In this diagram we see that 80 and 3x+4y are both vertical angles and vertical angles are congruent or always equal so we can set those two equations equal to each other then we can see that a line splits two angles making them supplementary (they equal 180 degrees) So we can have another equation, the two equations are:

3x+4y=80 and 3x+4y+7x-8y=180 (add like terms to simplify and get 10x-4y=180

Then use elimination to get rid of the y variables

10x-4y=180 (plus)

+3x+4y=80 (the negative 4 and positive 4 cancels each other out so you are left with:)

13x=160 (divide by x)

x=12.30769 which can be rounded to x=12.31

Then we have to plug in x into the first equation:

3(12.31) + 4y = 80

36.93 + 4y = 80 (subtract 36.93 from 80)

4y = 43.07 (divide)

y=10.7675 or rounded to 10.77

so x=12.31 and y=10.77

5 0

3 years ago

Solve the proportion: 20/16 = x/80 question 19 options: 6.25 1600 100 160

Aloiza [94]

$\dfrac{20}{16}=\dfrac{20:4}{16:4}=\dfrac{5}{4}\\\\\dfrac{5}{4}=\dfrac{x}{80}\ \ \ \ |cross\ multiply\\\\4x=5\cdot80\\\\4x=400\ \ \ \ |divide\ both\ sides\ by\ 4\\\\\boxed{x=100}$

8 0

3 years ago