Answer:
The answer is B
Step-by-step explanation:
plug 2 into x to see
A.
x^2 + 8
2^2 + 8
4 + 8 = 12
B.
3x^2 + 1
3(2)^2 + 1
3(4) + 1
12 + 1 = 13
C.
2x^3 + 5
2(2)^3 + 5
2(8) + 5
16 + 5 = 21
D.
x^2 + x
2^2 + 2
4 + 2 = 6
Answer:
x = 21, y = 25
Step-by-step explanation:
DEFG is a parallelogram.
Diagonals of a parallelogram bisects each other.
9514 1404 393
Answer:
A: 8x +24
B: not equivalent for any value of x
Step-by-step explanation:
<u>Part A</u>:
The factor of 4 on the outside of parentheses multiplies each term inside:
M = 4(2x) +4(6)
M = 8x +24 . . . . . expression equivalent to M
__
<u>Part B</u>:
Expressions M and N are not equivalent for any value of x. They are equivalent if their difference is zero or can be made to be zero. Subtracting N from M, we find the difference to be ...
M -N = (8x +24) -(8x +10) = 14
There is no value of x that will make the difference of 14 become zero.
For (2), start with the base case. When n = 2, we have
(n + 1)! = (2 + 1)! = 3! = 6
2ⁿ = 2² = 4
6 > 4, so the case of n = 2 is true.
Now assume the inequality holds for n = k, so that
(k + 1)! > 2ᵏ
Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have
((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!
Then by our hypothesis,
(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹
and k•2ᵏ ≥ 2•2² = 8, so
k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹
which proves the claim.
Unfortunately, I can't help you with (3). Sorry!
Answer:
12.5 hours
Step-by-step explanation:
2 hours translated to minutes is 120 minutes. 120 divided by 8 equals 15. Where it takes on average 15 minutes to finish 1 vase 15 (number of minutes to paint 1 vase) x 50 vases would equal 750 minutes or 12.5 hours to paint 50 vases.
