Answer:
LHS = RHS
Step-by-step explanation:

Since

Therefore,

Therefore LHS = RHS
The value of x and y in the given equation is determined -1 and -2 respectively.
<h3>
Value of x and y</h3>
The value of x and y can be determined by solving the two equations simultaneously.
y = -2x - 4 ----- (1)
y = 4x + 2 ----- (2)
solve (1) and (2) together
-2x - 4 = 4x + 2
-6x = 6
x = -1
y = 4(-1) + 2
y = -4 + 2
y = -2
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Do you understand trigonometry ? (sine, cosine, tangent)
Answers:
- Vertex form: y = -2(x-1)^2 + 8
- Standard form: y = -2x^2 + 4x + 6
Pick whichever form you prefer.
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Explanation:
The vertex is the highest point in this case, which is located at (1,8).
In general, the vertex is (h,k). So we have h = 1 and k = 8.
One root of this parabola is (-1,0). So we'll plug x = -1 and y = 0 in as well. As an alternative, you can go for (x,y) = (3,0) instead.
Plug those four values mentioned into the equation below. Solve for 'a'.
y = a(x-h)^2 + k
0 = a(-1-1)^2+8
0 = a(-2)^2+8
0 = 4a+8
4a+8 = 0
4a = -8
a = -8/4
a = -2
The vertex form of this parabola is y = -2(x-1)^2+8
Expanding that out gets us the following
y = -2(x-1)^2+8
y = -2(x^2-2x+1)+8
y = -2x^2+4x-2+8
y = -2x^2+4x+6 .... equation in standard form
Answer:
0.9783 = 97.83% probability that a can that gets shipped for use will be of perfect shape
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Shipped for use
Event B: Perfect shape
Probability of being shipped for use:
Perfect shape(0.9 probability) or unnoticeable dent(0.02 probability). So

Being shipped for use and being in perfect shape.
0.9 probability, so 
What is the probability that a can that gets shipped for use will be of perfect shape?

0.9783 = 97.83% probability that a can that gets shipped for use will be of perfect shape