Answer:
x
=
2
±
√
7
Explanation:
there are no whole numbers which multiply to - 3
and sum to - 4
we can solve using the method of
completing the square
the coefficient of the
x
2
term is 1
∙
add subtract
(
1
2
coefficient of the x-term
)
2 to
x2
−
4
x
⇒
x
2
+2(−
2
)
x
+
4
−
4
−
3
=
0
⇒
(
x
−
2
)2
−
7
=0
⇒
(
x
−
2
)
2
=
7
take the square root of both sides
⇒
x
−
2
=
±
√
7
←
note plus or minus
⇒
x
=
2
±
√
7←
exact solutions
I<span>f an inch would fit 12 characters and 1 yard has 36 inches. then, a yard would fit 432 characters.
</span>
Answer:
b
Step-by-step explanation:
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Angle 4 and Angle 2 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 2 is 127 degrees.
Angle 4 and Angle 3 are a linear pair, meaning that they are supplementary and add up to 180 degrees. Therefore, the measure of angle 3 is 53 degrees.
Angle 3 and Angle 1 are vertical angles, meaning that they are congruent. Therefore, the measure of angle 1 is 53 degrees.
Hope this helps!
Answer: maximum height of the football = 176 feet
Step-by-step explanation:
We want to determine the maximum height of the football from the ground. From the function given,
h(t) = -16t^2+96t +32, it is a quadratic function. Plotting graph if h will result to a parabolic shape. The maximum height of the football = the vertex of the parabola. This vertex is located at time, t
t = -b/2a
b = 96 and a= -16
t = -b/2a = -96/2×-16= 3
Substituting t = 3 into the function if h
h(t) = -16×3^2+96×3 +32
=-16×9 + 96×3 +32
= -144+ 288+32
=176 feet