What is the value of x, y, and z? (picture included)

16. x = 18

17. y = 7.5

18. z = 7

Step-by-step explanation:

16. Same-side interior angles are supplementary, so add to give 180°.

... (8x-7) + (3x-11) = 180

... 11x = 198 . . . . . . . . . . collect terms, add 18

... x = 18 . . . . . . . . . . . . divide by 11

17. Alternate interior angles are equal.

... (2y+23) = (4y+8)

... 15 = 2y . . . . . . . . . add -2y-8

... 7.5 = y . . . . . . . . . . divide by 2

18. Same-side interior angles are supplementary, or linear angles are supplementary. Either way, ...

... (3z² -5) + 38 = 180 . . . . . . . . we know 2y+23 = 2·7.5+23 = 38 from 17.

... 3z² = 147 . . . . . . . . . . . . . . . . subtract 33

... z² = 49 . . . . . . . . . . . . . . . . . . divide by 3

... z = 7 . . . . . . . . . . . . . . . . . . . . take the positive square root

answer: standard form is ax^2 + bx + c = 0

step-by-step explanation:

standard form is ax^2 + bx + c = 0

(2x + 1)(x - 2) = 0

distribute to get into standard form

2x^2 - 4x + x - 2 = 0

2x^2 - 3x - 2 = 0

a = 2, b= -3, c = -2

a is your answer