To answer this question, you first have to solve for x.

To do so, turn the log into an exponent:

log₅x = 2 means 5² = x

Thus, x = 25. The question asks for √x, so here’s your answer:

√x = √25 = 5

Plug the values into the distance formula:

Distance = \(\sqrt{\left ( x_{2} - x_{1} \right )^{2} + \left ( y_{2} - y_{1} \right )^{2}}\) = \(\sqrt{\left ( 1 - \left (-2 \right ) \right )^{2} + \left ( -2 - 4 \right )^{2}}\)

Simplify:

= \(\sqrt{3^{2} + 6^{2}} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}\)

Split the inequality |2x + 7| > 11 into two inequalities: 2x + 7 > 11 and 2x + 7 < –11.

Solve both for x: 2x + 7 > 11 ; 2x + 7 < –11 2x > 4 ; 2x < –18 x > 2 ; x < –9

Therefore, x < –9 or x > 2.

If Anne had $150 less, Katherine would have three times more than Anne.

Make this statement into an equation and simplify:

3(a – 150) = k

3a – 450 = k

And if Katherine had twice as much, she would have three times more than Anne:

2k = 3a

Substitute 3a – 450 for k into the last equation and solve for a

2(3a – 450) = 3a

6a – 900 = 3a

–900 = –3a

300 = a

Now substitute 300 for a into the same equation and solve for k:

2k = 3(300)

2k = 900

k = 450

Thus, together Anne and Katherine have 300 + 450 = 750, so the right answer is Choice (E).

Cormac McCarthy received 15% of the vote, so use your calculator to find 15% of 260 = 39.

Toni Morrison received 20% of the vote and John Steinbeck received 10%, so together they received 30%.

First, plot the point (3, 4) on a graph. A slope of 2 means “up 2, over 1,” so plot this point on a graph, too.

Here’s the resulting graph:

The line passes through the x-axis at 1, making the correct answer Choice (D).

For m > 1,000 — that is, beyond 1,000 minutes of usage — the plan charges a usage fee based on the number of minutes used plus a flat rate of $50.

With this information, you can create the following function:

f(m) = Usage fee + 50

The usage fee is $0.25 per minute; however, the first 1,000 minutes are already paid for.

So the usage fee is 0.25(m – 1,000).

Plug this value into the preceding function and simplify:

f(m) = 0.25(m – 1,000) + 50

f(m) = 0.25m – 250 + 50

f(m) = 0.25m – 200

The area of the square is 100, so each side of the square is 10 (because 10² = 100). The diameter of the circle is 10, so its radius is 5. Plug this value into the area formula for a circle:

A = πr² = π(5)² = 25 π

The shaded region is half of this area, which is \(\frac{25 \pi}{2}\).

The greatest common factor among the three terms in 12x²y³z⁴ – 30xy² + 24x²y⁵z is 6xy², so you can rule out Choices (C), (D), and (E).

When you factor out 6xy², the first term reduces to 2xyz⁴, so you also can rule out Choice (A).