Answer:
7. (4x +10)/(x^3 +3x^2 -16x -48)
9. -320/93
Step-by-step explanation:
7. As with adding any fractions, first you find a common denominator. When the fractions are rational expressions, it often helps to factor the denominators.
6/(x^2 -16) -2/(x^2 -x -12) = 6/((x -4)(x +4)) -2/((x -4)(x +3))
= (6(x +3) -2(x +4))/((x -4)(x +3)(x +4)) . . . . . using a common denominator
= (6x +18 -2x -8)/((x -4)(x +3)(x +4))
= (4x +10)/((x^2 -16)(x +3))
= (4x +10)/(x^3 +3x^2 -16x -48)
_____
9. First you simplify the denominator:
2/25 -5/16 = (2·16 -5·25)/(25·16) = -93/400
Then you perform the division. This can be done by multiplying by the inverse of the denominator.
(4/5)/(2/5 -5/16) = (4/5)·(-400/93) = -320/93
Answer:
12 and 24
Step-by-step explanation:
2 numbers, x in this case, with one being twice the other, one of them will be 2x, equals 36. Your equation would look like this: 2x+x=36. Simplify it to get 3x=36, divide the 3 and you get 12. 12 will be your small number then multiply by 2 to get your large one, 24.
512 as a power of a number is X^512
Answer:
(5,-3) in the 4th quadrant
Step-by-step explanation:
Given:
Choose a number between 0 and 20.
If the difference is less than 10 then Eric wins.
Let us x is Eric's number. 0 <u><</u> x <u><</u> 20
If Eric wins. |x -7| < 10
|x-7| < 10 → -10 < x-7 < 10 → -10 + 7 < x - 7 + 7 < 10 + 7 → -3 < x < 17
Taking into account that the number must be given between 0 and 20.
0 <u><</u> x <u><</u> 20
-3 < x < 17
→ 0 < x < 16
