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2 years ago

It says solve for the variable can you help me

Mathematics

2 answers:

Nastasia [14]2 years ago

8 0

Answer:

X=37

Step-by-step explanation:

Add 4x+2 and 30 it equals to 180. Then you get x.

german2 years ago

4 0

X=37 I agree with the other person

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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

What is the value of x in the equation 8+4 = 2(x-1)? 5 11/2 13/2 7

Citrus2011 [14]

Answer:

x = 7

Step-by-step explanation:

I hope this helps!

4 0

2 years ago

On a coordinate plane, line P Q goes through (negative 3, negative 3) and (3, negative 1). Point R is at (1, 1).

olga55 [171]

Answer:

0, 2/3

Step-by-step explanation:

Its the only one that make sense.

hope thats right

edge 2020

7 0

2 years ago

Read 2 more answers

If a equals 4b - 15 what is b

nlexa [21]

Answer:

b = a + 3.75

Step-by-step explanation:

a = 4b - 15

You are solving for b. Isolate the b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 15 to both sides

a (+15) = 4b - 15 (+15)

a + 15 = 4b

Next, divide 4 from both sides. Remember to divide from all terms.

(4a + 15)/4 = (4b)/4

b = (4a)/4 + (15)/4

b = a + 15/4

b = a + 3.75 is your answer

7 0

2 years ago

Without actual division prove that x4 +2x3 -2x2 +2x -3 is exactly divisible by x2 +2x-3

Brut [27]

Answer:

Step-by-step explanation:

$\displaystyle\Large\boldsymbol{} x^4+2x^3-2x^2+2x-3= \\\\\\x^4+2x^2(x-1)+2x-\underbrace{2-1}_{-3}= \\\\\\x^4-1+2x^2(x-1)+2x-2 = \\\\\\(x^2-1)(x^2+1)+2x^2(x-1)+2(x-1) = \\\\\\\underline{(x-1)}(x+1)(x^2+1)+2x^2\underline{(x-1)} +2\underline{(x-1)} =\\\\\\(x-1)((x+1)(x^2+1)+2x^2+2)=\\\\\\(x-1)(x^3+x^2+2x^2+x+2+1)=\\\\\\(x-1)(x^3+3x^2+x+3) =\\\\\\(x-1)( \underline{(x+3)}x^2+\underline{(x+3)})=(x^2+1)\underbrace{(x-1)(x+3)}_{x^2+2x-3}= \\\\\\(x^2+1)(x^2+2x-3) : (x^2+2x-3)=x^2+1$

7 0

2 years ago