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2 years ago

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Piper works at a camera store. He is paid an hourly rate 16% commission on everything he sells. One week, he is paid $365 for wo

rking 20 hours and selling $1500 worth of camera equipment. What is his hourly rate?

1 answer:

liraira [26]2 years ago

3 0

P=rt+0.16s

365=20r+0.16(1500)

365=20r+240

125=20r

r=6.25

So Piper makes $6.25 an hour.

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Through(-2,-3); parallel to 3x+2y=5

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Step-by-step explanation:

Hey there!

<u>Firstly </u><u>find </u><u>slope </u><u>of</u><u> the</u><u> </u><u>given</u><u> equation</u><u>.</u>

Given eqaution is: 3x + 2y = 5.......(i)

Now;

$slope(m1) = \frac{ - coeff. \: of \: x}{coeff. \: of \: y}$

$or \: m1 = \frac{ - 3}{2}$

Therefore, slope (m1) = -3/2.

As per the condition of parallel lines,

Slope of the 1st eqaution (m1) = Slope of the 2nd eqaution (m2) = -3/2.

The point is; (-2,-3). From the above solution we know that the slope is (-3/2). So, the eqaution of a line which passes through the point (-2,-3) is;

(y-y1) = m2 (x-x1)

~ Keep all values.

$(y + 3) = \frac{ - 3}{2} (x + 2)$

~ Simplify it.

$2(y + 3) = - 3x - 6$

$2y + 6 = - 3x - 6$

$3x + 2y + 12 = 0$

Therefore, the eqaution of the line which passes through the point (-2,-3) and parallel to 3x + 2y= 5 is 3x + 2y +12 =0.

<em><u>Hope </u></em><em><u>it</u></em><em><u> helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

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Answer:

$x = 7$

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

$\frac{1}{ {27}^{x - 8} } = 27$

2) Multiply both sides by 27^x - 8.

$1 = {27} \times 27^{1 + x - 8}$

3) Use the product rule: x^a x^b = x^a+b.

$1 = {27}^{1 + x - 8}$

4) Simplify 1 + x - 8 to x - 7.

$1 = {27}^{x - 7}$

5) Use Definition of Common Logarithm: b^a = x if and only if log<u>b</u><u> </u>(x) = a.

$log_{27}1 = x - 7$

6) Use Change of Base Rule.

$\frac{ log_1 }{ log{27} } = x - 7$

7) Use rule of 1: log 1 = 0.

$\frac{0}{ log_{27}} = x - 7$

8) Simplify 0/log_27 to 0.

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9) Add 7 to both sides.

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<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>7</u><u>.</u>

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