Abaseball diamond has an angle of 90 degrees at home plate. the manager assigns each of 3 assistant coaches a section of the ball field to monitor during a game. the angle measures of the sections at home plate can be ( 7x - 49); ( 2/3x + 21), and ( 3/4x + 17). what are the angle measures of each of the three sections? explain how you got your answer?

  the three angle measures are 35°, 29°, 26°

Step-by-step explanation:

The sum of the angle measures will be 90°, assuming the sections do not overlap. Then ...

  ( 7x - 49) + ( 2/3x + 21) + ( 3/4x + 17) = 90

  (8 5/12)x -11 = 90 . . . . . simplify

  x = 101/(8 5/12) = 12 . . . divide by the coefficient of x

Then the angles are ...

  7x -49 = 7·12 -49 = 35

  2/3x + 21 = 2/3·12 +21 = 29

  3/4x +17 = 3/4·12 +17 = 26

The angle measures are 35°, 29°, 26°.

Check

  35 +29 +26 = 90 . . . . the sum of the covered section angles is 90°

We assume you can manage addition of fractions and division by a mixed number or improper fraction. If not, convert all of the coefficients of x to multiples of 1/12. Instead of dividing by the coefficient of x, multiply by the inverse of the coefficient of x.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18