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3 years ago

Solve the system of equations and choose the correct answer from the list of options.

Mathematics

1 answer:

Igoryamba3 years ago

5 0

Answer:

x = -6/5

y = -8/5

Step-by-step explanation:

2x + y = -4

Y = 3x + 2

Substitute the second equation into the first equation

2x + 3x+2 = -4

Combine like terms

5x +2 = -4

Subtract 2 from each side

5x+2-2=-4-2

5x = -6

Divide by 5

5x/5 = -6/5

x = -6/5

Now we need to find y

y = 3x+2

y = 3(-6/5)+2

y = -18/5 + 10/5

y = -8/5

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Reem earns $16 per hour for the first 8 hours of her shift. For each additional hour she works beyond the first 8 hours, she ear

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The single shift worked by Reem is 16 hours long.

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3 years ago

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Use an induction proof to prove this statement:<br> For n≥1, 4^n+5 is divisible by 3.

Tpy6a [65]

Answer:

See below

Step-by-step explanation:

We shall prove that for all $n\in\mathbb{N},3|(4^n+5)$ . This tells us that 3 divides 4^n+5 with a remainder of zero.

If we let $n=1$ , then we have $4^{1}+5=9$ , and evidently, $9|3$ .

Assume that $4^n+5$ is divisible by $3$ for $n=k, k\in\mathbb{N}$ . Then, by this assumption, $3|(4^n+5)\Rightarrow4^k+5=3m,\: m\in\mathbb{Z}$ .

Now, let $n=k+1$ . Then:

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Since $3|(4^k+m)$ , we may conclude, by the axiom of induction, that the property holds for all $n\in\mathbb{N}$ .

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