ACT Math : Algebra
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Example Questions
Example Question #5 : How To Find The Solution To A Quadratic Equation A1
Two positive consecutive multiples of three have a product of 108. What is their sum?
Let 
and
So the equation to solve becomes
or
We factor to solve the quadratic equation to get 9 and 12 and their sum is 21.
Example Question #6 : How To Find The Solution To A Quadratic Equation A1
Two consecutive positive odd numbers have a product of 99, What is the sum of the two numbers?
Let 
So the equation to solve becomes
or
Solving the quadratic equation by factoring gives 9 and 11, so the sum is 20
Example Question #15 : Quadratic Equations
When asked how many home runs he hit in a season, Pablo Sanchez responded with, "If you square the number of home runs and subtract 50 times the number of home runs, it is equivalent to 50." How many home runs has Pablo hit?
49
–1
1
73
51
51
We can generate an equation for the number of home runs he has hit, x : x2 - 50x = 50. Reordering this, we get : x2 - 50x - 50 = 0. Using the quadratic equation: x = (-b± √(b2-4ac)) / (2a). In this case, a = 1, b = -50, c = -50. Plugging in these values, we obtain the simplified equation, x = (50±51.96)/2. Therefore, x = 50.98, -0.98. Because it doesn't make sense to have a negative number of home runs, x = 50.98, which rounds up to 51 home runs.
Example Question #19 : Quadratic Equations
If (x + a)(x + b) = x2 – 9x + 18, what are the values for a and b?
a = 3, b = –6
a = –3, b = –6
a = –3, b = 6
a = 3, b = 6
a = 6, b =3
a = –3, b = –6
a = –3, b = –6. The sum of a and b have to be equal to –9, and they have to multiply together to get +18. If a = –3 and b = –6, (–3) + (–6) = (–9) and (–3)(–6) = 18.
Example Question #10 : How To Find The Solution To A Quadratic Equation A1
Which of the following is the closest approximate solution for x where 11x2 – 7x – 8 = 0?
4
–29/22
7/11
19/22
27/22
27/22
Apply the quadratic formula directly to get [7 ± (49 – 4 * 11 * –8)0.5]/22, → [7 ± (≈ 20)]/22
So our approximate answers are 27/22 and –13/22, and 27/22 is our answer.
Example Question #273 : Equations / Inequalities
Two consecutive positive multiples of three have a product of 
Let 
We know that the first number times the second is 
Distributing the 
The question tells us that the integers are positive; therefore, 
If 
The sum of these numbers is 
Example Question #551 : Algebra
Find the solutions of this quadratic equation:
4y3 - 4y2 = 8y
2, 4
1, 2
–2, 4
–1, 2
–1, –2
–1, 2
4y3 - 4y2 = 8y
Divide by y and set equal to zero.
4y2 - 4y – 8 = 0
(2y + 2)(2y – 4) = 0
2y + 2 = 0
2y = –2
y = –1
2y – 4 = 0
2y = 4
y = 2
Example Question #552 : Algebra
Which of the following is a solution to:
You may use the quadratic formula (where 
Since the only solution that appears in the answer list is 
Example Question #553 : Algebra
2x + y3 + xy2 + y = x
If y = 1, what is x?
2
–1
1
0
3
–1
Plug in y = 1. Then solve for x.
2x + y3 + xy2 + y = x
2x + 1 + x + 1 = x
3x + 2 = x
2x = -2
x = -1
Example Question #554 : Algebra
What are the 
None of the other answers
We need to use the quadratic formula where 
Plugging in our values:
Simplifying:
Simplifying:
Simplifying:
Finally:
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