X = 4y
3x - y = 70
substitute the x in the second equation with the other half of the first equation.
3(4y) - y = 70
12y - y = 70
11y = 70
y = 6.36 repeating, or 6 4/11
now use this to solve first equation
x = 4 (6 4/11)
x = 25.45 repeating
done
X= 0.09629120 ..., —2.59629120...
The domain of f(x) = -6x^2 - 10x + 13 is all real values.
For the range f(x) = -6x^2 - 10x + 13 written in vertex form is -6(x^2 + 5/3x - 13/6) = -6(x^2 + 5/3x + 25/36 - 13/6 - 25/36) = -6(x + 5/6)^2 - 6(-103/36) = -6(x + 5/6)^2 + 103/6
Range is all real values less than or equal to 103/6
We want to get k separated in order to solve for it.
first, we can add 8j to both sides. this gives us m + 8j = -9k + 9
second, we can subtract 9 from both sides. this gives us m + 8j - 9 = -9k
our last step is to divide both sides by -9. so we get (m + 8j - 9)/-9 = k
A] Vertex form
Vertex form is given by:
y=(x-h)²+h0
where:
(h,k) is the vertex
Given that:
f(x)=x²-6x+13
The vertex will be evaluated as follows:
c=(b/2a)²
b=-6
thus
c=(-6/2*1)²=9
hence adding and subtracting 9 in the expression we get:
f(x)=x²-6x+9-9+13
f(x)=x²-6x+9+4
writing the above in vertex form we get
f(x)=(x-3)²+4
b] The minimum value of f(x) is at it's vertex. Thus from the function
f(x)=(x-3)²+4
the vertex is at (3,4)
hence the minimum value is at (3,4)
