If log_{5}x = 2, what is √x?

Solution
To answer this question, you first have to solve for x.
To do so, turn the log into an exponent:
log_{5}x = 2 means 5^{2} = x
Thus, x = 25. The question asks for √x, so here’s your answer:
√x = √25 = 5
On a standard xygraph, what is the distance between (–2, 4) and (1, –2)?

Solution
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:
= \(\sqrt{3^{2} + 6^{2}} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}\)
What is the solution set for x for the inequality 2x + 7 > 11?

Solution
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.
Anne and Katherine are both saving money from their summer jobs to buy bicycles. If Anne had $150 less, she would have exactly ^{1}⁄_{3} as much as Katherine. And if Katherine had twice as much, she would have exactly 3 times as much as Anne. How much money have they saved together?

Solution
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).
This question refers to the following figure, which shows a graph of the percentage of votes tallied by an online book club regarding the next author that the club should focus on.
If exactly 260 people voted, how many votes did Cormac McCarthy receive?

Solution
Cormac McCarthy received 15% of the vote, so use your calculator to find 15% of 260 = 39.
This question refers to the following figure, which shows a graph of the percentage of votes tallied by an online book club regarding the next author that the club should focus on.
Which of the following pairs of authors received exactly 30 percent of the votes altogether?

Solution
Toni Morrison received 20% of the vote and John Steinbeck received 10%, so together they received 30%.
What is the xintercept of a line that passes through the point (3, 4) and has a slope of 2?

Solution
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 xaxis at 1, making the correct answer Choice (D).
Anderson has a phone plan that charges a monthly rate of $50 for the first 1,000 minutes plus $0.25 for each additional minute. Which of the following functions models Anderson’s plan for all m> 1,000, with mas the number of minutes per month and f(m) as the monthly charge?

Solution
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
In the following figure, ABCD is a square and is a diameter of the circle centered at O. If the area of the square is 100, what is the area of the shaded region?

Solution
The area of the square is 100, so each side of the square is 10 (because 10^{2} = 100). The diameter of the circle is 10, so its radius is 5. Plug this value into the area formula for a circle:
A = πr^{2} = π(5)^{2} = 25 π
The shaded region is half of this area, which is \(\frac{25 \pi}{2}\).
Which of the following equals 12x^{2}y^{3}z^{4} – 30xy^{2} + 24x^{2}y^{5}z?

Solution
The greatest common factor among the three terms in 12x^{2}y^{3}z^{4} – 30xy^{2} + 24x^{2}y^{5}z is 6xy^{2}, so you can rule out Choices (C), (D), and (E).
When you factor out 6xy^{2}, the first term reduces to 2xyz^{4}, so you also can rule out Choice (A).