Standard form for a parabola:
( x - h )² = 4 p ( y - k )
Vertex: ( h, k ) = ( -4, 2 )
Displacement from vertex to focus:
p = 2/8 = 1/4
( x + 4 )² = 4 · 1/4 ( y - 2 )
y = ( x + 4 )² + 2
or general form:
x² + 8 x - y + 18 = 0
Formula to find perimeter
2(l + w) = perimeter
Input the algebra to the formula, and you'll find x
2(2x + 4 + 3x + 1) = 25
2(5x + 5) = 25
10x + 10 = 25
10x = 15
x = 1.5
Completing the Square
2. Solve the equation by completing the square. Show your work.
x^2 – 30x = –125
Step 1: Add to both sides of the equation. (2 points)
Add 225 both sides of the equation
x^2 – 30x + 225 = –125
+ 225
x^2 - 30x + 225 = 100
Step 2: Factor the left side of the equation. Show your work. (2 points)
Hint: It is a perfect square trinomial.
x^2 - 30x + 225 = 100
Factor the left side of the equation:
(x - 15)^2 = 100
Step 3: Take the square root of both sides of the equation from Step 2. (1 point)
√(x - 15)^2 = √100
Step 4: Simplify the radical and solve for x. Show your work. (1 point)
x - 15 = + - 10
x - 15 = 10
x = 25
x - 15 = -10
x = 5
Solutions x = 25, 5
Answer:
$122.9
Step-by-step explanation:
Given data
Principal= $114
Rate= 3.9%
Time= 2 years
The amount in the account is given as
A=P(1+rt)
substitute
A=114(1+0.039*2)
A=114(1+0.078)
A=114(1.078)
A=$122.9
<span>Reflection in the line y = x. A reflection in the line y = x can be seen in the picture below in which A is reflected to its image A'. The general rule for a reflection in the y-axis: (A, B) (B, A)</span>
