Step-by-step explanation:
The vertex form of the equation for a parabola is given by
where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as
Also, since the parabola passes through (4, -7), we can use this to find the value for a:
or
Therefore, the equation of the parabola is
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!
360°-90°(right angle)-90°(right angle)-52°=128°
X=128°
Hope this helps :)
The answer you have is good. You don't need to change anything.
Answer:
Step-by-step explanation:
hello :
5x=(2x-2)(m+6) equivalent : 5x = 2xm+12x-2m-12
5x-2xm -12x=-2m-12
x(5-2m-12) = -2m-12
x(-7-2m) = -2m-12
x(2m+7) = 2m+12
if : 2m+7 ≠ 0 means m ≠ -7/2 so : x= (2m+12)/(2m+7)
if : 2m+7 = 0 means : m = -7/2 you have : x(0) = 2(-7/2)+12
0= 5 ( false) ... x no exist
