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3 years ago

2r^2+3s^3-r^2+4t^2-r^2 if r=-2, s=-3, and t=5

Mathematics

1 answer:

dimulka [17.4K]3 years ago

3 0

$2(-2)^2+3(-3)^3-(-2)^2+4(5)^2-(-2)^2 = 19$

19 is the answer.

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Can somebody prove this mathmatical induction?

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Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

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So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

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is true.

Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

So, you have proved the initial statement

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Two families are shopping for a camping trip. The first family buys 3 flashlights and 4 sleeping bags at a cost of $118. The sec

Sliva [168]

Answer:

3x +4y = 118

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Step-by-step explanation:

Let x = the cost of a flashlight

Let y = the cost of a sleeping bag

3x +4y = 118

5x+6y =180

Multiply the first equation by -5

-5(3x +4y) = -5*118

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Multiply the second equation by 3

3(5x+6y) =3*180

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Add the modified equations together.

We are using elimination to eliminate the variable x

-15x -20y = -590

15x + 18y = 540

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-2y = -50

Divide by -2

-2y/-2 = -50/-2

y =25

Each sleeping bag costs $25

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