Answer:
we have:
8x³ + mx² - 6x + n
= 8x³ - 8x² + (m + 8)x²- (m + 8)x + (m + 2)x - (m + 2) + m + 2+ n
= 8x²(x - 1) + (m + 8)x(x - 1) + (m + 2)(x - 1) + (m + n + 2)
= (x - 1)[8x² + (m + 8)x + m + 2] + (m + n + 2)
because the remainder if divided by (x-1) is 2
=> m + n + 2 = 2
⇔ m + n = 0 (1)
we also have:
8x³ + mx² - 6x + n
= 8x³ - 12x² + (m + 12)x² - 3/2.x.(m + 12) + ( 12 + 3/2.m)x - (9/4.m + 18) + n +9/4m + 18
= 4x²(2x - 3) + 1/2.(m + 12)x(2x - 3) + (3/2m + 12).1/2.(2x - 3) + 9/4m + n + 18
= (2x - 3)(4x² + (m + 12)/2.x + 3/4m + 6) + 9/4m + n + 18
because the remainder if divided by (2x - 3) is 8
=> 9/4m + n + 18 = 8
⇔ 9/4m + n = -10 (2)
from (1) and (2), we have:
m + n = 0
9/4m + n = -10
=> m = -8
n = 8
Step-by-step explanation:
Answer:
x = 9 and y = 15
Step-by-step explanation:
An equilateral triangle, all sides and angles are congruent and each angle is equal 60 degrees
PQR is an equilateral triangle
So
PQ = QR = RP
Given:
PQ is 14y-59
QR is 9y+1
RP is 11y-23
Angle R is 7x-3
PQ = QR
Plug in
14y-59 = 9y+1
5y = 60
y = 15
Angle R is 7x-3, also <R = 60
So
7x - 3 = 60
7x = 63
x = 9
Answer
x = 9 and y = 15
Answer:
r=4
Step-by-step explanation:
Answer:
$4125
Step-by-step explanation:
Let 'a' represent the additional income Mrs. King must earn. In order for her disposable income to remain the same, we must have ...
(66000 +a)(1 -0.20) = 66000(1 -0.15)
66000 +a = 66000(0.85/0.80) = 66000(1 +0.05/0.80)
a = 66000(5/80) = 4125
Mrs King must earn $4125 more before tax to maintain her after-tax income.
Answer:
64 photographs
Step-by-step explanation:
432 ÷ 92 = 4.695
Since the whole number in the answer is 4, multiply it with 92.
92 x 4 = 368
After that, minus it with all the photographs he have.
432 - 368 = 64
(Final answer)
That is how much photographs have to be partially filled.