Mathematics College

NEED HELP PLS ASAP AND THX PIC IS ATTACHED

Answers

Answer 1

1 given
2 linear pair
3 both equal 180
4 subtract mL3 on both sides
5 measure of vertical angles is same from 4

Related Questions

Can you please help me with this?

Answers

the answer to your question is Y=0

18. Sam retires in 1996. He has an amount of R350 000 available to invest. He decides to buy a second house for 50% of the money, which he lets at an amount of R2000 per month. He increases the rent every year by an amount of R300. The balance of R175 000 he invests in the bank at a rate of 12%. He uses the interest every month to supplement his income, so the interest is not compounded. He also gets a pension of R3000 per month, which is increased by R300 per month every year. What was his monthly income in 1996? (1)

Answers

If Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

Given that Sam had Rs.350000,investment in house Rs.175000 at a rent of Rs.2000 per month and Rs.175000 in bank at rate of 12%, getting pension of Rs.3000 per month.

We are required to find the monthly income in 1996.

We have assumed that Sam was retired on 1st January, 1996 so the amount of rent, investment in bank and pension did not increase because they had to be increase in a year and we have to calculate the monthly income in which he was retired.

Monthly income=Rent of 1 month+Simple interest of 1 month+Pension per month

=2000+175000*1/100+3000

=2000+1750+3000

=Rs.6750

Hence if Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.

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If P(En F) = 0.036, P(E|F) = 0.09, and P(F|E) = 0.1, then (a) P(E) = (b) P(F) = = (c) P(EUF) (d) Are the events E and Findependent? =

Answers

The events E and F are not independent

How to determine the probabilities?

The given parameters are:

P(E n F) = 0.036

P(E|F) = 0.09

P(F|E) = 0.1

To calculate P(E), we use:

P(F|E) = P(E n F)/P(E)

This gives

P(E) = P(E n F)/P(F|E)

So, we have:

P(E) = 0.036/0.1

Evaluate

P(E) = 0.36

To calculate P(F), we use:

P(E|F) = P(E n F)/P(F)

This gives

P(F) = P(E n F)/P(E|F)

So, we have:

P(F) = 0.036/0.09

Evaluate

P(F) = 0.4

To calculate P(E U F), we use

P(E U F) = P(E) + P(F) - P(E n F)

So, we have:

P(E U F) = 0.36 + 0.4 - 0.036

Evaluate

P(E U F) = 0.724

The events E and F are independent if

P(E n F) = P(E) * P(F)

This gives

0.036 = 0.36 * 0.4

Evaluate

0.036 = 0.144 --- false

Hence, the events E and F are not independent

Answers

x^2=16
x= 4 OR x=-4

The picture attached below is your answer because it’s between 4 and -4.

(1)
Determine the equation of the line passing through the point (0; -1) and
parallel to the -axis. Do you remember what the gradient of this line is?

(2)
Determine the equation of the line passing through the point(-1;0) and
parallel to the -axis. Do you remember what the gradient of this line is?

Answers

We know that,

slope = [tex] \rm{\frac{(y2 - y1)}{(x2 - x1)} }[/tex]

Let (0,1)=(x 1 ,y 1 ) and (1,2)=(x 2,y 2 )

So,

Slope of line = [tex] \frac{(2 - 1)}{(1 - 0)} = 1[/tex]

Now,

The required line equaqtion is given by,

==> y−y 1 = m(x-x1)

==> y−1=1(x−0)

==> y−1=x

==> y=x+1

Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let PP represent Jeremiah's total pay on a day on which he sells xx dollars worth of computers. The table below has select values showing the linear relationship between xx and P.P. Determine how many dollars worth of computers Jeremiah would have to sell in order to get paid $130 on a given day.

Answers

Jeremiah has to sell 5000 dollars worth of computers to get paid $130 on a given day. Using the linear equation, the required value is calculated.

What is a linear equation?

An equation in which if the highest degree of the variable is 1(one), then that equation is said to be a linear equation.

General form: ax + b = c; where the power of the variable x is 1.

Calculation:

It is given that,

Jeremiah makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day.

Consider,

P - as total pay on a day, x - as the number of dollars worth of computers, B - as basic pay, and C - as commission percentage.

So, the linear equation that relates x and P is,

P = Cx + B ...(i)

On substituting the values from the given table we get,

122.5 = C(4500) + B ...(ii)

160 = C(7000) + B ...(iii)

175 = C(8000) + B ...(iv)

By solving equations (iii) and (iv), we get

C = 15/1000 = 0.015

B = 55

Finding x value when P = $130:

We have P = Cx + B. Then for P = 130,

130 = Cx + B

We know C = 0.015 and B = 55

On substituting these values,

130 = (0.015) x + 55

⇒ 0.015x = 130 - 55 = 75

∴ x = 75/0.015 = 5000

Therefore, the required computers are 5000 dollars worth.

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Disclaimer: The given question on the portal was incomplete. Here is the complete question.

Question: Jeremiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let P represent Jeremiah's total payments on a day on which he sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine how many dollars worth of computers Jeremiah would have to sell to get paid $130 on a given day.

Table:

x: 4500, 7000, 8000

P: 122.5, 160, 175

respectively.

According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x – 24.

–4, –3, 2, 3, 4

Which are actual roots of f(x)?
–4 and 3
–4, 2, and 3
–3 and 4
–3, 2, and 4

Answers

The actual roots of f(x) are -4 and 3

How to determine the actual roots?

The function is given as:

f(x) = 2x^2 + 2x – 24.

Expand the function

f(x) = 2x^2 + 8x- 6x – 24.

Factorize the function

f(x) = 2x(x + 4) - 6(x + 4)

Factor out x + 4

f(x) = (x + 4)(2x - 6)

Set to 0

(x + 4)(2x - 6) = 0

Solve for x

x = -4 and 2x = 6

This gives

x = -4 and x = 3

Hence, the actual roots of f(x) are -4 and 3

Answers

There are 60 questions on the test

Calculating percentages

Total number of questions = 42

Percentage equivalent= 70%

Let the total number of questions in the test be represented by x

42 = 70% of x

[tex]42=\frac{70}{100} \times x[/tex]

42 = 0.7x

Divide both sides by 0.7

42/0.7 = 0.7x/0.7

x = 60

Therefore, there are 60 questions on the test

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Ivanhoe Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $11.85 million. This investment will consist of $2.15 million for land and $9.70 million for trucks and other equipment. The land, all trucks, and all other equipment are expected to be sold at the end of 10 years for a price of $5.25 million, which is $2.00 million above book value. The farm is expected to produce revenue of $2.10 million each year, and annual cash flow from operations equals $1.90 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this investment. (Do not round factor values. Round final answer to 2 decimal places, e.g. 15.25.)

Answers

The NPV of this investment if the discount rate is 10 percent is: 1.58%.

Net present value (NPV)

Year Cash flow PVIF 10% Present value

0 ($11.86) 1.000 ($11.86)

1 1.90 0.909 $1.73

2 1.90 0.826 $1.57

3 1.90 0.751 $1.43

4 1.90 0.683 $1.30

5 1.90 0.621 $1.18

6 1.90 0.564 $1.07

7 1.90 0.513 $0.98

8 1.90 0.467 $0.89

9 1.90 0.424 $0.81

10 6.45 0.386 $2.49

NPV $1.58

1.9+5.25-2×35%=6.45

Hence, the NPV is $1.58.

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Jackson invested $4,200 in an account paying an interest rate of 9 1/2 compounded continuously. Julia invested $4,200 in an account paying an interest rate of 8 7/8 compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Julia's money to double than for Jackson's money to double?

Answers

It would Julia 0.60 years more to double the initial investment.

What is future value?

Future value means the initial investment multiplied by 2 since the future value is meant to double.

The formula for future value of a continuously interest rate is provided below:

FV=PV*e^(rt)

FV=future value=$4,200*2=$8,400

PV=initial investment=$4,200

e=exponential constant=2.7182818

r=interest rate=9.5%

t=number of years it takes for the investment to double=unknown

$8,400=$4,200*2.7182818^(9.5%*t)

$8,400/$4,200=2.7182818^(0.095t)

2=2.7182818^0.095t

take log of both sides

ln(2)=0.095t* ln(2.7182818)

0.095t=ln(2)/ln(2.7182818)

0.095t=0.69314718781684800

t=0.69314718781684800/0.095

t=7.30 years

The future value when interest is compounded quarterly is shown thus:

FV=PV*(1+r/4)^(N*4)

FV=$8,400

PV=$4,200

r=8 7/8%

r=8.875%

N=the number of years it would take for the initial investment to double=unknown

$8,400=$4,200*(1+8.875%/4)^(N4)

$8,400=$4,200*(1+0.0221875)^(N4)

$8,400/$4,200=(1+0.0221875)^(N4)

2=(1+0.0221875)^(N4)

2=(1.0221875)^(N4)

take log of both sides

ln(2)=N4*ln(1.0221875)

N4=ln(2)/ln(1.0221875)

N4=31.5857423180125

N=31.5857423180125/4

N=7.90

Difference in years=7.90-7.30

difference in years=0.60 years

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Find the first 10 terms of the sequence below :
g) the sequence whose terms are constructed sequen tially as follows: start with 1, then add 1, then mul
tiply by 1, then add 2, then multiply by 2, and so on
h) the sequence whose nth term is the largest integer k
such that k!

Answers

The first ten terms of the sequence are 1, 2, 8, 33, 148, 765, 4626, 32431, 259512, 2335689.

The n-th term of the sequence is aₙ ₊ ₁ = (aₙ + 1) · n.

How to generate the elements of a sequence

A sequence is a set of elements generated by at least one condition, usually an equation. In this case, the sequence is generated by a recurrence formula:

a₁ = 1, aₙ ₊ ₁ = (aₙ + 1) · n (1)

The first ten terms of the sequence are:

n = 1

a₂ = (a₁ + 1) · 1

a₂ = 2

n = 2

a₃ = (a₂ + 2) · 2

a₃ = 4 · 2

a₃ = 8

n = 3

a₄ = (a₃ + 3) · 3

a₄ = 11 · 3

a₄ = 33

n = 4

a₅ = (a₄ + 4) · 4

a₅ = 37 · 4

a₅ = 148

n = 5

a₆ = (a₅ + 5) · 5

a₆ = 153 · 5

a₆ = 765

n = 6

a₇ = (a₆ + 6) · 6

a₇ = (765 + 6) · 6

a₇ = 4626

n = 7

a₈ = (a₇ + 7) · 7

a₈ = 4633 · 7

a₈ = 32431

n = 8

a₉ = (a₈ + 8) · 8

a₉ = 32439 · 8

a₉ = 259512

n = 9

a₁₀ = (a₁₀ + 9) · 9

a₁₀ = 259521 · 9

a₁₀ = 2335689

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An equation is shown below: 8x + 2(x – 7) = 7x + 3x – 14 Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points) Part B: Name one property you used to solve this equation. (4 points) Source StylesNormalFontSize

Answers

Answer:

Infinitely ManyDistributive Property

Step-by-step explanation:

8x + 2(x - 7) = 7x + 3x - 14

8x + 2x - 14 = 7x + 3x - 14 Distributive property.

10x - 14 = 10x - 14 Combine the like terms.

-14 = -14 Subtraction.

0 = 0 Addition.

Since the statement 0 = 0 is true regardless of the value of x, there is infinitely many solutions.

!!!!!!!!!!!!!!!!!!!!!!helpppppppo

Answers

Answer:

(3x3+3)*2

Step-by-step explanation:

Does this appear to be a regular polygon? Explain.

Answers

Answer:

Yes

Step-by-step explanation:

All sides and angles look equal and appears to be a regular hexagon

Hope this helped and have a good day

Answer:

Yes.

Step-by-step explanation:

Hello!

A regular polygon is a closed shape with sides of equal length, and angles of equal degree. A regular polygon also forms around a general center.

This seems to be a regular polygon as all side lengths and angles seem to be equivalent, and there is a center point to the .

This shape is a hexagon, so the measure of the angles are 120°.

Solve for v. -8=-2/v

Answers

Answer is 1/4
Step by step
-8 = -2/v
First we want to isolate “v”
-2 is divided by “v”, so we will multiply both sides by “v”
-8v = -2
Now we can solve for v
Divide both sides by -8
v = 2/8, simplified to 1/4
(Remember when you multiply or divide two negatives it becomes a positive)

If you want to check your work, substitute your answer of 1/4 into the original equation.

-8= (-2) divided by (1/4)
-8 = -8
Problem solved!!

1. There are 50 contestants signed up for a TV show. There are 36 more female contestants than male contestants. How many female contestants have signed up to compete? Show your solution and explain how you plan to explain this to your students.

Answers

Answer:

males = 7

females = 43

Step-by-step explanation:

whilst it may seem intuitive to simply subtract 36 from 50, it is not saying "there are 36 males, how many females?" but instead, "the difference between the number of males and females is 36".

You can solve this equation most easily algebraically. For example:

Number of males = x

number of females = y

the question states that the total number of people = 50

therefore we can say that the total number of males (x) + the total number of females (y) = 50 people

therefore: x + y = 50

similarly, the question says that the number of males (x) + 36 = the total number of females (y)

therefore: x + 36 = y

we now have two equations:

x + y = 50

x + 36 = y

whilst both equations have two unknowns (x and y), therefore we can't simple solve for x or y, with the combination, we can see a pattern.

focusing on the second equation: x + 36 = y

we can add x to both sides, because you can pretty much do anything to the equation as long as you do it to both sides.

x + 36 + x = y + x

now this may seem very random, but you now see that one side of the equation equals y + x, and remember from the other equation, x + y = 50. Therefore we can substitute x + y in the second equation for 50.

our two equations:

x + 36 + x = y + x

x + y = 50

therefore:

x + 36 + x = 50

for the sake of clarity, we can combine like terms...

x + x = 2x

therefore:

x + 36 + x = 50

2x + 36 = 50

solve for x by subtracting 36 from both sides, then dividing both sides by 2

2x + 36 - 36 = 50 - 36

2x = 14

2x / 2 = 14 / 2

x = 7

now remember:

Number of males = 7 (we now know x = 7)

now that we've solved for x, we can go back to our original equation:

x + 36 = y

and substitute x...

7 + 36 = y

43 = y

Now remember:

Number of females = 43 (we now know y = 43)

therefore there are 7 males and 43 females. we can proof this by adding 7 and 43, and you'll see you reach 50, which is the correct total number of people.

hope this helps :)

help!! How do I solve for x and what is x

Answers

Answer:

x=75 degrees

Step-by-step explanation:

since the shape is quadrilateral, all the angles added together should equal 360 degrees so you use 360 to subtract all the given angles on the shape and you can find X

360-131-107-47=75

4x + 4y = 40
2x - 4y = 8

Answers

Answer:

x=8 y=2

Step-by-step explanation:

solve for x

1. 4x+4y=40

2. subtract 4y from both sides

3. 4x=40-4y

4. divide both sides by 40

5. [tex]\frac{4x}{4} = \frac{40-4y}{4}[/tex]

6. dividing by four undoes the multiplication by four

7. [tex]x=\frac{40-4y}{4}[/tex]

8. divide 40 - 4y by 4

9. x=10-y

10. use the last equation to solve the rest

20 pts and brainliest

Answers

The two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

What are the solutions to the quadratic equation?

Given the equation; 9x² + 4 = 0

First, we subtract 4 from both sides.

9x² + 4 = 0

9x² = -4

x² = -4/9

Take the square roots of both sides

x = ±√(-4/9)

Rewrite -4/9 as (2i/3)²

x = ±√(2i/3)²

x = ±(2i/3)

Hence,

x = 2i/3, -2i/3

Therefore the two solutions to the given quadratic equation are 2i/3, -2i/3 and they are both complex solutions.

Hence, option C is the correct answer.

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Answer:

but it says ill get 10 only

Step-by-step explanation:

Gene is tossing a normal quarter. He tosses the quarter 12 times and it lands on heads 9 times. If Gene tosses the quarter again, what is the probability that it lands on tails? Input your answer in fraction form.

Answers

Answer:

1/2

Step-by-step explanation:

This is an independent event. It does not matter what happened before the chances of getting a tail on one toss will always be what I want/all outcomes. There are only 2 outcomes: heads or tails. I am only looking for one of those outcomes, so 1/2.

Cycles travel at an the average speed of 20km/h for 1.5 Hours
calculate the distance she travels in 1.5

Answers

Answer:

30 km

Step-by-step explanation:

Distance = rate x time

Distance = 20 x 1.5

Distance = 30

[tex]20*1.5=30[/tex] [tex]km[/tex]

Correct answer:-

Avg. speed = [tex]20km/h[/tex]

Time = [tex]1.5 hour[/tex]

Distance traveled in 1.5 hours is Distance = Speed x Time

So,

[tex]D = 20 * 1.5 = 30.[/tex]

reference link-

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A zoo has a black rhinoceros that weighs 18 times as much as an average-size chimpanzee. The rhinoceros weighs 2,250 pounds.

How much does an average-size chimpanzee weigh?

Enter the answer in the box. [_]

Answers

Answer: 125 pounds

Step-by-step explanation:

Let's first represent the weight of the black rhinoceros and chimpanzee with variables. We will assign r for the rhinoceros and c for the chimpanzee.

In the question, we were given that the weight for a black rhinoceros is 18 times as much as an average-size chimpanzee. This makes 18 times the chimpanzee's weight equal to the rhinoceros' weight.

Let's put this into an equation.

[tex]r=18*c[/tex]

Now, let's put in the values we know to find the weight of the chimpanzee (i.e., c). We know the weight of a rhinoceros (represented by r) is 2250 pounds, so we can replace it for r in the equation.

[tex]2250=18*c[/tex]

To solve this equation, we can divide both sides by 18 to get c by itself and know what it's value is.

[tex]\frac{2250}{18}=\frac{18*c}{18}[/tex]

We can remove the [tex]\frac{18}{18}[/tex] from the right side to be left with c. We can also divide 2250 by 8 to get the weight of an average-size chimpanzee.

[tex]c=\frac{2250}{18}\\ c=125[/tex]

Hence, an average-size chimpanzee weighs 125 pounds.

Use the diagram to determine which statement is true

Answers

The answer is d.

Finding area of ABCD :

Find side lengthside = √3² + 4²side = 5

2. Apply formula to find area

area = 5²area = 25

Finding area of GHIA :

area = 4²area - 16

Finding area of DEFG :

area = 3²area = 9

Now, let's see whether is true.

Area (ABCD) - Area (GHIA) = Area (DEFG)25 - 16 = 99 = 9

∴ Hence, it is proved √

Find the integrals:
∫30x^2/√(x-4) dx
u=x-4 and u=√(x-4)

Answers

I assume you're asked to compute

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx[/tex]

using both of the substitutions provided.

With [tex]u=x-4[/tex], we have [tex]x=u+4[/tex] and [tex]dx=du[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{30(u+4)^2}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \frac{u^2 + 8u + 16}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \left(u^{3/2} + 8u^{1/2} + 16u^{-1/2}\right) \, du \\\\ ~~~~~~~~ = 30 \left(\frac25 u^{5/2} + \frac{16}3 u^{3/2} + 32 u^{1/2}\right) + C \\\\ ~~~~~~~~ = 12 u^{5/2} + 160 u^{3/2} + 960 u^{1/2} + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4 \sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

With [tex]u=\sqrt{x-4}[/tex], we have

[tex]u^2 = x-4 \implies x^2 = (u^2+4)^2[/tex]

and [tex]2u\,du=dx[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{60u \left(u^2+4\right)^2}u \, du \\\\ ~~~~~~~~ = 60 \int \left(u^4 + 8u^2 + 16\right) \, du \\\\ ~~~~~~~~ = 60 \left(\frac15 u^5 + \frac83 u^3 + 16u\right) + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4\sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3. Include
your work in your final answer. Type your answer in the box provided to submit your solution.

Answers

Answer:

y= 2x -6

Step-by-step explanation:

The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

To find the equation of a line, two information are needed:

Slope (given/ calculated)A pair of coordinated

Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:

y= 2x +c

Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.

2x -3y= 6

When x= 3,

2(3) -3y= 6

6- 3y= 6

3y= 6 -6

3y= 0

Divide both sides by 3:

y= 0

Coordinate that lies on the graph is (3, 0).

Substitute the point into the equation and solve for c:

y= 2x +c

When x= 3, y= 0,

0= 2(3) +c

0= 6 +c

c= -6

Substitute the value of c back into the equation:

Thus, the equation of the line in slope-intercept form is y= 2x -6.

Additional:

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A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80
seconds. Assume that at time t = 0, the Ferris Wheel is at its lowest height above
the ground of 2 m. You will develop the equation of a cosine graph that models your
height, in metres, above the ground as you travel on the Ferris Wheel over time, t in
seconds. To do this, answer the following questions.

1. State the amplitude of the graph.
2. State the value of k in the general form y = a cos [k(x − d)] + c.
-
3. State the value of d.
4. State the value of c.
5. State the cosine equation of the graph.

Answers

A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80 seconds. Assuming that at time t = 0, the Ferris Wheel is at its lowest height above the ground of 2 m, the cosine equation of the graph drawn is, y = 5 cos [( π/40)(x - (π/2))] + 3. Here, amplitude of the graph is 5, value of k is π/40, d is π/2 and c is 3.

Developing the Equation of a Cosine Graph

The given information constitutes the following,

Diameter = 10 m

⇒ Radius, r = 5 m

Time, t = 80 s

Height above the ground, h = 2 m

Thus, we can infer that,

Amplitude, A = 5 m

Period, T = 80 s

Minimum height = 2 m

The cosine function is given as,

a cos [k(x − d)] + c

Here, A is amplitude

B is cycles from 0 to 2π and thus period = 2π/k

d is horizontal shift

c is vertical shift (displacement)

Now, 2π/k = 80

⇒ k = 2π/80 = π/40

The value of c is given as,

c = Amplitude - Minimum height

c = 5 - 2

c = 3

For a shift to the left by π/2 gives, we have,

d = π/2

Thus, the desired equation of the drawn cosine graph is,

y = 5 cos [( π/40)(x - (π/2))] + 3

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lim x→-1 x^m + 1/x^n + 1

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I assume [tex]m,n[/tex] are integers to avoid (ir)rational powers of -1.

If [tex]m,n[/tex] are both even, or if [tex]m=n[/tex], then

[tex]\displaystyle \lim_{n\to-1} \frac{x^m+1}{x^n+1} = \frac{1+1}{1+1} = 1[/tex]

If [tex]m,n[/tex] are both odd and [tex]m\neq n[/tex], then we can factorize

[tex]\dfrac{x^m+1}{x^n+1} = \dfrac{(x+1)(x^{m-1} - x^{m-2} + \cdots - x + 1)}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)}[/tex]

Note that there are [tex]m[/tex] terms in the numerator and [tex]n[/tex] terms in the denominator.

In the limit, the factors of [tex]x+1[/tex] cancel and

[tex]\displaystyle \lim_{x\to-1} \frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^{m-1} - x^{m-2} + \cdots - x + 1}{x^{n-1}-x^{n-2}+\cdots-x+1} \\\\ ~~~~~~~~~~~~~~~~~~= \dfrac{1-(-1)+1-(-1)+\cdots-(-1)+1}{1-(-1)+1-(-1)+\cdots-(-1)+1} \\\\ ~~~~~~~~~~~~~~~~~~=\frac{1+1+\cdots+1}{1+1+\cdots+1} = \dfrac mn[/tex]

If [tex]m[/tex] is even and [tex]n[/tex] is odd, then we can only factorize the denominator and the discontinuity at [tex]x=-1[/tex] is nonremovable, so

[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{x^m+1}{(x+1)(x^{n-1}-x^{n-2}+\cdots-x+1)} \\\\ ~~~~~~~~~~~~~~~~~~= \frac2m \lim_{x\to-1} \frac1{x+1}[/tex]

which does not exist.

If [tex]m[/tex] is odd and [tex]n[/tex] is even, then we can factorize the numerator so that

[tex]\displaystyle \lim_{x\to-1}\frac{x^m+1}{x^n+1} = \lim_{x\to-1} \frac{(x+1)(x^{m-1}-x^{m-2} +\cdots -x+1)}{x^n+1} \\\\ ~~~~~~~~~~~~~~~~~~= \frac{0m}2 = 0[/tex]

questions 5 and 6 please!
will give brainliest to whoever answers
90 points

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Answer:

rise over run so

5/5 = 1

-2/4 = -0.5

I need help with this geometry question asap!

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No pair of lines can be proven to be parallel considering the information given, therefore, the answer is: D. None of the options are correct.

When are Two Lines Proven to be Parallel to each other?

Two lines that are cut across by a transversal can be proven to be parallel to each other if:

The alternate interior angles along the transversal and on the two lines are congruent [alternate interior angles theorem].The alternate exterior angles along the transversal and on the two lines are congruent [alternate exterior angles theorem].The same-side interior angles along the transversal and on the two lines are supplementary [same-side interior angles theorem].The corresponding angles along the transversal and on the two lines are congruent [corresponding angles theorem].

Thus, given the following information:

m∠2 = 115°

m∠15 = 115°

With only these two angles given, we can't use any of the theorems to prove that any of the two lines are parallel because angle 2 and angle 15 are located entirely on two different transversals that crosses two lines.

In summary, we can conclude that:

D. None of the options are correct.

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Consider the diagram shown and answer the following questions; the radius of this circle is 6 inches.

a. Define how lines a, b, c, and d relate to circle P. (What special names do these lines have in relation to the circle?)
b. If the measure of angle OPS is 139°, what extra information would we need to calculate the measure of angle ORS using intersecting chords? Explain how we can use this information to calculate the angle.
c. Segment NS is 14 the length of segment TO. Explain how theorem 65 would allow us to calculate the length of segments RO, RS, RV, and RT.

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The additional information needed to calculate ORS are the measures of SPR and PSR

The special names of the lines

The lines are given as:

Lines a, b, c and d

The special names of the lines are as follows:

Line a: A secant. This is because the line divides the circle into unequal segmentsLine b: A tangent: This is because the line touches the circle at a point on the circumferenceLine c: A diameter. This is because the line divides the circle into equal segmentsLine d: A secant. This is because the line divides the circle into unequal segments

The additional information needed

The angle is given as:

OPS= 139 degrees

Start by calculating SPR using

SPR = 180- 139

SPR = 41 degrees

So, the additional information needed to calculate ORS are the measures of SPR and PSR

How to calculate the lengths RO, RS, RV, and RT

The theorem 65 is not stated.

So, the question cannot be answered