I've been stuck on this problem forever now!
provide reasons for the proof.
given: angle 2=4
and 2 and 3 are supplementary
prove: angle 1=3
statement: reason
1. 2=4 1. given
2. m2=m4 2. angle congruence postulate
3. angles 2 and 3 are supplementary 3. given
4. m2+m3=180 4. definition of supplementary angles
5. angles 1 and 4 are supplementary 5. fill in blank
6. m1+m4=180 6. definition of supplementary angles
7. m1+m4=m2+m3 7. fill in blank
8. m1+m4=m4+m3 8. fill in blank
9. m1=m3 9. fill in blank
10. 1=3 10. fill in blank

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12

a ≈ 172.05

step-by-step explanation:

the pictures.