Answer: 2 bookcases.
Step-by-step explanation:
Let be "x" the number of bookcases that the custodian will be able to repaint completly with 5 gallons of paint.
According to the data given, the custodian needs 2 gallons of paint to repaint one bookcase. Since all the bookcases are equal, you can set up the following proportion:
Now you must solve for "x" in order to find its value:
Notice that the custodian will be able to repaint 2 bookcases completely, then you can say that:
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.
Answer: x=3.4
Step-by-step explanation:
0.5x + 4.2 = 5.9 \\ 0.5x = 5.9 - 4.2 \\ 0.5x = 1.7 \\ x = 1.7 \div 0.5 \\
<span>So we want to know how many students out of 144 practice martial arts every day if we know that 7/12 practice every day. So lets multiply the numerator and the denumerator with 12. We will get (12*7)/(12*12)=84/144. And we got our answer: 84 out of 144 students practice every day.</span>
Answer:D. The sign of each y- coordinate change.
Step-by-step explanation: because everything on the X axis stayed the same but on the Y axis it decreased
