You can write two equations using the given information:
.. L = W +8
.. L * W = 609
Using substitution, you get a quadratic.
.. (W +8) * W = 609
.. W^2 +8W -609 = 0
Not surprisingly, you're looking for factors of 609 that differ by 8.
.. 609 = 1*609 = 3*203 = 7*87 = 21*29
The last two are the factors of interest.
.. (W +29)(W -21) = 0
The width of the rectangle is 21 feet, the length is 29 feet.
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Sometimes it is easier to work with the average dimension. Here, let that be x. Then you have
.. (x +4)(x -4) = 609
.. x^2 -16 = 609
.. x^2 = 625 = 25^2 . . . . . . . one of your memorized math facts
So, the dimensions are
.. 25 +4 = 29 by 25 -4 = 21, that is, 29 ft by 21 ft.
Answer:
Pretty sure is 90 degrees
Step-by-step explanation:
Answer:
yes it is a function it passes the vertical line test
Answer:
A.32
Step-by-step explanation:
To find the quadratic of the form ax^2+bx+c=y set up a system of equations with the points provided...
a+b+c=4, 0a+0b+c=3, a-b+c=-6 getting differences:
a+b=1, -a+b=9 and getting difference again:
2a=-8, so a=-4, making a+b=1 become:
-4+b=1, so b=5, making a+b+c=4 become:
-4+5+c=4, so c=3
thus the quadratic that produces those three points is:
y=-4x^2+5x+3
...
The vertex occurs when the velocity is equal to zero, the derivative of the quadratic...
dy/dx=-8x+5, dy/dx=0 when x=5/8=0.625
Then you can find y(5/8)=4.5625
So the vertex is (0.625, 4.5625)
Or you may wish to remember that the vertex will always be:
(-b/(2a), (4ac-b^2)/(4a)) (this can be derived from conservation of energy under constant acceleration or the vertex form of the quadratic)
The axis of symmetry will be the vertical line about the x-coordinate of the vertex, in this case:
x=0.625
