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2 years ago

The grass on Julie's lawn was 4.5 centimeters tall right after she mowed it. Then the grass

Mathematics

1 answer:

telo118 [61]2 years ago

4 0

Answer: w = 2.1h + 4.5

Step-by-step explanation:

w is the number of weeks since Julie mowed the lawn

h is the height of the grass

w=the rate the grass grew at and the grass on Julies lawn

w=2.1h+4.5

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f(x) = 3x2 - 2x g(x) = x + 4 When finding f(x) · g(x), what could the first step look like? A) 3x2 + 12x2 - 2x2 - 8x B) 3x2 + 7x

Anna71 [15]

(3x^2 - 2x)(x + 4)

First step would be: distributive property.

3x^3 + 12x^2 - 2x^2 - 8x

Combine like terms.

3x^3 + 10x^2 - 8x is the simplified form of the functions multiplied.

Your answer is D.

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3 years ago

A system of equations has infinitely many solutions. If zy - 4x = 6 is one of the equations, which could be the other equation?

NemiM [27]

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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

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If the perimeter of a square is 18.48 cm, how long is one side of the square?

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Step-by-step explanation:

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