ACT Math : Algebra
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Example Questions
Example Question #1211 : Algebra
The function 
36
56
18
-36
24
24
Substitute -1 for 
If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that 
Example Question #56 : Algebraic Functions
A book binding company charges a fixed fee of $2.25 to bind a book and an additional $0.15 per page. Which equation accurately calculates the cost, C, of a book with p number of pages?
The company's binding process incorporates a fixed fee; therefore, we must use the formula for a linear equation:
The fixed fee means that the consumer pays a single fee of $2.25 to bind the book regardless of how many pages that book has; thus, the fixed fee is represented by the y-intercept, or b, of the equation. The problem states that each page will cost an additional $0.15 per page, which varies with depending on the number of pages in the book. The page cost is represented by the slope, m, of the equation. In order to calculate the total cost, 
Example Question #1212 : Algebra
If the function 
We can take each of the listed transformations of 
Next, take this equation and reflect it across the x-axis. If we reflect a function across the x-axis, then all of its values will be multiplied by negative one. So, 
Lastly, distribute the negative sign to arrive at the final answer.
Example Question #1213 : Algebra
For which value of 
5
2
6
4
3
4
It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).
Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
The correct answer is 4 because
F(x) = 2x + 3x + (9x/3) = 2(4) + 34 + ((9 * 4)/3) = 101, and
G(x) = (((24 + 44)/2) - 4 * 4) – 5(4) + 1 = 101.
Example Question #2701 : Act Math
Two consecutive negative odd numbers have a product of 15. What is the sum of the two numbers?
–8
–12
–6
–4
–10
–8
Define the variables x = first number and x + 2 = second number
The product is x(x + 2) = 15, so we need to solve the quadratic equation x2 + 2x – 15 = 0. Factoring we get (x + 5)(x – 3) = 0, so x = –5 or x = 3. The problem calls for negative numbers, so the answers are –5 and –3 and the sum is –8
Example Question #2702 : Act Math
What is the difference of the values of x that satisfy
4x2+ 3x – 1 = 0?
4/5
5/4
0
3
5/4
Factor the equation (4x – 1) (x + 1)
The solutions are x = –1 and x = 1/4.
The difference is (1/4) – (–1) = 5/4
Example Question #2703 : Act Math
2x + y = 1
What is the slope and the y-intercept of the given equation, respectively?
2, –2
2, 1
–2, 1
1, 1
1, 2
–2, 1
You put the equation into slope-intercept form (y = mx + b)
The new equation is y= –2x + 1
m = –2 and b = 1
Example Question #2704 : Act Math
How many solutions are there to: x2 – 9 = 0
0
2
1
Infinitely many
2
There are two solutions that make the solution true: 3 and –3.
Example Question #4 : How To Solve For A Variable As Part Of A Fraction
Solve for 
Cross multiply.
Dsitribute.
Solve for 
Example Question #1 : How To Solve For A Variable As Part Of A Fraction
The quotient of a fraction is 
Step 1: Set up the equation
Step 2: Solve for D
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