Answer:
(1, - 2 )
Step-by-step explanation:
Given the equations
9x + 2y = 5 ( subtract 9x from both sides )
2y = 5 - 9x ( divide terms by 2 )
y = 2.5 - 4.5x → (1)
7x - 3y = 13 → (2)
Substitute y = 2.5 - 4.5x into (2)
7x - 3(2.5 - 4.5x) = 13
7x - 7.5 + 13.5 = 13 , that is
7x + 6 = 13 ( subtract 6 from both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Substitute x = 1 into (1) and evaluate for y
y = 2.5 - 4.5(1) = 2.5 - 4.5 = - 2
solution is (1, - 2 )
While the standard quadratic form is a x 2 + b x + c = y , the vertex form of a quadratic equation is y = a ( x − h ) 2 + k .
Answer:
-51
Step-by-step explanation:
-17+2 is -15
2*4 is 8
8-2 is 6
6^2 is 36
-15--36 is 21
Answer:
Solution: Option C
Step-by-step explanation:
Our goal here is to factor the expression such that it is converted into the circle equation (x - a)² + (y - b)² = r² where r = radius centered at point (a,b).
(Factor the expression "x² + 8x")
(Factor the expression "y² - 12y")
That leaves us with the expression , or in other words . As you can see our solution is option c.
Let h(x) = 0.
Set each factor to 0 and solve for x.
-(x - 5) = 0
Disregard the negative sign in front of the parentheses.
x - 5 = 0
x = 5 is a zero.
x - 13 = 0
x = 13 is another zero.
The smaller zero is 5.
The larger zero is 13.
Both numbers make the quadratic function become zero.
Use the FOIL METHOD to express h(x) in standard form.
h(x) = -(x - 5)*x - 13)
After using FOIL, we get -x^2 + 18x - 65.
The square x term has a -1 in front. This number is the value of a in the formula below. The coefficient of x is 18. This is our b value.
x = -b/2a
x = -(18)/2(-1)
x = 18/2
x = 9
This number 9 just found is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, replace every x you see in the quadratic equation above with 9 and simplify.
h(9) = -(9)^2 + 18(9) - 65
h(9) = 16
The vertex is located at the point (9, 16).