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Cerrena [4.2K]
3 years ago
5

Proportions in similar triangles

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
4 0

Answer:

x = 4

Step-by-step explanation:

Given that DE is parallel to AC then DE divides the sides proportionally, so

\frac{BD}{DA} = \frac{BE}{EC} , substitute values

\frac{x+2}{x} = \frac{3}{2} ( cross- multiply )

3x = 2(x + 2) ← distribute

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

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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
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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

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The x intercepts of the function f(x) = 2x(x-5)^2(x+4)^3<br> are…
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Answer:

\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}

Step-by-step explanation:

A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,

\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3

For finding the x intercept , <u>equate the given function with 0, we have ;</u>

\sf \implies 2x ( x - 5 )^2(x+4)^3= 0

Equate each factor with 0 ,

\sf \implies 2x = 0

Divide both sides by 2 ,

\sf \implies\bf x = 0

Again ,

\sf \implies ( x - 5)^2=0

Taking squareroot on both sides,

\sf \implies x - 5 = 0

Add 5 to both sides,

\sf \implies \bf x = 5

Similarly ,

\sf \implies \bf x = -4

<u>Hence</u><u> the</u><u> </u><u>x </u><u>Intercepts</u><u> </u><u>are </u><u>-</u><u>4</u><u> </u><u>,</u><u> </u><u>0</u><u> </u><u>and </u><u>5</u><u> </u><u>.</u>

{ See attachment also for graph } .

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