Answer:
FE = 30°
Step-by-step explanation:
arc FGC = arc FG + arc GB + arc BC
220° = 90° + arc GB + 70° . . substitute known values
60° = arc GB . . . . . . . . . . . . . subtract 160°
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External angle A is half the difference of arcs EG and GB:
30° = (1/2)(arc FE +90° -60°) . . . substitute known values
60° = arc FE + 30° . . . . . . . . . . . multiply by 2 and simplify
30° = arc FE . . . . . . subtract 30°
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The key to this problem is the relationship between external angle A and the measures of the arcs it subtends.
There are infinite solutions to this , so and coordinate with than x value of 2 will lie on x=2
Part A: x = -5/4, 3 || (-5/4, 0) (3, 0)
To find the x-intercepts, we need to know where y is equal to 0. So, we will set the function equal to 0 and solve for x.
4x^2 - 7x - 15 = 0
4 x 15 = 60 || -12 x 5 = 60 || -12 + 5 = -7
4x^2 - 12x + 5x - 15 = 0
4x(x - 3) + 5(x - 3) = 0
(4x + 5)(x - 3) = 0
4x + 5 = 0
x = -5/4
x - 3 = 0
x = 3
Part B: minimum, (7/8, -289/16)
The vertex of the graph will be a minimum. This is because the parabola is positive, meaning that it opens to the top.
To find the coordinates of the parabola, we start with the x-coordinate. The x-coordinate can be found using the equation -b/2a.
b = -7
a = 4
x = -(-7) / 2(4) = 7/8
Now that we know the x-value, we can plug it into the function and solve for the y-value.
y = 4(7/8)^2 - 7(7/8) - 15
y = 4(49/64) - 49/8 - 15
y = 196/64 - 392/64 - 960/64
y = -1156/64 = -289/16 = -18 1/16
Part C:
First, start by graphing the vertex. Then, use the x-intercepts and graph those. At this point we should have three points in a sort of triangle shape. If we did it right, each of the x-values will be an equal distance from the vertex. After we have those points graphed, it is time to draw in the parabola. Knowing that the parabola is positive, we draw in a U shape that passes through each of the three points and opens toward the top of the coordinate grid.
Hope this helps!
No you could have left it as the last but one line or write them separately as
11/18 + √85 / 18 , 11/18 - √85/18
