Algebra

Help Questions

ACT Math › Algebra

Questions 1 - 10

Which of the following is the equation of a line parallel to the line given by the equation:

$y = \frac{1}{4}x +5$

$y = -\frac{1}{4}x + 5$

Explanation

Parallel lines have the same slope and different y-intercepts. If their y-intercepts and slopes are the same they are the same line, and therefore not parallel. Thus the only one that fits the description is:

Which of the given functions is depicted below?

Act_math_184_01

Explanation

The graph has x-intercepts at x = 0 and x = 8. This indicates that 0 and 8 are roots of the function.

The function must take the form y = x(x - 8) in order for these roots to be true.

The parabola opens downward, indicating a negative leading coefficient. Expand the equation to get our answer.

y = -x(x - 8)

y = -x2 + 8x

y = 8x - x2

Therefore, the answer must be y = 8x - x2

A circle has its origin at . The point is on the edge of the circle. What is the radius of the circle?

$r=\sqrt{74}$

$r=2\sqrt{18}$

$r=6\sqrt{2}$

$r=4\sqrt{21}$

There is not enough information to answer this question.

Explanation

The radius of the circle is equal to the hypotenuse of a right triangle with sides of lengths 5 and 7.

$r=\sqrt{74}$

This radical cannot be reduced further.

Which of the following equations represents a line that is parallel to the line represented by the equation ?

$y=\frac{5}{2}x+1$

$y=-\frac{5}{2}x+1$

$y=\frac{2}{5}x+2$

$y=-\frac{2}{5}x+3$

Explanation

Lines are parallel when their slopes are the same.

First, we need to place the given equation in the slope-intercept form.

Subtract from both sides of the equation.

Simplify.

Divide both sides of the equation by .

$\frac{-4y}{-4}=\frac{-10}{-4}+\frac{26}{-4}$

Simplify.

$y=\frac{10}{4}x-\frac{26}{4}$

Reduce.

$y=\frac{5}{2}x-\frac{13}{2}$

Because the given line has the slope of $\frac{5}{2}$ , the line parallel to it must also have the same slope.

Three consecutive positive numbers have the sum of 15. What is the product of these numbers?

120

Explanation

Define the variables as x = the first number, x + 1, the second number, and x + 2 the thrid number.

The sum becomes x + x + 1 + x + 2 = 15 so 3x + 3 = 15. Subtract 3 from both sides of the equation to get 3x = 12 → 3x/3 = 12/3 → x = 4

The three numbers are 4, 5, and 6 and their product is 120.

Give the lines y = 0.5x+3 and y=3x-2. What is the y value of the point of intersection?

Explanation

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

What is ?

Explanation

is distributed first to and is distributed to . This results in and . Like terms can then be added together. When added together, , , and . This makes the correct answer .

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Cannot be determined

Explanation

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

Give the coefficient of $x^{5}$ in the binomial expansion of $\left ( 0.2x+ 5 \right )^{7}$ .