Use the equation y=x2−3x+2 to answer the following questions. Part A: What numeric expression should be added in order to complete the square for the given equation? Part B: What equation is equivalent to the given equation after completing the square? Select two answers: one for Part A and one for Part B.

The equation of the vectors are

35. y = (-1/2)x + 2

36. y = (1/2)x + 5/2

37. y = 2x + 3

38. y = (2/3)x - 52/3

Exercise 35:

P(2, 1)

v = i + 2j

To find the equation of the line passing through P and perpendicular to v, we need to determine the slope of the line. The slope of a line perpendicular to a vector is the negative reciprocal of the slope of the vector.

The vector v = i + 2j has a slope of 2/1 = 2. The negative reciprocal of 2 is -1/2. Therefore, the slope of the line perpendicular to v is -1/2.

Using the point-slope form of a line, we can write the equation of the line passing through P as follows:

y - y₁ = m(x - x₁)

Substituting the values of P(2, 1) and the slope (-1/2), we get:

y - 1 = (-1/2)(x - 2)

Simplifying the equation, we have:

y - 1 = (-1/2)x + 1

y = (-1/2)x + 2

Exercise 36:

P(-1, 2)

v = -2i - j

The slope of the vector v = -2/1 = -2. The negative reciprocal of -2 is 1/2.

Using the point-slope form, we can write the equation of the line passing through P(-1, 2) as:

y - 2 = (1/2)(x + 1)

Simplifying the equation, we have:

y - 2 = (1/2)x + 1/2

y = (1/2)x + 5/2

Exercise 37:

P(-2, -7)

v = -2i + j

The slope of the vector v = 1/(-2) = -1/2. The negative reciprocal of -1/2 is 2.

Using the point-slope form, the equation of the line passing through P(-2, -7) is:

y - (-7) = 2(x - (-2))

Simplifying the equation, we have:

y + 7 = 2(x + 2)

y = 2x + 3

Exercise 38:

P(11, 10)

v = 2i - 3j

The slope of the vector v = -3/2. The negative reciprocal of -3/2 is 2/3.

Using the point-slope form, the equation of the line passing through P(11, 10) is:

y - 10 = (2/3)(x - 11)

Simplifying the equation, we have:

y - 10 = (2/3)x - 22/3

y = (2/3)x - 52/3

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Complete Question:

In Exercises 35–38, find an equation for the line through P perpendicular to v. Then sketch the line. Include v in your sketch as a vector starting at the origin.

35. P(2, 1), v = i + 2j

36. P(-1, 2), v =-2i - j

37. P(-2, -7), v =-2i + j

38. P(11, 10), v = 2i - 3j.

The firm's WACC given a tax rate of 32 percent is 7.86%.

The WACC (weighted average cost of capital) of the firm, given a tax rate of 32% can be calculated as follows;

Cost of Equity (Re) = 16%

Cost of preferred stock (Rp) = 6.5%

Pre-tax cost of debt (Rd) = 8.1%

Tax rate = 32%

Target capital structure = 41% common stock, 4% preferred stock, and 55% debt.

WACC = [(Re × E) / V] + [(Rp × P) / V] + [(Rd × D) / V × (1 - TC)]

Where;

E = market value of the firm's equity

P = market value of the firm's preferred stock

D = market value of the firm's debt

V = total market value of the firm's capital = E + P + D

The proportion of each component is;

E/V = 0.41P/V = 0.04D/V = 0.55

The cost of equity (Re) can be calculated using the CAPM (capital asset pricing model) equation;

Re = Rf + β × (Rm - Rf)

Where;

Rf = risk-free rate = 2.8%

Rm = market return = 10%

β = beta = 1.25

Re = 2.8% + 1.25 × (10% - 2.8%) = 2.8% + 1.25 × 7.2% = 2.8% + 9% = 11.8%

The cost of preferred stock (Rp) is given and remains 6.5%.

The after-tax cost of debt (Rd) can be calculated as follows;

Rd = pre-tax cost of debt × (1 - tax rate) = 8.1% × (1 - 0.32) = 8.1% × 0.68 = 5.508%

The total market value of the firm's capital (V) can be calculated as follows;

V = E + P + D

Assume that;

Total market value of equity (E) = $100,000

Market value per share of equity (Po) = $32

Market value of preferred stock (P) = $5,000

Market value of debt (D) = $95,000

The number of shares of equity (E) can be calculated as follows;

E = Po × number of shares outstanding

Number of shares outstanding = E / Po = $100,000 / $32 = 3,125 shares

Therefore;

E = Po × number of shares outstanding = $32 × 3,125 = $100,000

V = E + P + D = $100,000 + $5,000 + $95,000 = $200,000

Substituting the known values into the formula above gives;

WACC = [(Re × E) / V] + [(Rp × P) / V] + [(Rd × D) / V × (1 - TC)] = [(0.118 × $100,000) / $200,000] + [(0.065 × $5,000) / $200,000] + [(0.05508 × $95,000) / $200,000 × (1 - 0.32)] = (0.118 × 0.5) + (0.065 × 0.025) + (0.05508 × 0.475 × 0.68) = 0.059 + 0.001625 + 0.017995424 = 0.0786 or 7.86%

Therefore, the firm's WACC, given a tax rate of 32%, is 7.86%.

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Answer:

Step-by-step explanation:

Hello, please consider the following.

\(6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)\)

And the we know that if the discriminant is

***** \(\Delta\) < 0, meaning 8-3k<0, meaning

\(\boxed{k>\dfrac{8}{3}}\)

then, there is no real solution.

***** \(\Delta = 0\), meaning

\(\boxed{k=\dfrac{8}{3}}\)

There is 1 solution.

***** \(\Delta\) > 0, meaning

\(\boxed{k<\dfrac{8}{3}}\)

There are 2 solutions.

Thank you

PS: To give more details...

\(8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}\)

We are asked to model the given problem using a function in the form of y=mx +c

In this case, our "y" will be the total amount spent while m as the co-efficient of x will equal the amount spent per bag. Lastly the $10.5 dollars that needs to be spent per order has been given independent of how many bags are ordered. This is our value for "c".

Correct option: g(x) = 16.49x + 10.5

We will then calculate the cost of buying 12 bags by substituting this into our equation:

g(12) = 16.49(12) + 10.5

= $208.38

The size of the angle to the nearest degree of tan v = 0.9657 will be 44°.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

As per the given,

tan v = 0.9657

Take inverse tan on both sides of the above expression,

v = \(tan^{-1} 0.9657\)

v = 44°

Hence "The angle at tan v = 0.9657 will be 44° to the closest degree.".

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Answer:

m=-2

Step-by-step explanation:

i hope i helped!

Answer:

12

Step-by-step explanation:

9^2 + b^2 = 15^2

=

81 + b^2 = 225

=

b^2 = \(\sqrt{144}\)

b = 12

Hope this helps :)

Comment of you need mroe help!!

To solve the problem, let's go step by step.

1) Draw the K-map and find all prime implicants:

The given function f has 4 variables (d, c, b, a). So, we need to draw a 4-variable Karnaugh map (K-map). The K-map will have 2^4 = 16 cells.

The K-map for f is as follows:

```

        cd

ab     00 01 11 10

00 |   1   2   8   7

01 |   3   4   12 15

11 |   X   5   X   14

10 |   X   9   X   10

```

Now, let's find all the prime implicants:

- A: Group (1, 2, 3, 4) with d = 0.

- B: Group (2, 3, 7, 8) with b = 0.

- C: Group (3, 4, 12, 15) with a = 0.

- D: Group (2, 3, 4, 5) with c = 1.

- E: Group (7, 8, 14, 15) with b = 1.

- F: Group (4, 5, 9, 10) with a = 1.

- G: Group (8, 9, 12, 15) with c = 0.

- H: Group (12, 14, 15, 10) with d = 1.

2) Minimize f:

To minimize f, we need to simplify it by combining the prime implicants.

The minimized form of f can be expressed as the sum of prime implicants A, B, D, and E:

f = A + B + D + E

This can be further simplified, if desired, using Boolean algebra techniques.

Note: Please double-check the given function f and the tabulation method steps to ensure accuracy in the K-map and prime implicant identification.

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Answer:

I can't see the ques

Step-by-step explanation:

Can u please post it again

Answer Its 84

Step-by-step explanation:

80 plus 5% equals 84%  

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Answer:

f(4) = 13

Step-by-step explanation:

f(4) = 2(4)+5
f(4) = 13

Answer:

13

Step-by-step explanation:

f ( x ) = 2x + 5

To find : f ( 4 )

f ( 4 ) = f ( x )

Here,

x = 4

So,

f ( 4 ) = 2 ( 4 ) + 5

        = 2*4 + 5

        = 8 + 5

f ( 4 ) = 13

Let Q be the point (a, b). Since the midpoint of P (2, 3) and Q (a, b) is (4, 6), we have

(2 + a)/2 = 4

(3 + b)/2 = 6

Solve for a and b :

(2 + a)/2 = 4

2 + a = 8

a = 6

(3 + b)/2 = 6

3 + b = 12

b = 9

So the coordinates of Q are (6, 9).

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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Answer: 11 weeks

Step-by-step explanation:

G(t) = 25 + 14t

A(t) = 80 + 9t

set G equal to A and find t

25 + 14t = 80 + 9t

5t = 55

t = 11

Apply the compound interest formula:

A= P (1+r/n)^nt

Where:

A: future value of the investment

P: Principal amount

r: interest rate (in decimal form)

n: number of compounding periods in each year

t: years

Replacing:

A= 20,000 (1+0.08/12)^12x40

A = 20,000 (1.0067)^480

A= 485,467.7116

It will take 3 weeks for both of us to have collected  the same amount. Each of us will have collected 23 items at that  time.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Let x = weeks

Me: y = 14+3x

Friend: y = 8+5x

Equating the two equations

14+3x=8+5x

14=8+2x

6=2x

dividing both sides by 2

3=x

y=14+3(3)=23

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The corresponding values for the triangle in the larger circle are;

1. Perimeter of Δ BSH = 71.4 cm

2. The measure of ∠SBH = 102°.

3.  The area of Δ BSH = 41.54 cm²

4. The length of the circumference of circle B = 52.275 cm

1. The ratio of the perimeters of similar triangles is equal to the ratio of their corresponding sides. Since OB/OA = 4.25, we have:

Perimeter(Δ BSH) = Perimeter(Δ ARG) × 4.25

Perimeter(Δ BSH) = 16.8 cm × 4.25 = 71.4 cm

2. Since the triangles are similar, their corresponding angles are congruent. Therefore, ∠SBH = ∠RAG = 102°.

3. The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding sides. Since OB/OA = 4.25, we have:

Area(Δ BSH) = Area(Δ ARG) × (4.25)²

Area(Δ BSH) = 2.3 cm² × (4.25)² = 2.3 cm² × 18.0625 = 41.54 cm²

4. The ratio of the circumferences of similar circles is equal to the ratio of their radii or diameters. Since OB/OA = 4.25, we have:

Circumference(circle B) = Circumference(circle A) × 4.25

Circumference(circle B) = 12.3 cm × 4.25 = 52.275 cm

The above answers are in response to the following questions below;

Dante created the following measurements and calculations:

He then made the following measurements and calculations:

He calculated the ratio OB = 4.25.

                                      OA

He measured the perimeter of Δ ARG, and found it to be 16.8 cm.

He measured ∠RAG = 102°.

He calculated the area of Δ ARG, and found it to be 2.3 cm2.

He calculated the circumference of circle A, and found it to be approximately 12.3 cm.

He would now like to calculate corresponding values for the triangle in the larger circle, and he needs your help.

Calculate the following, using your knowledge that all circles are similar, along with the data already collected by Noah..

5. Find the perimeter of Δ BSH.

6. Find the measure of ∠SBH.

7. Find the area of Δ BSH.

8. Find the length of the circumference of circle B.

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The length of the rectangle in centimeters is 15.60 cm.

The correct way to report the length of the rectangle in centimeters is 15.60 cm. To calculate the length of the rectangle, we must first calculate the distance between the two edges of the rectangle. To do this we can use the formula Distance = Final Position - Initial Position. Therefore, the distance between the two edges of the rectangle is 15.600 cm - 0 cm = 15.600 cm. This is the length of the rectangle, so the correct way to report the length of the rectangle in centimeters is 15.60 cm.

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Then according to the above statement, we have the following equation:-

\(3 + 4x = 6x - 5\)

Subtract 4x from both sides , we get

\(3 = 2x - 5\)

Add 5 on both the sides , we get

\(8 = 2x\)

Divide both sides by 2 , we get

\(4 = x\)

Hence, the number is 4

The first four-term of the sequence is found by the given equation \(a_{n-1} = 4a_n\) is given as 144, 36, 9, and 9/4.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The given equation will be

\(\rm a_n = \dfrac{a_{n-1}}{4} \\\\a_{n-1} = 4a_n\)

And

\(a_4 = 2 \dfrac{1}{4} = \dfrac{9}{4}\)

For n = 4, we have

\(\rm a_{4-1} = 4a_4\\\\a_3 \ \ \ = 4*\dfrac{9}{4} \\\\ a_3 \ \ \ = 9\)

For n = 3, we have

\(\rm a_{3-1} = 4a_3\\\\a_2 \ \ \ = 4*9 \\\\ a_2 \ \ \ = 36\)

For n = 2, we have

\(\rm a_{2-1} = 4a_2\\\\a_1 \ \ \ = 4*36 \\\\ a_1 \ \ \ = 144\)

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Answer:

144

36

9

Step-by-step explanat

Answer:

-12 + 9p

Step-by-step explanation:

Original Equation:

-12 - 5p + 2(6p + p)

Distributive property.

2 x 6p = 12p

2 x p = 2p

Equation:

-12 - 5p + 12p + 2p

Subtract 5p from 12p

-12 + 7p + 2p

Add.

-12 + 9p

Hope this helped :)

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The vertex and sides of the angles are:

The angles are:

The measure of the angles

Here, there is no parameter to determine the measure of each angle.

This means that the measures of angles cannot be calculated; however, the angles can be classified.

The classification of the angles are:

The vertex and sides of the angles

The vertex is the point where two lines meet, while the sides are the lines

So, the vertex and sides of the angles are:

Name each angle in four way

The vertex is the point where two lines meet, while the sides are the lines

In this case, the angles are:

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Answer:the slope is 5

Step-by-step explanation: your slope is always next to your x remember the formula mx+b=y in this case m = slope and b=y intercept so 5 is your slope :)

The slope of the line is 3/5, the y - intercept is 3, the slope of any line perpendicular to the given line is -5/3 and the graph is attached below.

Y-intercept:

The equation of the line in the slope-intercept form is,

y=mx + b.

By the definition of the slope-intercept form itself,

m is slope of the line

b is the y-intercept of the line.

Given,

Here we have the equation

3x - 5y = -15

nd we need to find the slope, y-intercept, perpendicular slope and the graph for the equation.

First we have to convert the equation into standard form,

So,

-5y = -15 - 3x

multiply (-) on both sides,

5y = 15 + 3x

divide 5 on both sides.

y = 3 + 3/5 x

So, the resulting equation is,

y = 3/5 x + 3

So, the slope is 3/5 and y intercept is 3.

Then the perpendicular slope of the line is,

m = -1/(3/5)

m = -5/3

And the graph of the equation is attached below.

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Answer: For every apple you sell, you earn 4 bucks. y is the number of apples, 4 is the constant price.

The probability that she picks two white socks is 0.0357

The given parameters are:

Socks = 8

Black = 4

White = 2

Brown = 1

Red = 1

The probability of picking a white sock at first is:

P(White) = 2/8

Now, there are 7 socks left

The probability of picking a white sock next is

P(White) = 1/7

The required probability is:

P = 2/8 * 1/7

Evaluate

P = 0.0357

Hence, the probability that she picks two white socks is 0.0357

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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