Answer:
<h2>b) 4,5,15</h2><h2 />
Step-by-step explanation:
In a triangle of sides‘s length a , b and c
in order to be able to form (construct) this triangle we must have :
c - a < b < c + a
in fact this work with cases a) ,c) and d)
but not b)
because 15 - 4 is not < to 5
in other words 15 - 4 > 5
Answer:
x = -8
Step-by-step explanation:
-23 + 7 = -16
-16 ÷ 2 = -8
2 × -8 =-16 - 7 = -23
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:
The expression that represents the volume would be: <span>C) 6x^3+39x^2+54x</span>
Proof of the calculation:
V = Lwh
V = (x+2) (3x) (2x+9)
V= (3x^2 + 6x) (2x + 9)
V = (6x^3 + 27X^2 +12x^2 + 54x)
V = 6x^3 + 39x^2 + 54x
Answer:
Problem 8 is No and Problem 9 is Yes
