A student is constructing a triangle with the following dimensions: side length of 10 inches side length of 30 inches Which meas
2 answers:
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Answer:
2) A = (3, 0) and C = (-3, 0)
4) AC = 6 units and OB = 9 units
Step-by-step explanation:
Given functions:
Given points:
- H = (-1, 4)
- T = (4, -1)
As points H and T lie on f(x), substitute the two points into the function to create two equations:
Subtract the first equation from the second to eliminate c:
Therefore m = -1.
Substitute the found value of m and one of the points into the function and solve for c:
Therefore the equation for function f(x) is:
Function f(x) crosses the x-axis at point A. Therefore, f(x) = 0 at point A.
To find the x-value of point A, set f(x) to zero and solve for x:
Therefore, A = (3, 0).
As g(x) = ax² + b, its axis of symmetry is x = 0.
A parabola's axis of symmetry is the midpoint of its x-intercepts.
Therefore, if A = (3, 0) then C = (-3, 0).
<h3><u>Part (3)</u></h3>Points on function g(x):
- A = (3, 0)
- G = (1, -8)
Substitute the points into the given function g(x) to create two equations:
Subtract the second equation from the first to eliminate b:
Therefore a = 1.
Substitute the found value of a and one of the points into the function and solve for b:
Therefore the equation for function g(x) is:
The length AC is the difference between the x-values of points A and C.
Point B is the y-intercept of g(x), so when x = 0:
Therefore, B = (0, -9).
The length OB is the difference between the y-values of the origin and point B.
Therefore, AC = 6 units and OB = 9 units