In QRS, mQ= 8x-17,mR=19x+4,and mS=5x+1. Classify QRS by its angles and sides

Option (3) and Option (5)

Step-by-step explanation:

By the property of a triangle,

Sum of interior angles of a triangle is 180°.

m∠Q + m∠R + m∠S = 180°

By substituting the measures of angles in the equation,

(8x - 17)° + (19x + 4)° + (5x + 1)° = 180°

32x - 12 = 180

32x = 192

x = 6

m∠Q = (8x - 17)° = 48 - 17

                          = 31°

m∠R = (19x + 4)° = 114 + 4

                           = 118°

m∠S = (5x + 1) = 30 + 1

                       = 31°

Since, one interior angle measures 118° which is grater than 90°.

Therefore, triangle QRS is an obtuse triangle.

Since, m∠Q = m∠R = 31°

It's an isosceles triangle.

Option (3) and Option (5) are the correct options.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

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