What is the equation of the line that passes through (-2,2) and (1,-4)?

Mathematics

1 answer:

adelina 88 [10]3 years ago

6 0

Answer:

y=-2x-2

Step-by-step explanation:

Slope: -4-2/1-(-2)=-6/3=-2

Equation: y=-2x+b

Substitute: 2=-2(-2)+b

2=4+b

b=-2

Therefore, y=-2x-2

I hope this helped and have a good rest of your day!

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Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).

irinina [24]

$3^{x} = 4^{y} = 12^{z}$
$3^{x} = 4^{y} = (4 \cdot 3)^{z}$
$3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$

$\text{Let a } = 3^{x} = 4^{y} = 4^{z} \cdot 3^{z}$
$log_3a = x$
$log_4a = y$
$log_{(4 \cdot 3)}a = z$

Using change of base:
$x = \frac{lna}{ln3}$
$y = \frac{lna}{ln4}$
$z = \frac{lna}{ln(4 \cdot 3)}$

$ln3 = \frac{lna}{x}$
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Now, ln(4 · 3) = ln(4) + ln(3)

$\frac{lna}{z} = \frac{lna}{x} + \frac{lna}{y}$
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8 0

4 years ago

mrs xu lives 10.7 miles away from her place of work. she drives to work and back six days a week. how many miles does she travel

rewona [7]

Answer:

128.4 Miles

Step-by-step explanation:

She goes to work and goes 10.7 miles, and then goes back home aswell which is also 10.7 miles. So total miles in one day = 10.7 + 10.7 = 21.4 miles in one day.

so 1 week = 21.4 x 6

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we times it by 6 because she works 6 days a week only.

hope it helped :)

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3 years ago

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Answer:

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