The correct answer is C: 1/(x + 4)(x - 5)
Why? Well, let's first simplify x^2 - 3x - 10 and x^2 + x - 12; the two denominators. Each of these should become an (x +/- number), and to figure out the number, as well as whether it is positive or negative, we can do a simple trick
Look at the factors of the right number (In this case, -10 and -12)
-10 -12
1 * -10 1 * -12
-1 * 10 -1 * 12
-2 * 5 -2 * 6
2 * -5 2 * -6
-3 * 4
4 * -3
Now for part 2
Which of these pairs add up to the middle number? One of the pairs of -10 should make -3, and likewise, one of the pairs of -12 should make 1 (when x has no number in front of it you may safely assume it is 1).
2 - 5 = -3 and 4 - 3 = 1, so we now know that the 2 fraction equations simplified is
x + 2 / (x + 2)(x - 5) * x - 3/(x -3)(x + 4)
Notice anything repeating? As long as they are apart of the same fraction, we can cross out anything that has the same x - number. Crossing out both x + 2 and x - 3, we now simply have x - 5 * x + 4. Because we crossed out both numerators, the top numbers both become 1, thus giving our answer, C.
<span>First, use the equation of the trend line to find the IQ that is expected by the GPA. Next, use the other equation of the trend line to find the SAT that is predicted by the IQ.</span>
The slope of this line is
−
12
5
.
Perpendicular lines have opposite reciprocal slopes. To find an opposite reciprocal, multiply by
−
1
and flip the numerator and denominator.
Hence the opposite reciprocal of
−
12
5
and the slope of a line perpendicular to a line with a slope of
−
12
5
is
5
12
.
Change 15/20 to 3/4
Now we have
multiply 6 to 3= 18 ÷ 4 = 4.5
x = 4.5
