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Lena [83]
3 years ago
15

Parallel to y=2/3x+6 through (-3, 6)

Mathematics
1 answer:
Lana71 [14]3 years ago
7 0

Answer:

y = (2/3)x + 8

Step-by-step explanation:

Parallel lines have the same slope. In the given equation, the slope is 2/3 so the slope of the parallel line will also be 2/3.

y = (2/3)x + ?

Plug in (-3, 6) for (x, y) in the equation.

6 = (2/3)(-3) + ?

6 = -2 + ?

? = 8

Final equation: y = (2/3)x + 8

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Mary deposits $400 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in the
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$16

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Simple interest is based on the principal amount of a loan or deposit, whereas compound interest is based on the principal amount and the interest that accumulates on it in every period.

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Answer:

A: 6x^2(x^8-16)

B: 6x^2(x^4+4)(x^2+2)(x^2-2)

Step-by-step explanation:

<u>A:</u>

Our expression is 6x^{10}-96x^2. We need to find some common factors. Clearly, we can see that both terms share the x² part, so we can definitely take that out:

6x^{10}-96x^2

x^2(6x^8-96)

Let's see if 96 is divisible by 6:

96 ÷ 6 = 16; since there's no remainder / the remainder is 0, we know 96 is divisible by 6, so we can also factor out 6:

x^2(6x^8-96)

6x^2(x^8-16)

Thus, the answer to part A is 6x^2(x^8-16).

<u>B:</u>

Look at the x^8-16 part of the above factored expression. Notice that it is a difference of squares (because x^8=(x^4)^2 and 16 = 4²), so we can write this as:

x^8-16

(x^4+4)(x^4-4)

Now take a look at the (x^4-4) part. Again, it's a difference of squares because x^4=(x^2)^2 and 4 = 2², so rewrite that as:

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(x^2+2)(x^2-2)

Put it all together:

6x^2(x^4+4)(x^2+2)(x^2-2)

Thus, the answer to part B is 6x^2(x^4+4)(x^2+2)(x^2-2).

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