ACT Math : Expressions
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Example Questions
Example Question #23 : How To Evaluate Algebraic Expressions
If 
Substituting x+y for 5, we get
6(5) - 52 + (1/5)(5) + 8
30 - 25 + 1 + 8
= 14
Example Question #62 : Expressions
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).
Example Question #63 : Expressions
If st – 4r = 8, what is the value of t in terms of r and s?
s(4r + 8)
(4r + 8)/s
(8 – 4s)/r
(8 – 4r)/s
(4s + 8)/r
(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
Example Question #61 : Expressions
Which of the following is equal (10 – 6)2 if x = 10?
(x + 6)(x – 4)
(x + 8)(x + 2)
(x + 6)(x – 6)
(x + 4)(x – 4)
(x – 8)(x – 2)
(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).
Example Question #961 : Algebra
If 
The value of 
Note that 
Since 
Example Question #31 : Evaluating Expressions
If 
The function 
For the value that follows 
Then simplify:
Example Question #67 : Expressions
A dress that normally costs $80 before tax is on sale for 15% off. After the discount is subtracted, a 7% sale tax is added. What is the final price of the dress?
Need more information
The word problem can be simplified into two steps. First, subtracting the 15% discount:
Second, adding the sales tax to the result from the first step:
The percentage is represented as a decimal by dividing the percentage by 100.
So, for the numbers provided:
New Price =
Final Price =
Example Question #68 : Expressions
Evaluate the expression:
for 
Plug in the values for the variables and use PEMDAS to dictate the order of the operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Using this order of operations we get
Next we deal with the exponents,
Then, we deal with the multiplication,
Finally, we plug these simplified values back into the equation and solve,
Example Question #69 : Expressions
Tickets for a circus show cost 
What is the minimum number of tickets they need to sell at the door on opening night to reach their goal?
Since 
Since each ticket costs 
Note: the answer is NOT 
Example Question #70 : Expressions
If 
Since 
Here, the denominator becomes 
Hence,
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