Answer:
The vertex is at (-3/2, 33/4)
x=-3/2
Step-by-step explanation:
y= -x^2 -3x+6
Factor out a negative from the first two terms
y = -(x^2 +3x) +6
Complete the square
Take 3 /2 and square it (3/2)^2 = 9/4
The - on the outside of the parentheses means we really are subtracting it so we need to add it on the outside
y = -(x^2 + 3x + 9/4) +9/4 +6
= -(x+3/2)^2 + 9/4 +6
Get a common denominator of 4
= -(x+3/2)^2 + 9/4 +6*4/4
y =- (x+3/2)^2 + 9/4 +24/4
y = -(x+3/2)^2 + 33/4
y = a(x-h)^2 +k where (h,k) is the vertex
y = -(x - -3/2)^2 + 33/4
The vertex is at (-3/2, 33/4)
The axis of symmetry is at the x coordinate of the vertex
x=-3/2
Answer:
(-3,9)
Step-by-step explanation:
Reflections over the x-axis is just multiplying the y-value by -1
Place (3x + 1)/12, and (4x)/15 (Note: the bottom triangle's base is 12 + 3)
Set the two equal to each other
(3x + 1)/12 = (4x)/15
Cross multiply
15(3x +1)/12(12) = 12(4x)/15(15)
15(3x + 1) = 12(4x)
Distribute the 15 to the two terms in the parenthesis, and 12 to 4x
15(3x) = 45x
15(1) = 15
12(4x) = 48x
45x + 15 = 48x
Isolate the variable, subtract 45x from both sides
45x (-45x) + 15 = 48x (-45x)
15 = 48x - 45x
Simplify
15 = 3x
Isolate the x, divide 3 from both sides
15/3 = 3x/3
x = 15/3
x = 5
5 is your answer
hope this helps
Simplifying the expression would be 19.76.
Answer:
x = 11/42
Step-by-step explanation:
2x + 3 = 44x - 8
44x - 2x = 3 + 8
42x = 11
x = 11/42
x = 0.262
