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suter [353]
3 years ago
11

Describe the transformation from the graph of f(x) =ax^2 to the graph of g(x) = a(x-h)^2+k

Mathematics
1 answer:
MrRa [10]3 years ago
8 0

Answer: Step-by-step explanation:

f(x)=ax^2→g(x)=a(x-h)^2+k

The horizontal shift depends on the value of h. The horizontal shift is described as:  

g(x)=f(x+h) - The graph is shifted to the left h units.

g(x)=f(x−h) - The graph is shifted to the right h units.

Hence, in the question above, Horizontal Shift: Right h Units

The vertical shift depends on the value of k. The vertical shift is described as:

g(x)=f(x)+k - The graph is shifted up k units.

g(x)=f(x)−k - The graph is shifted down k units.

Therefore, in the question above, Vertical Shift: Up k Units

 

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The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $1,020,00
tatyana61 [14]

1. The Year-0 net cash flow is -$1,061,500.

2. The net operating cash flows in Years 1, 2, and 3 are as follows:

Year 1: $288,750 ($386,000 x 1 - 0.25)

Year 2: $288,750 ($386,000 x 1 - 0.25)

Year 3: $288,750 ($386,000 x 1 - 0.25)

3. The additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital) is $468,750 {($599,000 x 1 - 0.25) + $19,500}.

4. The NPV of the project is ($13,139).

5. The machine should not be purchased because it does not yield a positive NPV.

<h3>What is the net present value?</h3>

The net present value (NPV) shows the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

It is determined by calculating the present values of cash flows using their present value factors as below:

<h3>Data and Calculations:</h3>

Initial cash outlay = $1,061,500 ($1,020,000 + $22,000 + $19,500)

Salvage value = $599,000

Increase in net working capital = $19,500

Annual savings before tax = $386,000

Tax rate = 25%

Annuial savings after tax = $288,750 ($386,000 x 1 - 0.25)

<h3>Determination of Net Present Value (NPV):</h3>

Year      Cashflows        PV Factor     Present Value

0          -$1,061,500               1             -$1,061,500

1              $288,750          0.901           $260,164

2             $288,750          0.812          $234,465

3             $288,750          0.731            $211,076

3             $468,750          0.731          $342,656

Net present value                                -$13,139

Thus, the project should not be undertaken by The Campbell Company due to the negative NPV that it yields.

Learn more about determining the NPV at brainly.com/question/18848923

#SPJ1

5 0
2 years ago
Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slop
OLEGan [10]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The line is y  =  -4 x

Step-by-step explanation:

From the question we are told that

The line is y  =  \frac{1}{4} x  + 8

The point is P(0,0 )

Generally the equation for a line is yn =  mx  + c

Now comparing this with the given equation we see that

m  =\frac{1}{4} =  slope

C  =8  =  intercept

Generally the slope of the perpendicular to the given line is mathematically evaluated as

m_1  = -  \frac{1}{m}

=> m_1  = -  \frac{1}{ \frac{1}{4}}

=> m_1  = -4

Generally from the univesal equation of a line and the given point we have that

y = mx + c at p(0,0) and m_1 =  -4 is

0 = -4 (0 ) + c

=> c = 0

Hence the equation perpendicular to the line given at the point given is

y  =  -4 x

8 0
3 years ago
Factor the polynomial completely 6x^2-3x+2
fenix001 [56]

Answer:

can't be factored

answer is D

7 0
2 years ago
Read 2 more answers
Which is the slope of the line that passes through the points (2,10) and (5,8)?
german
It is -3/2, 2/10 - 5/8 = -3/2
6 0
3 years ago
How many solutions does the system of equations have? y=4x-7 and y=4x+2
Alex17521 [72]

Answer:

no solution

Step-by-step explanation:

4x-7=4x+2

-4x +7 -4x +7

0 = 9

0 doesn't equal 9, so there is no solution.

6 0
3 years ago
Read 2 more answers
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