Evaluating Expressions - ACT Math
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Given that x = 2 and y = 3, how much less is the value of 3_x_2 – 2_y_ than the value of 3_y_2 – 2_x_?
Given that x = 2 and y = 3, how much less is the value of 3_x_2 – 2_y_ than the value of 3_y_2 – 2_x_?
First, we solve each expression by plugging in the given values for x and y:
3(22) – 2(3) = 12 – 6 = 6
3(32) – 2(2) = 27 – 4 = 23
Then we find the difference between the first and second expressions’ values:
23 – 6 = 17
First, we solve each expression by plugging in the given values for x and y:
3(22) – 2(3) = 12 – 6 = 6
3(32) – 2(2) = 27 – 4 = 23
Then we find the difference between the first and second expressions’ values:
23 – 6 = 17
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Evaluate 4x2 + 6x – 17, when x = 3.
Evaluate 4x2 + 6x – 17, when x = 3.
Plug in 3 for x, giving you 36 + 18 – 17, which equals 37.
Plug in 3 for x, giving you 36 + 18 – 17, which equals 37.
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John has a motorcycle. He drives it to the store, which is 30 miles away. It takes him 30 minutes to drive there and 60 minutes to drive back, due to traffic. What was his average speed roundtrip in miles per hour?
John has a motorcycle. He drives it to the store, which is 30 miles away. It takes him 30 minutes to drive there and 60 minutes to drive back, due to traffic. What was his average speed roundtrip in miles per hour?
The whole trip is 60 miles, and it takes 90 minutes, which is 1.5 hours.
Miles per hour is 60/1.5 = 40 mph
The whole trip is 60 miles, and it takes 90 minutes, which is 1.5 hours.
Miles per hour is 60/1.5 = 40 mph
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If (xy/2) – 3_w_ = –9, what is the value of w in terms of x and y?
If (xy/2) – 3_w_ = –9, what is the value of w in terms of x and y?
–3_w_ = –9 – (xy/2)
w = 3 + (xy/6)
–3_w_ = –9 – (xy/2)
w = 3 + (xy/6)
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Evaluate 5_x_2 + 16_x_ + 7 when x = 7
Evaluate 5_x_2 + 16_x_ + 7 when x = 7
Plug in 7 for x and you get 5(49) + 16(7) + 7 = 364
Plug in 7 for x and you get 5(49) + 16(7) + 7 = 364
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If x = y – 3, then (y – x)3 =
If x = y – 3, then (y – x)3 =
Solve for equation for y – x = 3. Then, plug in 3 into (y – x)3 = 27.
Solve for equation for y – x = 3. Then, plug in 3 into (y – x)3 = 27.
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If 
, what is the value of:
If
Substituting x+y for 5, we get
6(5) - 52 + (1/5)(5) + 8
30 - 25 + 1 + 8
= 14
Substituting x+y for 5, we get
6(5) - 52 + (1/5)(5) + 8
30 - 25 + 1 + 8
= 14
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What is the value of z that satisfies the equation: 10(z – 6) = 8z + 4
What is the value of z that satisfies the equation: 10(z – 6) = 8z + 4
Distribute: 10z – 60 = 8z + 4
Move all like terms together: 2z = 64
Solve: z = 32
Distribute: 10z – 60 = 8z + 4
Move all like terms together: 2z = 64
Solve: z = 32
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If 
, then which of the following is an expression for 
in terms of 
and 
?
If
Divide both sides by 
, giving you
.
Divide both sides by
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A company rents cars for a rental fee of $37.00 per day, with an additional charge of $0.45 per mile driven. Which of the following expressions represents the cost, in dollars, of renting the car for 2 days and driving it m miles?
A company rents cars for a rental fee of $37.00 per day, with an additional charge of $0.45 per mile driven. Which of the following expressions represents the cost, in dollars, of renting the car for 2 days and driving it m miles?
To determine cost we add the initial rental fee of $37, times two days giving us $74 plus the mileage rate, 0.45, times the number of miles. Giving an equation of 0.45m+74.
To determine cost we add the initial rental fee of $37, times two days giving us $74 plus the mileage rate, 0.45, times the number of miles. Giving an equation of 0.45m+74.
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Sally is ordering snacks for her class trip. She needs 85 cookies. The cookies come in cases of 6 boxes, with 7 cookies in each box. Sally can't order a partial box. What is the smallest number of cases she should order?
Sally is ordering snacks for her class trip. She needs 85 cookies. The cookies come in cases of 6 boxes, with 7 cookies in each box. Sally can't order a partial box. What is the smallest number of cases she should order?
We first determine how many cookies are in each box. There are 7 cookies in a box, multiplied by 6 boxes, making 42 cookies in a case. We then divide the total number of cookies she needs, 85, by the number in each case, 42, giving us 2 with a remainder. This means Sally must order 3 cases of cookies.
We first determine how many cookies are in each box. There are 7 cookies in a box, multiplied by 6 boxes, making 42 cookies in a case. We then divide the total number of cookies she needs, 85, by the number in each case, 42, giving us 2 with a remainder. This means Sally must order 3 cases of cookies.
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Find the value of 
where:
Find the value of
This problem requires utilization of the opposite operations to both sides principle.
Adding +2 to both sides yields
Subtracting 2y from both sides yields
This problem requires utilization of the opposite operations to both sides principle.
Adding +2 to both sides yields
Subtracting 2y from both sides yields
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When graphed in the (x,y) coordinate plane, at what point do the lines -2x + 4y = 5 and y = -2 intersect?
When graphed in the (x,y) coordinate plane, at what point do the lines -2x + 4y = 5 and y = -2 intersect?
Plugging in y=-2 in the second equation, gives x=-13/2. This is the point where the graphs intersect.
Plugging in y=-2 in the second equation, gives x=-13/2. This is the point where the graphs intersect.
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The length in cm of a plastic container is 5cm less than triple its width. Which of the following equations is an accurate description of the length, l, as a function of the width, w?
The length in cm of a plastic container is 5cm less than triple its width. Which of the following equations is an accurate description of the length, l, as a function of the width, w?
This problem requires the development of an equation. We are told that the length is 5cm less than 3 times its width. So we should set up an equation that describes this situation. The equation l = 3w – 5 demonstrates how the length is 5 cm less than 3 times the width of the container.
This problem requires the development of an equation. We are told that the length is 5cm less than 3 times its width. So we should set up an equation that describes this situation. The equation l = 3w – 5 demonstrates how the length is 5 cm less than 3 times the width of the container.
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A batting average is determined by calculating the amount of hits a batter accumulates in the amount of at-bats that they have had in a season. However when a batter walks the at-bat is not counted in the calculation of the batter's batting average. Walks also have no effect on a batter's hit count.
Let:
Total at-bats, including times a batter has walked = a
Number of hits = b
Number of walks = c
What is an appropriate expression for the calculation of a hitter's batting average?
A batting average is determined by calculating the amount of hits a batter accumulates in the amount of at-bats that they have had in a season. However when a batter walks the at-bat is not counted in the calculation of the batter's batting average. Walks also have no effect on a batter's hit count.
Let:
Total at-bats, including times a batter has walked = a
Number of hits = b
Number of walks = c
What is an appropriate expression for the calculation of a hitter's batting average?
To conform to the way in which a batting average is calculated the equation must be set up so that the amount of hits a batter has accumulated is divided by the amount of at-bats the batter has had, without including at-bats that have resulted in a walk. So the equation should be (hits)/((at-bats) – (walks)), this is acheved by b/(a – c).
To conform to the way in which a batting average is calculated the equation must be set up so that the amount of hits a batter has accumulated is divided by the amount of at-bats the batter has had, without including at-bats that have resulted in a walk. So the equation should be (hits)/((at-bats) – (walks)), this is acheved by b/(a – c).
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Which of the following is equal (10 – 6)2 if x = 10?
Which of the following is equal (10 – 6)2 if x = 10?
First, you set up and solve the original equation. Set up (10 – 6)2, then solve it, giving you 16. We can then plug in 10 for x in the answer choices until you find the choice that always gives you 16, which is (x – 8)(x – 2).
First, you set up and solve the original equation. Set up (10 – 6)2, then solve it, giving you 16. We can then plug in 10 for x in the answer choices until you find the choice that always gives you 16, which is (x – 8)(x – 2).
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If st – 4_r_ = 8, what is the value of t in terms of r and s?
If st – 4_r_ = 8, what is the value of t in terms of r and s?
We rearrange the equation st – 4r=8 by adding 4r to the right side; then divide by s → t = (4r + 8)/s
We rearrange the equation st – 4r=8 by adding 4r to the right side; then divide by s → t = (4r + 8)/s
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The expression x(9 + x)(x – 2) = 4 is a polynomial of which degree?
The expression x(9 + x)(x – 2) = 4 is a polynomial of which degree?
The highest power this polynomial can achieve is 3.
The highest power this polynomial can achieve is 3.
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If 
, then what is the value of 
?
If
The value of 
is 
Note that 
, so 
must equal 
, which is 
Since 
, we can see that 
The value of
Note that
Since
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Let 
for all integers 
and 
. Which of the following is the value of 
?
Let
In order to solve the expression, replace 
with 
and 
with 
in the definition given:
In order to solve the expression, replace
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