Answer:
Length of the room is 180 ft
Step-by-step explanation:
We have a rectangular room with dimensions:
width = 70 ft and length "x" (unknown)
Perimeter of a rectangle is 2*w + 2*x and according to problem statement 500 ft of lights will fit exactly in room perimeter then:
2*70 + 2*x = 500
140 + 2*x = 500
2*x = 500 - 140
2*x = 360
x = 360/2
x = 180 ft
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Answer: 8 and 9
Step-by-step explanation: 8*8=64 and 9*9=81
<h3>Given</h3>
Two positive integers x and y
x - y = 4
x² + y = 68
<h3>Find</h3>
x and y
<h3>Solution</h3>
Add the two equations together.
... (x - y) + (x² + y) = (4) + (68)
... x² + x = 72
Rearrange to standard form and factor.
... x² + x - 72 = 0
... (x + 9)(x - 8) = 0
Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.
... x + 9 = 0 ⇒ x = -9
... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution
Then we can find y from
... 8 - y = 4
... y = 4 . . . . . . . add y-4 to the equation
The two positive integers are 8 and 4.
