If triangle pqr is an equilateral triangle, solve x and y.

pq is 14y-59
qr is 9y+1
rp is 11y-23
angle r is 7x-3

20 points

x = 9 and y = 15

Step-by-step explanation:

An  equilateral triangle, all sides and angles are congruent and each angle is equal 60 degrees

PQR is an equilateral triangle

So

PQ = QR = RP

Given:

PQ is 14y-59

QR is 9y+1

RP is 11y-23

Angle R is 7x-3

PQ = QR

Plug in

14y-59  = 9y+1

5y = 60

 y = 15

Angle R is 7x-3, also <R = 60

So

7x - 3 = 60

7x = 63

 x = 9

Answer

x = 9 and y = 15

x= 9 and y= 12

Step-by-step explanation:

Given : Triangle PQR is an equilateral triangle.

PQ is 14y-59

QR is 9y+1

RP is 11y-23

Angle R is 7x-3                 (1)

We know that , In an equilateral triangle

All sides are equal.

⇒ PQ = QR

⇒  14y-59 = 9y+1

⇒ 14y-9y =1+59  [Subtract 9y and add 59 on both sides]

⇒ 5y=60

⇒ y= 12    [Divide both sides by 5]

All angle angles of equilateral triangle are equal and have measure 60° .

⇒ Angle R =  60°

⇒  7x-3=  60      [From (1)]

⇒ 7x= 63  [Add 3 on both sides]

⇒ x= 9  [Divide both sides by 7]

Hence, the value of x= 9 and y= 12.

the correct answer is the second option

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!