The limit from the left is equal to the value of the function:
.. f(0) = 0
The limit from the right is the value that x^2 approaches as x approaches 0. That is 0^2 = 0.
Left and right limits are the same, so the limit as x approaches zero is 0.
Answer:
1. L1 = 
2. O2 = 
Step-by-step explanation:
Given: x = 
1. To make L1 the subject of formula;
x =
cross multiply to have;
L2 - L1 = xL1(O2 - O1)
collect like terms,
L2 = xL1(O2 - O1) + L1
factorize the right hand side;
L2 = L1[x(O2 - O1)]
L1 =
2. To make O2 the subject of formula;
x =
cross multiply to have;
L2 - L1 = xL1(O2 - O1)
open the bracket to have;
L2 - L1 = xL1O2 - xL1O1
⇒ xL1O2 = L2 - L1 + xL1O1
O2 = 
=
You already have the equation! If you want it in vertex form, do this:
y = x^2 + 8x + 16 - 16 - 51, or y = x^2 + 8x + 16 -67, or
y = (x+4)^2 - 67.
The vertex is at (-4,67).
<h3>
Answer: Choice D) 7.5 cm</h3>
==========================================================
Explanation:
We are told that quadrilateral ABCD is similar to quadrilateral EFGH.
The order of the four letter sequence is important.
- For ABCD, we have AB as the first pair of letters.
- For EFGH, we have EF as the first pair of letters.
Therefore, AB and EF are corresponding sides.
So AB = 10 and EF = x pair up together. We can form the ratio AB/EF which becomes 10/x.
The diagram shows that AD = 8. Notice that A and D are the first and last letters of ABCD. The first and last letters of EFGH are E and H. We can see that AD and EH correspond to one another because of this.
AD = 8 and EH = 6 forming the ratio AD/EH = 8/6
Because the quadrilaterals are similar, the corresponding ratios must be the same. Therefore, AB/EF is the same as AD/EH.
-----------------------
Let's set up a proportion to solve for x
AB/EF = AD/EH
10/x = 8/6
10*6 = x*8
60 = 8x
8x = 60
x = 60/8
x = 7.5 Answer is choice D
Answer:
y - 2 = 1/2(x + 6)
General Formulas and Concepts:
<u>Algebra I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
- x₁ - x coordinate
- y₁ - y coordinate
- m - slope<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
Point (-6, 2)
Slope <em>m</em> = 1/2
<u>Step 2: Find</u>
- Substitute in variables [Point-Slope Form]: y - 2 = 1/2(x - -6)
- Simplify: y - 2 = 1/2(x + 6)
