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3 years ago

Find the value of y. 4 5 7 2

Mathematics

1 answer:

Debora [2.8K]3 years ago

4 0

Angles (7x+17)° and (5x-5)° are consecutive interior angles, that means they add up to 180°.
So we can make an equation to solve for x, which eventually will help us solve for y.
180 = (7x+17) + (5x -5)

re arrange that:
180 = 7x + 5x + 17 - 5

180 = 12x + 12
- 12 -12

168 = 12 x
 12 12

14 = x

Now we will plug it into (5x - 5) to help us solve for y,
Angle (5x - 5) and (23y) are supplementary angles, meaning they equal to 180°.
 180 = (23y) + (5(14) - 5)

180 = (23y) + (70 - 5)

180 = 23y + 65
- 65 - 65

115 = 23y
23 23

___ = y

Good luck!

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Read 2 more answers

You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod

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Answer:

a. $y=830*(0.87)^x$

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

$13\%=\frac{13}{100}=0.13$

Upon substituting our given values in exponential decay function we will get

$y=830*(1-0.13)^x$

$y=830*(0.87)^x$

Therefore, the exponential model $y=830*(0.87)^x$ represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

$y=830*(0.87)^2$

$y=830*0.7569$

$y=628.227\approx 628.23$

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be $\frac{830}{2}=415$ .

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

$415=830*(0.87)^x$

Upon dividing both sides of our equation by 830 we will get,

$\frac{415}{830}=\frac{830*(0.87)^x}{830}$

$0.5=0.87^x$

Let us take natural log of both sides of our equation.

$ln(0.5)=ln(0.87^x)$

Using natural log property $ln(a^b)=b*ln(a)$ we will get,

$ln(0.5)=x*ln(0.87)$

$\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}$

$\frac{ln(0.5)}{ln(0.87)}=x$

$\frac{-0.6931471805599}{-0.139262067}=x$

$x=4.977286\approx 4.98$

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

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