Algebra

Help Questions

ACT Math › Algebra

Questions 1 - 10

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.

Add and .

Explanation

To add the trinomials, simply eliminate the parentheses and add like terms.

Simplify

Explanation

Simplifying an inequality like this is very simple. You merely need to treat it like an equation—just don't forget to keep the inequality sign.

First, subtract from both sides:

Then, divide by :

Find the slope of the tangent line to where .

Explanation

To find the slope of the tangent line, we must take the derivative.

By using the Power Rule we will be able to find the derivative:

$f(x)=a^n \rightarrow f'(x)=na^{n-1}$

Therefore derivative of is .

Now we plug in , giving us .

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.

Which of the following is the square of $5 \sqrt{x} +3 \sqrt{y}$ ?

You may assume both and are positive.

$25x + 9y+ 30 \sqrt{xy}$

$25x + 9y+ 15\sqrt{xy}$

$5x + 3y+ 15\sqrt{xy}$

$5x + 3y+ 30\sqrt{xy}$

Explanation

Use the square of a sum pattern, substituting $5 \sqrt{x}$ for and $3 \sqrt{y}$ for in the pattern:

$(A+ B)^{2}= A^{2}+ 2AB + B^{2}$

$(5 \sqrt{x}+3 \sqrt{y})^{2}= (5 \sqrt{x})^{2}+ 2 (5 \sqrt{x})\left (3 \sqrt{y} \right ) + \left (3 \sqrt{y} \right )^{2}$

$(5 \sqrt{x}+3 \sqrt{y})^{2}= 25x+ 30 \sqrt{xy} + 9y$

$25x + 9y+ 30 \sqrt{xy}$

If 5 + x is 5 more than 5,what is the value of 2_x_?

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

$$500$

$$250$

$$750$

$$300$

$$625$

Explanation

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

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.

Page 1 of 100

Return to subject