In the figure above, $top enclose B D end enclose$ is parallel to $top enclose A E end enclose$ . What is the length of $top enclose C E end enclose$ ?

If $a to the power of b over 4 end exponent equals 16$ for positive integers a and b, what is one possible value of b?

If $square root of x plus square root of 9 equals square root of 64$ , what is the value of x?

A bricklayer uses the formula n = 7 l h to estimate the number of bricks, n, needed to build a wall that is l feet long and h feet high. Which of the following correctly expresses l in terms of n and h

If $x equals 2 over 3 y$ and y = 18, what is the value of 2x − 3 ?

4x² − 9 = (px + t)(px − t)
In the equation above, p and t are constants. Which of the following could be the value of p ?

What is the sum of the complex numbers 2 + 3i and 4 + 8i, where i = $square root of negative 1 end root$

A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

2x² − 4x = t
In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?

Which of the following is equivalent to $fraction numerator 4 x squared plus 6 x over denominator 4 x plus 2 end fraction$ ?

The vertex of the parabola in the xy-plane above is (0, c). Which of the following is true about the
parabola with the equation y = −a(x − b)² + c ?

Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to
represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal?

x

w(x)

t(x)

1

-1

-3

2

3

-1

3

4

1

4

3

3

5

-1

5

The table above shows some values of the functions w and t. For which value of x is w(x) + t(x) = x ?

6x − 9y > 12
Which of the following inequalities is equivalent to the inequality above?

Equivalent Inequalities
Equivalent inequalities are defined as inequalities that transmit the same information.
There are several methods for creating equal inequalities.
An inequity is equal to its mirror image, to start with. Let's take a look at what that appears to be:
x > 4
4 < x
Keep in mind that one inequality is effectively the reverse of the other. The inequality symbol's pointed portion always points in the direction of 4! In this situation, the disparities are equal. You must, however, pay VERY close attention to the inequality sign's orientation.
Example 1: The pointed portion of the inequality sign in the first inequality points to 4, whereas the pointy portion in the second inequality points to x, making these two inequality NOT equal:
x > 4
4 < x

6x − 9y > 12
Which of the following inequalities is equivalent to the inequality above?