Use the relationship between the angles in the figure to answer the question.

Which equation can be used to find the value of x?

Answer:

Simplified: -4a²b²+18a³-2b³

3a(6a²-4ab²)+8a²b²-2b³

Multiply 3a by 6a² and-4ab²

18a³-12a²b²+8a²b²-2b³

combine like terms (-12a²b² and 8a²b²)

-4a²b²+18a³-2b³

Hope this helps

Step-by-step explanation:

Here we have to simplify the polynomial :

[tex] \\ \longrightarrow \sf \qquad3a(6a^2-4ab^2)+8a^2b^2-2b^3\\ \\[/tex]

Using Distributive property we get :

[tex]\longrightarrow \sf \qquad18a^3- {12}^{2} b^2+8a^2b^2-2b^3\\ \\[/tex]

Combining the like terms we get :

[tex]\longrightarrow \sf \qquad18a^3-4a^2b^2-2b^3\\ \\[/tex]

Therefore,

Answer: 75 degrees

Step-by-step explanation:

Answer:

1. The cost of equity can be derived from the share price, which is the present value of the expected dividend one year from now(using the present value of growing perpetuity) as shown below:

share price=D1/(r-g)

share price=$500

D1=expected dividend one year from now=$4

r=cost of equity=unknown

g=constant growth rate=9%

$500=$4/(r-9%)

$500*(r-9%)=$4

r-9%=$4/$500

r=($4/$500)+9%

r=9.8

the Cost of Equity for the project is 9.8%

2. Compute the relevant cost of debt for this project is 5.53%

Market Value= 1,150

Face Value= 1,000

Term= 5 years, 10 semi-annual periods

Coupon Rate= 9%, 4.5% semi-annual rate

Tax Rate= 30%

N=10(semiannual coupons in 5 years)

PMT=45(semiannual coupon=face value*coupon rate/2=$1000*9%/2=$45)

PV=-1150(current market price)

FV=1000(face value of the bond is $1,000)

CPT(press compute)

I/Y=2.762766%(semiannual yield)

annual yield=2.762766%*2

annual yield=5.53%

3. The weighted average cost of capital is the sum of equity and the after-tax cost of debt multiplied by their respective market value weights

WACC=(cost of equity*weight of equity)+(after-tax cost of debt*weight of debt)

cost of equity=9.80%

the market value of equity raised=shares issued*market price of the share

the market value of equity raised=80,000*$500

the market value of equity raised=$40 million

weight of equity=market value of equity/total amount raised

weight of equity=$40 million/$100 million

weight of equity=40.00%

weight of debt=1-weight of equity

weight of debt=1-40.00%

weight of debt=60.00%

after-tax cost of debt=bond yield*(1-tax rate)

the after-tax cost of debt=5.53%*(1-30% )

the after-tax cost of debt=3.87%

WACC=(9.80%*40.00%)+(3.87%*60.00%)

WACC= 6.2426% or 6.24%

Therefore the WACC is 6.2426% or 6.24% rounded off to 2decimal place

4. Determine the initial cash flow for the project =$100 million

The initial cash outlay is the sum of the plant and machinery and net working capital investment required to commence the project

Plant and machinery= $80 million

Networking capital = $20 million

Total Initial Cash Flow= $100 million

5. Determine the earnings before taxes for years 1 through 5

Year

1 2 3 4 5

Revenue

120,000,000 120,000,000 120,000,000 120,000,000 120,000,000

Expenses

(80,000,000) (80,000,000) (80,000,000) (80,000,000) (80,000,000)

Depreciation (20,000,000) (15,000,000) (11,250,000) (8,437,500) (6,328,125)

EBT

20,000,000 25,000,000 28,750,000 31,562,500 33,671,875

Step-by-step explanation:

5. Depreciation schedule:

Year 1 = 80 × 25% = 20

Year 2 = (80-20) × 25% = 15

Year 3 = (80-20-15) × 25% = 11.25

Year 4 = (80-20-15-11.25) × 25% = 8.4375

Year 5 = (80-20-15-11.25-8.4375) × 25% = 6.328125

EBT = revenue - Expenses - depreciation

Year 1 = 120 - 80 - 20 = 20 Million

Year 2 = 120-80- 15 = 25 Million

Year 3 = 120-80- 11.25 = 28.75 Million

Year 4 = 120-80- 8.4375 = 31.5625 Million

Year 5 = 120-80- 6.328125 = 33.671875Million

The cost of equity of the project through the use of Gordan's formula will be 9.87%.

It should be noted that the price of stock is computed thus:

= Previous dividend + Growth / Cost of equity - Growth

Po = Do + g/Ke - g

500 = 4 + 9%/Ke - 9%

500 = 4 + (0.09 × 4) / Ke - 9%

500 = 4.36/Ke - 9%

500(Ke - 9%) = 4.36

500Ke = 4.36 + 45

500Ke = 49.36

Ke = 49.36/500

Ke = 9.87%

The cost of debt will be:

= Interest rate (1 - Tax rate)

= 9% × (1 - 30%)

= 9% × 0.7

= 6.30%

The amount of the cost of debt will be:

= $1000 × 6.30%

= $63.00

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The amount of profit the investor earns is 9340 dollars. Then the correct option is D.

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

An investor buys 400 shares of stock in a fund when the net asset value is $19.62 and the offer price is $19.84.

The investor sells these shares when the net asset value is $43.19 and the offer price is $43.56.

Then total cost price of the shares will be

→ 19.84 × 400 = $7936

The total selling price of the shares will be

→ 43.19 × 400 = $17,276

Then the profit is the difference between the total cost price of shares and the total selling price of the shares.

→ 17276 - 7936 = $ 9340

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[tex]\log_{10} (3y+2) - 1 = \log_{10}(y-4)\\\\\implies \log_{10} (3y+2) - \log_{10} 10 = \log_{10} (y-4)\\\\\implies \log_{10} \left( \dfrac{3y+2}{10} \right) = \log_{10} (y-4)\\\\\implies \dfrac{3y+2}{10} = y-4\\\\\implies 3y+2 = 10y-40\\\\\implies 10y-3y = 40+2\\\\\implies 7y = 42\\\\\implies y = \dfrac{42}7\\\\\implies y = 6[/tex]

Answer:

well, y=8 and x=50

Step-by-step explanation:

you actually have the angle 128 wrong, and  it is suppose to be 32 degrees, which changes it up and all you have to do to find y because angle 32 and 4y are vertical, is divide 32/4=y which is 8, for x, it is vertical to 148 making those even, and it would be as simple as reversing the equation so, 148+2=150, and ddivided by 3 is 50 degrees

Answer:

x=50

y=8

Step-by-step explanation:

3x-2 and 148 are vertical angles and vertical angles are equal

3x-2 =148

Add 2 to each side

3x-2+2 =148+2

3x= 150

Divide by 3

3x/3 =150/2

x = 50

148 and the empty angle form a straight line so they add to 180

180-148 = 32

The empty angle is 32

4y  and 32 are vertical angles so they are the same

4y = 32

4y/4 = 32/4

y = 8

(7-2)² - 5/5

Do the math in the parentheses first.

7 - 2 = 5

Now the equation should read

(5)² - 5/5     or just       5² - 5/5

Do the exponent(s).

5² = 25

25 - 5/5

Do the division.

5/5 = 1

25 - 1 = 24

Therefore, according to our equation, the answer is 24.

I hope this answered your question.

[tex]\large{\mathcal{QUESTION:}}[/tex]

if p(x) = -2x²-3x+1, find p( -2)

[tex]\large{\mathcal{ANSWER:}}[/tex]

the answer is on the photo

the volume of the pot.

bolume of a triangular prism= BH

area of a triangle= 1 / 2 × base × height

B = 1 / 2 × b × h

b = 3 units

h = 5 units

B = 1 / 2  × 3 × 5

B = 15 / 2

B = 7.5 units²

H = 26 units

 B = 7.5 units²

V = 7.5 × 26

V= 195 unit³

so, the volume of the pot is 195 unit³.

Answer:

[tex]9\frac{52}{69} - 1 \frac{29}{50} [/tex]

[tex] \frac{673}{69} - \frac{79}{50} [/tex]

[tex] \frac{673}{69} to \: the \: nearest \: whole \: number \: is \: 10[/tex]

[tex] \frac{79}{50} to \: the \: nearest \: whole \: number \: is \: 2[/tex]

[tex] > > > 10 - 2 = 8[/tex]

Answer:

False, it would actually be 106 beads. If this was a multiplication problem, that would also be false, because 6 times 100 is 600, not 350.

But let's attempt to make this statement true.

First/Last step: Find the missing beads.

The missing beads are 144.

Why?

Because you must add 144 to reach 250, there is no other way but to multiply. In this case, because the key word is, "In all" we are adding.

Answer:

Step-by-step explanation:

Below statements include the required information or property

The standard deviation of the dataset is the square root of the variance

The mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

The dataset is given as;

25, 24, 32, 16, 22, 34. 19. 27, 18, 29

Calculate the mean using:

μ = Sum/Count

So, we have:

μ = (25+ 24+ 32+ 16+ 22+ 34+ 19+ 27+ 18+ 29)/10

Evaluate

μ = 24.6

The standard deviation is then calculated using:

[tex]\sigma =\sqrt{ \frac{\sum(x - \mu)^2}{n}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{(25 - 24.6)^2 + .................. + (27- 24.6)^2 + (18- 24.6)^2 + (29- 24.6)^2}{10}}[/tex]

Evaluate

[tex]\sigma = \sqrt{32.44}[/tex]

Evaluate the square root

[tex]\sigma = 5.70[/tex]

Hence, the mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

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Step-by-step explanation:

Each square has a side length of 1/4 inch but you have said each square=1/4

Once you have found the amount of 1/4 inches you multiply the two numbers together, only then do you multiply it to $11 for the square area.

Area:-

Cost:-

Answer:

tan theta = root3/3

see image

Step-by-step explanation:

The tangent is y/x in the unit circle. Use Keep-Change-Flip to simplify. See image. You also cannot leave a radical (square root) on the bottom of a fraction, so we need to "fix" that also. Multiply to rationalize (the "fix") see image.

Answer:

47,200,000,000

Step-by-step explanation:

[tex]4.72*10^{10}[/tex]  is in scientific form (notation).

To change this to standard form, we must move the decimal over the amount in the exponent. In this case, that is 10.

Answer:

Step-by-step explanation:

Q = mcΔt

Q = 14 x 0.385 x (85-50)

Q = 161.7 J

Answer:

900 in^2

Step-by-step explanation:

Triangle area = ( b x h )/ 2

rectangle area = b x h

------------------------------------------

triangle:

30 * 40 / 2 = 600 in^2

rectangle:

30 * 20/2 = 300 in^2

---------------------------------------

600 + 300 = 900 in^2

The equation of the blue line is y = 7x - 8 and the equation of the red line is y = -2x + 2

Equations are written as a function of two or more variables with input and output.

The standard linear equation is given in the form y = mx + b

m is the slope

b is the y-intercept

For the red line, the y-intecept is 2

Using the coordinate point on the red line (0,2) and (1, 0)

Slope = -2/1
Slope = -2

Equation of the  red line is y = -2x + 2

For the blue line, we will use the coordinate points (2, 6) and (1, -1)
m = -7/-1

m = 7

-1 = 7(1) + b

-1 - 7 = b

b = -8

Hence the equation of the blue line is y = 7x - 8

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Answer:

{x,y} = {7,-9/2}

Step-by-step explanation:

System of Linear Equations entered :

 [1]           25-x=-4y

 [2]           3x-2y=30

Equations Simplified or Rearranged :

  [1]    -x + 4y = -25

  [2]    3x - 2y = 30

Graphic Representation of the Equations :

   4y - x = -25        -2y + 3x = 30  

Solve by Substitution :

// Solve equation [1] for the variable  x

 [1]    x = 4y + 25

// Plug this in for variable  x  in equation [2]

  [2]    3•(4y+25) - 2y = 30

  [2]    10y = -45

// Solve equation [2] for the variable  y

  [2]    10y = - 45

  [2]    y = - 9/2

// By now we know this much :

   x = 4y+25

   y = -9/2

// Use the  y  value to solve for  x

   x = 4(-9/2)+25 = 7

Solution :

{x,y} = {7,-9/2}

Answer:

x=7, y=-4.5 or (7, -4.5)

Step-by-step explanation:

Hi there!

We are given the following system of equations:

25-x=-4y

3x-2y=30

Before we do anything, let's move our x and y values to one side, while keeping the numbers on the other side

So for 25-x=-4y, start by adding 4y to both sides

25-x=-4y

  +4y  +4y

_____________

25 + 4y - x = 0

Now subtract 25 from both sides

4y - x = -25

Now the system is this:

4y-x=-25

3x-2y=30

We can solve this equation by substitution, where we solve one of the equations for one of the variables, and then use the expression that the variable is equal to, in order to find the value of the other variable. Then, once the value of that variable is found, use that value to find the value of the first variable.

Start with 4y-x=-25

Subtract 4y from both sides

-x=-4y-25

Now multiply both sides by -1

x=4y+25

Substitute 4y+25 as x in 3x-2y=30

3(4y+25)-2y=30

Multiply

12y+75-2y=30

Simplify

10y+75=30

Subtract 75 from both sides

10y=-45

Divide both sides by 10

y = -4.5

Now substitute -4.5 as y in x=4y+25

x=4(-4.5)+25

Subtract

x= -18 +25

x= 7

The answer is x=7, y=-4.5. As a point, it's (7, -4.5)

Hope this helps!

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Answer:

i believe its 150

Step-by-step explanation:

Answer:

6(2a+4)-4(3a-4)= (12a+24) +(-12a+16) = 40

Answer:

the robot can travel 26 feet in 3 minutes

Step-by-step explanation:

The robot goes 11 feet per minute and 11 x 3 equals 33 which is more than 26.   33 < 26

Answer:

See below.

Step-by-step explanation:

Because same-side interior angles are supplementary, and becasue these two angles are equal, each angle must be one-half of 180°, or each angle must have a measure of 90°.

b=-3

The equation, -11b + 7 = 40, can be solved using the properties of equality.

Solving For b

First, subtract 7 from both sides

Then, divide both sides by -11

Checking the Answer

We can check our answer by plugging the answer back into the original equation.

First, rewrite the equation with the answer

Next, multiply out the terms

Then, add together like terms

Because this is a true statement, the answer must be correct.