Let $P$ and $Q$ be constants. The graphs of the lines $x + 5y = 7$ and $15x + Py = Q$ are perpendicular and intersect at the point $(-8,3).$ Enter the ordered pair $(P, Q).$

(3, 69)

Step-by-step explanation:

First, let's write our equations with one variable isolated in one side.

for the first one we have:

x + 5y = 7

we can isolate x:

x = 7 - 5*y.

For the other equation we have:

15*x + P*y = Q

here isolating x we get:

x = Q/15 + (P/15)*y

So our equations are:

x = (P/15)*y + Q/15

x = - 5*y + 7

Now, for a line:

x = a*y + b

a perpendicular line would be:

x = -(1/a)*x + c

So we must have that:

(P/15) = -(1/--5) = 1/5

P/3 = 1

P = 3.

Now, this equation needs to pass through the point (-8, 3)

so we have:

3 = (3/15)*-8 + Q/15 = -1.6 + Q/15

3 + 1.6 = Q/15

4.6*15 = Q = 69

Then P = 3 and Q = 69

the ordered pair is (3, 69)

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

step-by-step explanation: