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2 years ago

Rewrite each equation in vertex form. Then find the vertex Y=x^2+ 9x + 5

Mathematics

1 answer:

8090 [49]2 years ago

3 0

Answer:

Step-by-step explanation:

The answer to life the universe and everything is 42

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Given the endpoint A(1, 3) and the midpoint C(6, 2), find the other endpoint B(x, y).

Tpy6a [65]

Right away we know we don't have fractions; the midpoint is the average of the coordinates, so if it and one endpoint are integers so is the other endpoint.

We can do a kind of point arithmetic:

C = (A+B)/2

2C = A+B

B = 2C - A

B = 2(6,1) - (1,3) = (12,2)-(1,3)=(11,-1)

Answer: That's none of the above, but a typo away from the first choice.

6 0

2 years ago

If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

2 years ago

Find the value of X.

Tju [1.3M]

Answer:

A number

Step-by-step explanation:

it cant be nothing

4 0

3 years ago

60=F(15) Please solve this and show work, please

Lubov Fominskaja [6]

Answer:

f = 4

Step-by-step explanation:

60= 15f

divide both side by 15

f = 4

3 0

3 years ago

What is the distance?

Arlecino [84]

Answer:

.25 it 1/4 or an inch should be correct

5 0

2 years ago