Answer:
a b c d e f
Step-by-step explanation:
Answer:
t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Step-by-step explanation:
To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.
h(t) = -16t² + 96t
= -16(t² - 6t)
= -16(t² - 6t + 9) - (-16) * 9
= -16(t - 3)² + 144
Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".
Answer:
Mixed number - 2 8/15
decimal - 2.53
Step-by-step explanation:
3+9+26=38
denominator is 15
38/15 convert to a mixed number =
2 8/15 as a decimal is 2.53
Answer:
3/4
Step-by-step explanation:
In the above equation the y-intercept is -1 and the slope of the equation is 3/4
Answers:
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Explanation:
Part (a)
Lines LN and PN have the point N in common. This is the intersection point.
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Part (b)
To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.
I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.
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Part (c)
Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K
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Part (d)
Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.
We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.
Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.
