How to evaluate algebraic expressions
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ACT Math › How to evaluate algebraic expressions
If , then which of the following is an expression for
in terms of
and
?
Explanation
Divide both sides by , giving you
.
A company establishes a rewards program such that the bonus received by an employee is given by the model , where
is the number of sales an employee completed. If Alex earned \$2700 at the end of the month, how many sales has he completed?
Explanation
Alex’s bonus of
Evaluate the expression for
Explanation
The answer is
To solve this expression subsitute for
. This results in
. Simplify to get
as the answer.
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?
1
2
3
4
6
Explanation
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.
If st – 4_r_ = 8, what is the value of t in terms of r and s?
(4r + 8)/s
(8 – 4r)/s
(4s + 8)/r
(8 – 4s)/r
s(4r + 8)
Explanation
We rearrange the equation st – 4r=8 by adding 4r to the right side; then divide by s → t = (4r + 8)/s
Which of the following is equal (10 – 6)2 if x = 10?
(x + 6)(x – 6)
(x + 4)(x – 4)
(x + 6)(x – 4)
(x – 8)(x – 2)
(x + 8)(x + 2)
Explanation
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).
The expression x(9 + x)(x – 2) = 4 is a polynomial of which degree?
0
2
3
4
1
Explanation
The highest power this polynomial can achieve is 3.
If , then what is the value of
?
Explanation
The value of is
Note that , so
must equal
, which is
Since , we can see that
If x = y – 3, then (y – x)3 =
–27
–9
3
9
27
Explanation
Solve for equation for y – x = 3. Then, plug in 3 into (y – x)3 = 27.
If , what is the value of:
Explanation
Substituting x+y for 5, we get
6(5) - 52 + (1/5)(5) + 8
30 - 25 + 1 + 8
= 14