Recall the inclusion/exclusion principle:
which means
which means
What is the answer to 8x - 6x = -18
2 answers:
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The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x – 11)² – 57.
<h3>What is a quadratic equation?</h3>It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The quadrattic equation is f(x) = 2x² – 44x + 185.
Take common 2 from the equation, we have
Add and subtract 121, we have
And we know that the standard equation
f(x) = a(x - h)² + k
On comparing, we have
The vertex (h, k) is (11, -57).
More about the quadratic equation link is given below.
Answer:
Step-by-step explanation:
Given: The triangle with coordinate A(4,6), B(2,-2) and C(-2,-4). D is the mid point of AB and E is the mid point of AC.
To prove: DE is parallel to BC.
Construction: Join DE.
Proof: If we prove the basic proportionality theorem that is , then it proves that DE is parallel to BC.
Now, Mid Point D has coordinates= and Mid Point E has coordinates=
Now, AD=
DB=
AE=
EC=
Now,
=
Hence,
Thus, By basic proportionality theorem, DE is parallel to BC.