1. Answer: C.
Begin by setting up an equation representing the average. (2 + x + 31) ÷ 7 = 24. Solve for x to find 135 and recognize that this x represents the sum of the remaining 5 scores. To find the average, divide 135 by 5 to find 27.
2. Answer: D.
If a triangle has side lengths a, b, and c, the sum of the lengths of any 2 sides must be larger than the length of the 3rd side. So in this case, 5 + 6 = 11 must be larger than side length c. From the answer choices, 12 is the only length greater than 11, so it cannot be the length of the third side.
3. Answer: B.
Recall that vertex- form of a parabola is:
a(x − h)2 + k, where (h, k) represents the vertex.
We wish to translate our vertex from (0,0) to (4,−6) so h = 4 and k = −6.
ƒ(x) = (x − 4)2 – 6
4. Answer: B.
Recall that slope-intercept form is y = mx + b where m is the slope and b is the y-intercept. Solve for y:
8x − 2y = −6
2y = 8x + 6
Divide everything by 2:
y = 4x + 3
5. Answer: C.
The circumference of a circle is the distance around defined by π * diameter. The diameter, in this case, can be found through the difference between the x values:
3 − (−3) = 6, so π * 6 is the circumference.
6. Answer: C.
| 2(x – 1) – 15 | = 7
| 2x – 2 – 15 | = 7
| 2x – 17 | = 7
2x – 17 = – 7 and 2x – 17 = 7
2x = 10 and 2x = 24
x = 5 and x = 12
The solution set: { 5,12 }
7. Answer: B.
If the product of two numbers is positive, the two numbers must have the same sign. That is, if ab > 0, then either a > 0 and b > 0, or a < 0 and b < 0.
We are told that A < −1 (which implies that A < 0).
So we know that B < 0.
We also know that AB = 1, so A = 1/B
Since A = 1/B, and A < -1, we can infer that 1/B < -1
If we take reciprocals on both sides of the last inequality, we must flip the inequality sign. Hence: B > −1
So we know that B < 0, and B > −1. We can represent this as a compound inequality: −1 < B < 0
8. Answer: C.
For this question, you have to examine all the answer options individually in order to eliminate all those that cannot be true. First, if x is positive and y is negative, their product must be negative, so (A) is incorrect.
Next, the sum of a positive and a negative number could be either positive or negative, depending on which number has the greater absolute value; this rules out (B) because it’s not always true.
ESTÁS LEYENDO
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Ciencia Ficción"You may encounter many defeats, but you must not be defeated. In fact, it may be necessary to encounter the defeats, so you can know who you are, what you can rise from, how you can still come out of it." -Maya Angelou Learning from your mistakes i...
