The following equation was correctly simplified:
1 answer:
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Answer:
Option (2)
Step-by-step explanation:
Given question is incomplete; here is the complete question.
Point A is the midpoint of side XZ and point B is the midpoint of side YZ.
Triangle XYZ is cut by line segment AB. Point A is the midpoint of side XZ and point B is the midpoint of side YZ. The length of XY is (5x - 7), the length of AB is (x + 1), and the lengths of XA and ZA are (2x - 2). The lengths of YB and BZ are congruent.
What is AX ?
2 units
4 units
6 units
8 units
From the figure attached,
XYZ is a triangle having A and B as the midpoints of the sides XZ and YZ.
By the theorem of midpoints,
AB =
Since AB = (x + 1) and XY = (5x - 7)
(x + 1) =
2x + 2 = 5x - 7
5x - 2x = 2 + 7
3x = 9
x = 3
Therefore, side AB = 3 + 1 = 4 units
Side XY = (5x - 7)
= 15 - 7
= 8 units
Side XA = 2(x - 1)
= 4 units
Therefore, Option (2) will be the answer.
9514 1404 393
Answer:
y = (5/27)(x -7)^2 -5/3
Step-by-step explanation:
Use the given points to find the unknowns in the equation.
If the axis of symmetry is x=7, then the equation can be written in the form ...
y = a(x -7)^2 +b
Filling in the two point values, we have two equations:
0 = a(4 -7)^2 +b ⇒ 9a +b = 0
5 = a(1 -7)^2 +b ⇒ 36a +b = 5
__
Subtracting the first equation from the second, we have ...
(36a +b) -(9a +b) = (5) -(0)
27a = 5
a = 5/27
Substituting that value into the first equation gives ...
9(5/27) +b = 0
5/3 +b = 0
b = -5/3
So, the quadratic can be written in vertex form as ...
y = (5/27)(x -7)^2 -5/3
