Lines XY and ZW are parallel and are bisected by line AB.

As you can see in the diagram from the question, these lines form two triangles.

Because the lines XY, YZ, and ZW are equal, the sides of the triangles that are created are also equal.

The triangle with ∠s is a reflection of the triangle with ∠t, so ∠s = ∠t.

If ∠t = 45°, then ∠s = 45°

This problem requires you to understand absolute value.

Absolute value is the distance of the given value from zero on the number line, without regard to its sign.

So, |−2|²+| − 5| − 3 = 2² + 5 − 3, which is 4 + 5 − 3 = 6.

The easiest way to solve this problem is to cross-multiply and solve for x:

\(\frac{4x}{x − 1}=\frac{4x}{2x + 2}\)

4x(2x + 2) = 4x(x − 1)

8x² + 8x = 4x² − 4x; combine like terms

4x² + 12x = 0; simplify by factoring out 4x

4x(x + 3) = 0

4x = 0, so x = 0

x + 3 = 0, so x = −3

The two solutions are 0 and –3. The sums of these solutions is 0 + −3, or −3.

The sine of an angle is the length of the opposite side divided by the length of the hypotenuse \(\left ( \frac{opp}{hyp} \right )\).

You are given the measure of the opposite side, but you are not given the hypotenuse.

So you must use the Pythagorean Theorem to find the measure of the hypotenuse:

(1)² + (5)² = (hypotenuse)²

1 + 25 = (hypotenuse)²

26 = (hypotenuse)², so the hypotenuse = \(\sqrt{26}\).

Now, you can find sin C: \(\left ( \frac{opp}{hyp} \right )\)= \(\frac{1}{\sqrt{26}}\).

You are given that x ≤ y and y ≤ z.

If x = y and y = z, then x = z could be true.

Eliminate answer choices F, J, and K, which show that Roman Numeral I (x = z) is NOT true.

If x < y and y < z, then x < z could be true. But x > z could not be true in either case.

So only II CANNOT be true, answer choice G.

You are given that 1 gallon of paint can cover 36 square feet.

The room is 8 feet by 12 feet, or 96 square feet. Set up a proportion:

\(\frac{1}{36}=\frac{x}{96}\)

Cross-multiply and solve for x:

36x = 96

x = approximately 2.666

The question asks you to round to the nearest whole gallon, so round up to 3 gallons.

You are given that angle P is 55°.

Since PQR is a right triangle, angle Q is 90°.

So, angle R must be 180° − (55° + 90°) or 35°.

You are given that x = 3 is one solution, which means that (x − 3) is one of the factors of 2x²−5x−a = 0.

Since the coefficient of the x²–term is 2, you can set up the other factors as follows:

(2x + )(x − 3)

The x terms must equal –5, so apply the FOIL method to find the missing term:

−6x + x = −5x

−6x + x = −5x; the missing term must be 1.

Use FOIL again to solve for a:

(2x + 1)(x − 3)

2x² − 6x + x − 3

2x² − 5x − 3

Thus, a = 3.

First, factor the numerator and denominator:

\(\frac{x^{2} − 6x + 9}{6x − 18}=\frac{(x − 3)(x − 3)}{6(x − 3)}\)

Next, cancel out an (x −3) from the numerator and denominator, which leaves you with \(\frac{(x − 3)}{6}\).

To solve this problem, combine like terms. Remember to keep track of the negative signs!

x² − (3x − 2) + 2x(4x − 1)

x² − 3x + 2 + 8x² − 2x

9x² − 5x + 2