What is the solution set of x2 + y2 = 26 and x − y = 6? A. {(5, -1), (-5, 1)} B. {(1, 5), (5, 1)} C. {(-1, 5), (1, -5)} D. {(5,
Rus_ich [418]
He two equations given are
x^2 + y^2 = 26
And
x - y = 6
x = y +6
Putting the value of x from the second equation to the first equation, we get
x^2 + y^2 = 26
(y + 6) ^2 + y^2 = 26
y^2 + 12y + 36 + y^2 = 26
2y^2 + 12y + 36 - 26 = 0
2y^2 + 12y + 10 = 0
y^2 + 6y + 5 = 0
y^2 + y + 5y + 5 = 0
y(y + 1) + 5 ( y + 1) = 0
(y + 1)(y + 5) = 0
Then
y + 1 = 0
y = -1
so x - y = 6
x + 1 = 6
x = 5
Or
y + 5 = 0
y = - 5
Again x = 1
So the solutions would be (-1, 5), (1 , -5). The correct option is option "C".
<span>Absolute value of -98 is 98
Hope I helped:D </span>
Answer:
vertex = (- 10, - 10 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
h(x) = x² + 20x + 90
add/subtract ( half the coefficient of the x- term )²
h(x) = x² + 2(10)x + 100 - 100 + 90
= (x + 10)² - 10 ← in vertex form
with (h, k ) = (- 10, - 10 )
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Step-by-step explanation:
In the right triangle, one of the angles has measure 60 deg, so the remaining angle has measure 30 deg. In such a 30-60-90 triangle, the sides occur in a ratio of 1 to 
to 2 (shorter leg to longer leg to hypotenuse). This means
making the answer C.
