Answer: Let length = 2x + 3
Let width = x
Area = 54 ft2
length × width = Area
x(2x + 3) = 54
2x2 + 3x = 54
2x2 + 3x - 54 = 0
(2x - 9)(x + 6) = 0
x = 9/2 and x = -6
x = 4.5 and x = -6
We accept x = 4.5 because length cannot be a negative value. Substituting this value into the dimensions:
width = 4.5 ft
length = 2(4.5) + 3 = 9 + 3 = 12 ft
Step-by-step explanation:
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Answer:
A) -4
B) 4 units apart
C) no values of x
Step-by-step explanation:
1) slope of m: (3-2)/(10-8) = ½
m(x) = ½x + c
2 = ½(8) + c
c = -2
m(x) = ½x - 2
m(16) = 6
h(4) = (4-2)²/2 = 4/2 = 2
h(4)-m(16) = 2-6 = -4
B) y-intercept of:
*h(x) = ½(0-2)² = 2
*m(x) = -2
from the equation found before
2 - (-2) = 4 units apart
C) m(x) = (x-4)/2
m(x) > h(x)
(x-4)/2 > ½(x-2)²
x-4 > x²-4x+4
x²-5x+8 < 0
(x - 2.5)² + 1.75 < 0
Never negative
The answer would be the first one.
