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2 years ago

7

Side XY of triangle XYZ is extended to point W, creating a linear pair with ∠WYZ and ∠XYZ.

1 answer:

Vedmedyk [2.9K]2 years ago

7 0

Answer:

$x= 80^o$

Step-by-step explanation:

Given

$\angle Z = 36^o$

$\angle WYZ = 100^o$

Required

Find x

$\angle WYZ$ and x are on a straight line.

So:

$\angle WYZ + x= 180^o$

Make x the subject

$x= 180^o -\angle WYZ$

Substitute known value

$x= 180^o -100^o$

$x= 80^o$

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3 years ago

Helppop!!A car and van are driving on a highway. The table shows the amount y (in gallons) of gas in the cars gas tank after dri

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Answer:

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Step-by-step explanation:

Given

The table represents the car mileage

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First, calculate the car's slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

From the table, we have:

$(x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)$

So, we have:

$m = \frac{10.5 - 13.5}{180 - 60}$

$m = \frac{-3}{120}$

$m = -\frac{1}{40}$

Calculate the equation using:

$y = -\frac{1}{40}(x - 60)+13.5$

$y = -\frac{1}{40}x + 1.5+13.5$

$y = -\frac{1}{40}x + 15$

$m = -\frac{1}{40}$ implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

$y = -\frac{1}{5}x + 31$ --- The van

By comparison to: $y = mx + b$

$m = -\frac{1}{5}$

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

$1/40 < 1/5$

This means that the car uses less gas

Solving (b): Distance traveled for them to use the same amount of gas.

We have:

$y = -\frac{1}{5}x + 31$ --- The van

$y = -\frac{1}{40}x + 15$ --- The car

Equate both

$-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15$

Collect like terms

$\frac{1}{40}x -\frac{1}{5}x =-31 + 15$

$\frac{1}{40}x -\frac{1}{5}x =-16$

Take LCM

$\frac{x - 8x}{40} = -16$

$\frac{- 7x}{40} = -16$

Solve for -7x

$-7x = -640$

Solve for x

$x = \frac{640}{7}$

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