Aline segment beginning at point a(−7,−10) and ending at point b(5,8) is drawn on a coordinate plane. point c(−3,−4) is plotted on ab⎯⎯⎯⎯⎯⎯⎯ . point c divides ab⎯⎯⎯⎯⎯⎯⎯ into a ratio of : . (express the ratio in simplest integer form.)

The total x-distance from A to B is 5 - (-7) = 12.

The x-distance from C to A is -3 -(-7) = 4.

Then the x-distance from C to B is 12 - 4 = 8.

The ratio AC : CB is 4 : 8. These ratio values have a common factor of 4, so we can divide by that to get the simplest integer form:

... AC : CB = 1 : 2 . . . . . the ratio into which point C divides the line segment.

If you perform the same math on y-coordinates, you should get the same answer. If you don't, it means that point C is not on the line AB.

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.