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Alona [7]
3 years ago
15

Which expression is equivalent to 8x - 12y +32

Mathematics
2 answers:
prisoha [69]3 years ago
6 0

The answer is shown above

lord [1]3 years ago
3 0

Answer:

The equivalent equation is

4(2x - 3y +8)=0

Step-by-step explanation:

This problem seeks to test our idea on factorization

Step one :

Given the expression expression

8x - 12y +32

To find an expression equivalent to it we need to look for a common factor of all the terms in the equation

Step two

From inspection the common factor is 4

So pulling 4 out from all the terms we have

Step three

4(2x - 3y +8)=0

which is equivalent to the original equation 8x - 12y +32

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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 <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. 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 <em>n</em> = <em>k</em> + 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
3 years ago
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Ronch [10]

Answer:

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Step-by-step explanation:

Ammount he receives per year times 4.

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= £160

6 0
2 years ago
Three people play a game on each spinner in the previos problem.
arlik [135]

Answer:

Step-by-step explanation:

All other things being equal, spinner A is fine. It is a fair spinner.

Spinner B is not fair. Players 1 and 3 have only 1 number each. Player 2 on the other hand, has 2 numbers that work for him. If player 2 puts in two dollars and players 1 and 3 one dollar each, that should even up the odds. Now you want it just to be fair. So I think player 2 has to put up 2 dollars and players 1 and 3 each put up one. The pot is 4 dollars each time it is played.

Spinner 3 is not fair either. Player one has 2 chances. Player 2 has 3 chances and player 3 has but one chance. There are 6 chances in all. Player 1 should put up 2 dollars to play player 1 should put up 3 dollars and player 1 should put up 1 dollar.

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3 years ago
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Sedaia [141]

Answer:

3b \geq -22

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At least means greater than or equal too.

3b \geq -22

3 0
2 years ago
A lawn mowing service charges customers a flat fee plus an hourly rate for their services. The expression 55x + 15 is used to ca
EastWind [94]

Answer:

JK+7]BBUH ,.H,YT MKY,TFY7YKJKKKKKKKKKJKJKHNJ[KL-L;*

Step-by-step explanation:

JK ITS B

6 0
3 years ago
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