In the graph, rectangle BCDE is rotated to form rectangle B’C’D’E’. Use the diagram to complete the statement.
2 answers:
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First we need to convert the given equation to standard form, only then we can find the center and radius of the circle.
![x^{2} + y^{2} +18x+14y+105=0 \\ \\ x^{2} +18x+ y^{2}+14y=-105 \\ \\ x^{2} +2(x)(9)+ y^{2}+2(y)(7)=-105 \\ \\ x^{2} +2(x)(9)+ 9^{2} + [y^{2}+2(y)(7)+7^{2}] =-105+9^{2}+7^{2} \\ \\ (x+9)^{2}+ (y+7)^{2}=25 ](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2B%20y%5E%7B2%7D%20%2B18x%2B14y%2B105%3D0%20%5C%5C%20%20%5C%5C%20%0A%20x%5E%7B2%7D%20%2B18x%2B%20y%5E%7B2%7D%2B14y%3D-105%20%5C%5C%20%20%5C%5C%20%0A%20x%5E%7B2%7D%20%2B2%28x%29%289%29%2B%20y%5E%7B2%7D%2B2%28y%29%287%29%3D-105%20%5C%5C%20%20%5C%5C%20%0Ax%5E%7B2%7D%20%2B2%28x%29%289%29%2B%209%5E%7B2%7D%20%2B%20%5By%5E%7B2%7D%2B2%28y%29%287%29%2B7%5E%7B2%7D%5D%20%20%3D-105%2B9%5E%7B2%7D%2B7%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%0A%20%28x%2B9%29%5E%7B2%7D%2B%20%28y%2B7%29%5E%7B2%7D%3D25%20%20%0A%20%20)
The standard equation of circle is:
with center (a,b) and radius = r
Comparing our equation to above equation, we can write
Center of circle is (-9, -7) and radius of the given circle is 5
The standard equation of circle is:
with center (a,b) and radius = r
Comparing our equation to above equation, we can write
Center of circle is (-9, -7) and radius of the given circle is 5
Answer:
C
Step-by-step explanation:
Given
2x² + x - 1 = 2 ( subtract 2 from both sides )
2x² + x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 3 = - 6 and sum = + 1
The factors are - 2 and + 3
Use these factors to split the x- term
2x² - 2x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(2x + 3) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = -
Answer:
He is 20 at oldest, or
Step-by-step explanation:
The first step in finding a possible age is:
Subtract 10 from 51, and you get 41. Divide by 2, and you get about 20.5.
This means Joe is younger than or 20 years old.