I believe your answer is 6 seconds.
Because the height of the ball = -16(x² - 5x - 6), when the height of the ball is 0, which is when it is on the ground, we can set -16(x² - 5x - 6) equal to 0. This also allows us to divide by -16, and then we can solve the equation:
x² - 5x - 6 = 0
(x - 6)(x + 1) = 0
So x = 6 or x = -1, and because a quantity of time cannot be negative, x would have to be 6, which means it takes 6 seconds for the ball to reach 0 feet.
I hope this helps!
A^2 + B^2 = C^2
6^2 + B^2 = 7^2
36 + B^2 = 49
B^2 = 13
B = 3.61
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The correct question is
<span>
Penelope determined the solutions of the quadratic function by completing the square.f(x) = 4x² + 8x + 1
–1 = 4x² + 8x
–1 = 4(x² + 2x)
–1 + 1 = 4(x² + 2x + 1)
0 = 4(x + 2)²
0 = (x + 2)²
0 = x + 2
–2 = x
What error did Penelope make in her work?
we have that
</span>f(x) = 4x² + 8x + 1
to find the solutions of the quadratic function
let
f(x)=0
4x² + 8x + 1=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(4x² + 8x)=-1
Factor the
leading coefficient
4*(x² + 2x)=-1
Complete the square Remember to balance the equation
by adding the same constants to each side.
4*(x² + 2x+1)=-1+4 --------> ( added 4 to both sides)
Rewrite as perfect squares
4*(x+1)²=3
(x+1)²=3/4--------> (+/-)[x+1]=√3/2
(+)[x+1]=√3/2---> x1=(√3/2)-1----> x1=(√3-2)/2
(-)[x+1]=√3/2----> x2=(-2-√3)/2
therefore
the answer is
<span>
Penelope should have added 4 to both sides instead of adding 1.</span>
80,400 or eighty thousand four hundred
