Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
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<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
Answer:
21
Step-by-step explanation:
Given the following expressions
f(x) = x³-2x
g(x) =-x-2
We are to find (fog)(-5)
fog = f(g(x))
f(g(x)) = f(-x-2)
Replace x with -x-2 in f(x)
f(-x-2) = (-x-2)³-2(-x-2)
f(-x-2) = (-x-2)³+2x+4
fog = (-x-2)³+2x+4
Substitute x = -5 into the result
fog(-5) = (-x-2)³+2x+4
fog(-5) = (-(-5)-2)³+2(-5)+4
fog(-5) = (5-2)³-10+4
fog(-5) = 3³-6
fog(-5) = 27-6
fog(-5) = 21
Hence the required result of the composite function is 21
Answer:
at least $1,050,000
Step-by-step explanation:
Deandre's salary will be ...
12000 + 0.06·sales
He wants that to be at least 75000, so the sales must meet the requirement ...
12000 + 0.06·sales ≥ 75000
0.06·sales ≥ 63000 . . . . . . . . . . . . subtract 12000
sales ≥ 63000/0.06 . . . . . . . . . . . .divide by 0.06
sales ≥ 1,050,000 . . . . . . . . . . . . . .evaluate
He will need to have at least $1,050,000 in total sales to have a yearly income at least $75,000.
One solution- if the graphs of the equations intersect, then there is one solution that is true for both solutions.
No solutions- If the graphs of the equation do not intersect (example-if they are parallel) there are no solutions that there are true for both equations.
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I think it is 96 but I could be wrong
