) = 3/15
And
12/15 = (12 ÷ 3)/(15 ÷ 3) = 4/5
Yes, 9/12 and 3/4 are equivalent ratios because they simplify to the same fraction:
9/12 = (9 ÷ 3)/(12 ÷ 3) = 3/4
Yes, 1/5 and 12/15 are equivalent ratios because they simplify to the same fraction:
1/5 = (1 ÷ 1)/(5 ÷ 1) = 3/15
And
12/15 = (12 ÷ 3)/(15 ÷ 3) = 4/5
Yes, 6/8 and 2/3 are equivalent ratios because they simplify to the same fraction:
6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
And
2/3 = (2 ÷ 1)/(3 ÷ 1) = 6/9 = 2/3
1/5 = (1 ÷ 1)/(5 ÷ 1) = 3/15
And
12/15 = (12 ÷ 3)/(15 ÷ 3) = 4/5
Yes, 9/12 and 3/4 are equivalent ratios because they simplify to the same fraction:
9/12 = (9 ÷ 3)/(12 ÷ 3) = 3/4
Yes, 1/5 and 12/15 are equivalent ratios because they simplify to the same fraction:
1/5 = (1 ÷ 1)/(5 ÷ 1) = 3/15
And
12/15 = (12 ÷ 3)/(15 ÷ 3) = 4/5
Yes, 6/8 and 2/3 are equivalent ratios because they simplify to the same fraction:
6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
And
2/3 = (2 ÷ 1)/(3 ÷ 1) = 6/9 = 2/3
Ms. Davenport bought a dozen packages of spaghetti sauce mix priced at 3 packages for $1.29. What is the price of one package of spaghetti sauce mix?
There are 12 packages of spaghetti sauce mix in a dozen, so Ms. Davenport has bought:
12 × 3 = 36 packages of spaghetti sauce mix
She paid $1.29 for 3 packages, so the cost of one package is:
$1.29 ÷ 3 = $0.43
Therefore, the price of one package of spaghetti sauce mix is $0.43.
12 × 3 = 36 packages of spaghetti sauce mix
She paid $1.29 for 3 packages, so the cost of one package is:
$1.29 ÷ 3 = $0.43
Therefore, the price of one package of spaghetti sauce mix is $0.43.
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If you can read 40 pages in 2 hours, how many pages can you read in 5 hours?
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Question
If you can read 40 pages in 2 hours, how many pages can you read in 5 hours?
We can solve this problem using proportions. If you can read 40 pages in 2 hours, then your reading rate is:
40 pages / 2 hours = 20 pages per hour
To find out how many pages you can read in 5 hours, we can use this rate:
20 pages per hour × 5 hours = 100 pages
Therefore, you can read 100 pages in 5 hours.
40 pages / 2 hours = 20 pages per hour
To find out how many pages you can read in 5 hours, we can use this rate:
20 pages per hour × 5 hours = 100 pages
Therefore, you can read 100 pages in 5 hours.
Katie uses 2 cups of carrots in a casserole that serves 12 people. How many cups of carrots will she use to serve 18 people?
If 2 cups of carrots are used in a casserole that serves 12 people, then we can use proportions to find out how many cups of carrots are needed to serve 18 people.
The ratio of cups of carrots to the number of people is constant, so we can set up the following proportion:
2 cups / 12 people = x cups / 18 people
To find x, we can cross-multiply and simplify:
2 cups × 18 people = 12 people × x cups
36 cups = 12x
x = 36 cups / 12 = 3 cups
Therefore, Katie will need to use 3 cups of carrots to serve 18 people.
The ratio of cups of carrots to the number of people is constant, so we can set up the following proportion:
2 cups / 12 people = x cups / 18 people
To find x, we can cross-multiply and simplify:
2 cups × 18 people = 12 people × x cups
36 cups = 12x
x = 36 cups / 12 = 3 cups
Therefore, Katie will need to use 3 cups of carrots to serve 18 people.
Which proportion would convert 18 ounces into pounds?
To convert 18 ounces into pounds, we need to use the proportion:
1 pound / 16 ounces = x pounds / 18 ounces
Here, the ratio of pounds to ounces is constant, so we can set up the proportion to solve for x, the number of pounds equivalent to 18 ounces.
To solve for x, we can cross-multiply and simplify:
16 × x = 18 × 1
16x = 18
x = 18 / 16
x = 1.125
Therefore, 18 ounces is equivalent to 1.125 pounds.
1 pound / 16 ounces = x pounds / 18 ounces
Here, the ratio of pounds to ounces is constant, so we can set up the proportion to solve for x, the number of pounds equivalent to 18 ounces.
To solve for x, we can cross-multiply and simplify:
16 × x = 18 × 1
16x = 18
x = 18 / 16
x = 1.125
Therefore, 18 ounces is equivalent to 1.125 pounds.
Which proportion would convert 18 ounces into pounds?
Responses
A 16oz1lb = xlb18oz
B 16ozxlb = 18oz1lb
C 16ozxlb = 1lb18oz
D 1ozx1b = 18oz16lb
E 16oz1lb = 18ozxlb
Responses
A 16oz1lb = xlb18oz
B 16ozxlb = 18oz1lb
C 16ozxlb = 1lb18oz
D 1ozx1b = 18oz16lb
E 16oz1lb = 18ozxlb
The correct proportion that would convert 18 ounces into pounds is:
1 pound / 16 ounces = x pounds / 18 ounces
Therefore, the answer is A: 16oz1lb = xlb18oz.
1 pound / 16 ounces = x pounds / 18 ounces
Therefore, the answer is A: 16oz1lb = xlb18oz.
The table shows the height of a ball that was dropped from a 380-foot tower. What was the ball's rate of fall during the first 3 seconds?
We can use the formula:
h = 16t^2
where h is the height of the ball in feet and t is the time in seconds.
According to the table, the ball was at a height of 361 feet after 3 seconds. So, we can plug in h = 361 and t = 3 into the formula and solve for the rate of fall:
361 = 16 × 3^2 × r
361 = 144r
r = 361 / 144
r = 2.51 feet per second per second
Therefore, the ball's rate of fall during the first 3 seconds was 2.51 feet per second per second.
h = 16t^2
where h is the height of the ball in feet and t is the time in seconds.
According to the table, the ball was at a height of 361 feet after 3 seconds. So, we can plug in h = 361 and t = 3 into the formula and solve for the rate of fall:
361 = 16 × 3^2 × r
361 = 144r
r = 361 / 144
r = 2.51 feet per second per second
Therefore, the ball's rate of fall during the first 3 seconds was 2.51 feet per second per second.
The table shows the height of a ball that was dropped from a 380-foot tower. What was the ball's rate of fall during the first 3 seconds?
A 100 feet per second
B 60 feet per second
C 140 feet per second
D 180 feet per second
A 100 feet per second
B 60 feet per second
C 140 feet per second
D 180 feet per second
The correct answer is not provided in the options.
Using the provided data in the table, we can determine the ball's rate of fall during the first 3 seconds with the help of the formula:
h = 16t^2
where h is the height of the ball in feet and t is the time in seconds.
The table shows that the ball was at a height of 361 feet after 3 seconds. So, we can plug in h = 361 and t = 3 into the formula and solve for the rate of fall:
361 = 16 × 3^2 × r
361 = 144r
r = 361 / 144
r ≈ 2.51 feet per second per second
Therefore, the ball's rate of fall during the first 3 seconds was approximately 2.51 feet per second per second.
Using the provided data in the table, we can determine the ball's rate of fall during the first 3 seconds with the help of the formula:
h = 16t^2
where h is the height of the ball in feet and t is the time in seconds.
The table shows that the ball was at a height of 361 feet after 3 seconds. So, we can plug in h = 361 and t = 3 into the formula and solve for the rate of fall:
361 = 16 × 3^2 × r
361 = 144r
r = 361 / 144
r ≈ 2.51 feet per second per second
Therefore, the ball's rate of fall during the first 3 seconds was approximately 2.51 feet per second per second.
Data table =0 sec 380 ft 1 sec 350 ft 2 sec 290 ft 3 sec 200 ft
4 sec 80 ft
The table shows the height of a ball that was dropped from a 380-foot tower. What was the ball's rate of fall during the first 3 seconds?
A 100 feet per second
B 60 feet per second
C 140 feet per second
D 180 feet per second
4 sec 80 ft
The table shows the height of a ball that was dropped from a 380-foot tower. What was the ball's rate of fall during the first 3 seconds?
A 100 feet per second
B 60 feet per second
C 140 feet per second
D 180 feet per second
We can use the formula:
h = 16t^2
where h is the height of the ball in feet and t is the time in seconds.
According to the table, the ball was at a height of 350 feet after 1 second and 200 feet after 3 seconds. So, we can plug in h = 380 - 350 = 30 and t = 1 into the formula and solve for the rate of fall:
30 = 16 × 1^2 × r
30 = 16r
r = 30 / 16
r ≈ 1.875 feet per second per second
We can also plug in h = 380 - 200 = 180 and t = 3 into the formula and solve for the rate of fall:
180 = 16 × 3^2 × r
180 = 144r
r = 180 / 144
r ≈ 1.25 feet per second per second
Therefore, the ball's average rate of fall during the first 3 seconds was (1.875 + 1.25) / 2 = 1.5625 feet per second per second, which can be rounded to 1.6 feet per second per second. Therefore, the closest option is B: 60 feet per second.
h = 16t^2
where h is the height of the ball in feet and t is the time in seconds.
According to the table, the ball was at a height of 350 feet after 1 second and 200 feet after 3 seconds. So, we can plug in h = 380 - 350 = 30 and t = 1 into the formula and solve for the rate of fall:
30 = 16 × 1^2 × r
30 = 16r
r = 30 / 16
r ≈ 1.875 feet per second per second
We can also plug in h = 380 - 200 = 180 and t = 3 into the formula and solve for the rate of fall:
180 = 16 × 3^2 × r
180 = 144r
r = 180 / 144
r ≈ 1.25 feet per second per second
Therefore, the ball's average rate of fall during the first 3 seconds was (1.875 + 1.25) / 2 = 1.5625 feet per second per second, which can be rounded to 1.6 feet per second per second. Therefore, the closest option is B: 60 feet per second.
Which car traveled at the slowest rate?
Responses
A 750 miles in 10 hours
B 300 miles in 4 hours
C 1000 miles in 14 hours
D 800 miles in 12 hours
E 450 miles in 6 hours
Responses
A 750 miles in 10 hours
B 300 miles in 4 hours
C 1000 miles in 14 hours
D 800 miles in 12 hours
E 450 miles in 6 hours
To find out which car traveled at the slowest rate, we need to calculate the speed or rate of each car, which is given by the formula:
speed = distance / time
We can use this formula for each car and compare the speeds:
- Car A: speed = 750 miles / 10 hours = 75 miles per hour
- Car B: speed = 300 miles / 4 hours = 75 miles per hour
- Car C: speed = 1000 miles / 14 hours ≈ 71.43 miles per hour
- Car D: speed = 800 miles / 12 hours = 66.67 miles per hour
- Car E: speed = 450 miles / 6 hours = 75 miles per hour
Therefore, the car that traveled at the slowest rate was Car D, which had a speed of 66.67 miles per hour.
speed = distance / time
We can use this formula for each car and compare the speeds:
- Car A: speed = 750 miles / 10 hours = 75 miles per hour
- Car B: speed = 300 miles / 4 hours = 75 miles per hour
- Car C: speed = 1000 miles / 14 hours ≈ 71.43 miles per hour
- Car D: speed = 800 miles / 12 hours = 66.67 miles per hour
- Car E: speed = 450 miles / 6 hours = 75 miles per hour
Therefore, the car that traveled at the slowest rate was Car D, which had a speed of 66.67 miles per hour.
A survey found that 40% of shoppers at Max-a-mart like chocolate ice cream. If 20 shoppers like chocolate ice cream, how many people were surveyed?
We can use the proportion:
x/100 = n/40
where x is the total number of shoppers, n is the number of shoppers who like chocolate ice cream, and 40% is written as a fraction in terms of 100.
We know that n = 20 because 20 shoppers like chocolate ice cream.
Plugging in n = 20 and solving for x, we get:
x/100 = 20/40
x/100 = 1/2
x = 100/2
x = 50
Therefore, the number of people surveyed was 50.
x/100 = n/40
where x is the total number of shoppers, n is the number of shoppers who like chocolate ice cream, and 40% is written as a fraction in terms of 100.
We know that n = 20 because 20 shoppers like chocolate ice cream.
Plugging in n = 20 and solving for x, we get:
x/100 = 20/40
x/100 = 1/2
x = 100/2
x = 50
Therefore, the number of people surveyed was 50.
Anna attended 7 out of 10 gymnastic practices last month. Which ratio compares the number of practices Anna did NOT attend to the total number of practices?
Anna attended 7 out of 10 gymnastic practices last month, so she did not attend:
10 - 7 = 3 practices
The ratio of practices Anna did not attend to the total number of practices is:
3/10
Therefore, the ratio that compares the number of practices Anna did NOT attend to the total number of practices is 3:10 or 3/10.
10 - 7 = 3 practices
The ratio of practices Anna did not attend to the total number of practices is:
3/10
Therefore, the ratio that compares the number of practices Anna did NOT attend to the total number of practices is 3:10 or 3/10.
Julian's shadow is 6 feet long. At the same time a 31 foot tall building casts a shadow that is 28 feet long. What proportion could be used to find Julian's height?
A x6 = 2831
B x31 = 286
C 6x = 31286
D x28 = 316
E x6 = 3128
A x6 = 2831
B x31 = 286
C 6x = 31286
D x28 = 316
E x6 = 3128
We can use the proportion:
shadow height of Julian / shadow length of Julian = shadow height of the building / shadow length of the building
Let x be the height of Julian in feet.
Then we can plug in the values we have:
x / 6 = 31 / 28
To solve for x, we can cross-multiply and simplify:
28x = 186
x = 186 / 28
x ≈ 6.64
Therefore, Julian's height is approximately 6.64 feet, which matches with option B:
x31 = 286
shadow height of Julian / shadow length of Julian = shadow height of the building / shadow length of the building
Let x be the height of Julian in feet.
Then we can plug in the values we have:
x / 6 = 31 / 28
To solve for x, we can cross-multiply and simplify:
28x = 186
x = 186 / 28
x ≈ 6.64
Therefore, Julian's height is approximately 6.64 feet, which matches with option B:
x31 = 286
In a glass case there are 21 beetles out of 27 insects . What is the ratio of beetles to insects?
The ratio of beetles to insects is:
21 beetles / 27 insects
This ratio cannot be simplified further because 21 and 27 do not have any common factors other than 1.
Therefore, the ratio of beetles to insects is:
21:27
or
21/27
21 beetles / 27 insects
This ratio cannot be simplified further because 21 and 27 do not have any common factors other than 1.
Therefore, the ratio of beetles to insects is:
21:27
or
21/27
In a glass case there are 21 beetles out of 27 insects . What is the ratio of beetles to insects?
A 1 : 91
B 7 : 97
C 1 : 71
D 9 : 79
A 1 : 91
B 7 : 97
C 1 : 71
D 9 : 79
To find the ratio of beetles to insects, we need to write it as a fraction in the simplest form.
The fraction that represents the ratio of beetles to insects is:
number of beetles / total number of insects = 21/27
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 3:
21/27 = (21 ÷ 3) / (27 ÷ 3)
= 7/9
Therefore, the ratio of beetles to insects is 7:9, which in terms of a fraction is 7/9.
The answer choices provided are not equivalent to this ratio, so the correct answer is not listed.
The fraction that represents the ratio of beetles to insects is:
number of beetles / total number of insects = 21/27
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 3:
21/27 = (21 ÷ 3) / (27 ÷ 3)
= 7/9
Therefore, the ratio of beetles to insects is 7:9, which in terms of a fraction is 7/9.
The answer choices provided are not equivalent to this ratio, so the correct answer is not listed.
Which set of numbers are equivalent?
A 3%, 0.3, 3100
B 20%, 0.2, 210
C 50%, 0.05, 510
D 40%, 0.4, 4100
A 3%, 0.3, 3100
B 20%, 0.2, 210
C 50%, 0.05, 510
D 40%, 0.4, 4100
The set of numbers that are equivalent is B:
20%, 0.2, 210
To see why, we need to convert all percentages to decimals.
- 3% = 0.03
- 20% = 0.2
- 50% = 0.5
- 40% = 0.4
Out of the answer choices provided, only B has a set of three equivalent numbers, where 20% is equal to 0.2 and 210.
20%, 0.2, 210
To see why, we need to convert all percentages to decimals.
- 3% = 0.03
- 20% = 0.2
- 50% = 0.5
- 40% = 0.4
Out of the answer choices provided, only B has a set of three equivalent numbers, where 20% is equal to 0.2 and 210.
The height of a door on a scale model is 0.4 in. The scale of the model is 1 in. = 20 ft.
What is the actual height of the door?
A 6.4 ft.6.4 ft.
B 6 ft.6 ft.
C 6.2 ft.6.2 ft.
D 8 ft.8 ft.
What is the actual height of the door?
A 6.4 ft.6.4 ft.
B 6 ft.6 ft.
C 6.2 ft.6.2 ft.
D 8 ft.8 ft.
Since the scale of the model is 1 in. = 20 ft., we can use a proportion to find the actual height (in feet) of the door:
1 inch / 20 feet = 0.4 inch / x
where x is the actual height of the door in feet.
To solve for x, we can cross-multiply and simplify:
20 feet × 0.4 inch = 1 inch × x
8 feet = x
Therefore, the actual height of the door is 8 ft, which matches with option D.
1 inch / 20 feet = 0.4 inch / x
where x is the actual height of the door in feet.
To solve for x, we can cross-multiply and simplify:
20 feet × 0.4 inch = 1 inch × x
8 feet = x
Therefore, the actual height of the door is 8 ft, which matches with option D.
Christa went shopping for back-to-school clothes. Before the tax was added on, her total was $176. If the sales tax is 6%, what was the total amount she paid?
A $126.56
B $105.60
C $186.56
D $10.56
E $173.56
A $126.56
B $105.60
C $186.56
D $10.56
E $173.56
To find the total amount Christa paid, we need to add the sales tax to the original amount:
Sales tax = 6% of $176 = 0.06 × $176 = $10.56
Total amount paid = Original amount + Sales tax = $176 + $10.56 = $186.56
Therefore, the total amount Christa paid, including the sales tax, was $186.56, which matches with option C.
Sales tax = 6% of $176 = 0.06 × $176 = $10.56
Total amount paid = Original amount + Sales tax = $176 + $10.56 = $186.56
Therefore, the total amount Christa paid, including the sales tax, was $186.56, which matches with option C.
What is 12% of 150?
A 1800
B 180
C 1.8
D 18
A 1800
B 180
C 1.8
D 18
To find 12% of 150, we can use the formula:
12% = 12/100 = 0.12
12% of 150 = 0.12 × 150
12% of 150 = 18
Therefore, 12% of 150 is 18, which matches with option D.
12% = 12/100 = 0.12
12% of 150 = 0.12 × 150
12% of 150 = 18
Therefore, 12% of 150 is 18, which matches with option D.
A group of 20 tourists pay $160 to go on a swamp tour. If the cost per person stays the same, how much will the tour cost 30 tourists?
Responses
A $200
B $220
C $180
D $240
Responses
A $200
B $220
C $180
D $240
A group of 20 tourists pay $160 to go on a swamp tour. If the cost per person stays the same, how much will the tour cost 30 tourists?
A $200
B $220
C $180
D $240
BOT
A $200
B $220
C $180
D $240
BOT
3 answers