What is the value of x, given that PQ||BC?
1 answer:
Answer:
Option D is correct.
Value of x is, 10 units.
Step-by-step explanation:
Triangle Proportionality theorem states that if a line parallel to one side of a triangle intersects the other two sides of a triangle, then the line divide these two sides proportionality.
Given that:
From the given figure, we have;
AP = 3 units , PB = 6 units , QC = 20 units and AQ = x units.
then, by triangle proportionality theorem;
Substitute the given values, to find the value of x;
By cross multiply we have;
Divide both sides by 6 we get;
10 = x
Therefore, the value of x is, 10 units
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The vertex form of the given quadratic equation is
.
According to the given question.
We have a quadratic equation
Since, for the standard quadratic form is , the vertex form of a quadratic equation is
where (h, k) is the vertex.
And h and k can be calculated as
h = -b/2a and y = k
So, for the given equation the vertex (h, k) is given by
h = -(-8)/2(4) = 8/8 = 1 (X coordinate of vertex)
and,
substitute x = 1 in the above equation for the value of k
Y = 4(1)(1) - 8(1) + 20
⇒ Y = 4 - 8 + 20
⇒ Y = -4 + 20
⇒ Y = 16
so, k = 16 (Y coordinate of vertex)
Now, substitute the value of a, k and h in .
⇒
Therefore, the vertex form of the given quadratic equation is
.
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