The base of a triangle is 2 ft. The
2 answers:
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Answer:
The height of the ball is the same after 1.5 seconds and 3.5 seconds. ⇒ (A)
Step-by-step explanation:
<em>The quadratic function is represented by a parabola</em>
- The parabola is symmetric about its vertex.
- The average of the x-coordinates of any opposite points (points have the same y-coordinates) on the parabola is equal to the x-coordinate of its vertex point.
- The axis of symmetry of it passes through the x-coordinate of its vertex point.
- The equation of its axis of symmetry is x = h, where h is the x-coordinate of its vertex point.
∵ The quadratic function modeling the height of a ball over time
∴ f(t) = at² + bt + c
→ t is the time in second, f(t) is the height of the ball after t seconds
∵ It is symmetric about the line t = 2.5
∴ The x-coordinate of its vertex is 2.5
→ That means the average of the x-coordinates of any two
opposite points belong to f(t) is 2.5
∵ The average of 1.5 and 3.5 =
∴ 1.5 and 3.5 have the same value of f(t)
∴ 1.5 and 3.5 have the same height
The height of the ball is the same after 1.5 seconds and 3.5 seconds.
The equation of line perpendicular to line containing points (-3, 4) and (1, 0) and passes through (-2, 6) in point slope form is y = x + 8
<h3><u>Solution:</u></h3>Given that line m contains points (-3, 4) and (1, 0)
We are asked to find the equation of line perpendicular to line containing points (-3, 4) and (1, 0) and passes through (-2, 6)
<em><u>Let us first find slope of the line "m"</u></em>
Given two points are (-3, 4) and (1, 0)
Thus slope of line m is -1
We know that <em>product of slope of given line and perpendicular line are always -1</em>
So, we get
So we have got the slope of perpendicular line is 1 and it passes through (-2, 6)
Let us use the point slope form to find the required equation
<em><u>The point slope form is given as:</u></em>
and m = 1
y - 6 = 1(x - (-2))
y - 6 = x + 2
y = x + 8
Thus equation of required line in point slope form is y = x + 8