Q6. The first three terms of an arithmetic series are 60, 4p and 2p-6 respectively (a) Show that p= 9 (b) Find the value of the 20th term of this series. (c) Prove that the sum of the first n terms of this series is given by the expression 12n (6 - n)

Answers

Answer 1

Answer:

p=9

t20=516

Step-by-step explanation:

a

4p-60=2p-6-2p

6p=54

p=9

b

a=60.. d=24

t20=a+19d

=60+19×24

=516

c

Sn=12.5+12.3+12.1

=12n(6-n)


Related Questions

) What is the slope and y-intercept of this line?

y = –4x + 7



Question 8 options:

slope: 4, y-intercept: –7


slope: –4, y-intercept: 7


slope: 7, y-intercept: –4


slope: -7, y-intercept: -4

Answers

Answer:

slope: -4 y intercept 7

Step-by-step explanation:

when using the formula y=mx+b

The slope is the fraction for m -4/1 or -4.

The y intercept is 7 and thats where the graoh starts.

Answer: slope: -4, y-intercept: 7

Step-by-step explanation: I just took the test :)

25 PTS Help pls
If a single card is drawn from a standard 52-card deck, what is the probability it is a diamond or a face card (Jack, Queen, or King)?
A. 11/26
B. 2/7
C. 1/4
D. 2/52

Answers

Using it's concept, it is found that the probability that the card is a diamond or a face card is given by:

D. 25/52

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A standard deck has 52 cards, of which 13 are diamond and 12 are face, hence:

p = (13 + 12)/52 = 25/52.

Which means that option D(25/52) is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

The diagram shows the shape of Jane's backyard find the area of Jane's backyard.

Answers

Answer:

1065 square feet

Step-by-step explanation:

seperate the composite shape into two rectangles:

Calculate the area of shape 1:

A=bh

To get the base 55-20= 35

35x15 = 525


calculate the area for shape 2:

A=bh

20x27 = 540


525+540= 1065

Answer:

1065 square feet

Step-by-step explanation:

Area of backyard

Left rectangle + Right rectangle27 x 20 + 15 x (55 - 20)540 + 15 x 35540 + 5251065 square feet

can i have help with this

Answers

Answer:

Option D

Step-by-step explanation:

Square:

     Side = 25 ft

    Area of square = side * side

                              = 25*25

                              = 625 square ft

Area of semicircle:

diameter = 25 ft

r = 25/2 = 12.5 ft

[tex]\boxed{\text{Area of semicircle =$ \dfrac{\pi r^{2}}{2} $}}[/tex]

                              [tex]=\dfrac{3.14 * 12.5*12.5}{2}\\\\\\= 245.3 \ square \ ft[/tex]

Area of the shaded region = area of square - area of semicircle

                                              = 625 - 245.3

                                              = 379.7 square ft

Awnser ASAP please
Tom buys a condominium for $42,600. He makes a down payment of 15%, and pays these closing costs: survey $225; inspection, $110; mortgage fee, $852; legal fees, $450; title insurance, $286. What is the amount of the down payment? What are the total closing costs? How much will he need to bring to the closing (down payment + closing costs)?





Kerri takes out a mortgage for $55,000 at 9% for 25 years. What are her monthly payment, the total amount paid, and the cost of the mortgage?






Fred takes out a mortgage for $60,000 at 7% for 20 years. What are his monthly payment, the total amount paid, and the cost of the mortgage?






The Roger’s applied for a $70,000 mortgage for 30 years at 9%. Since they had a good credit history, they actually qualified for a 25 year mortgage at 7%. What were the payments on the 9% loan, and the 7% loan? What do they save monthly? What is the total repayment on the 9% loan and the 7% loan, and what do they save over the life of the loan?

Answers

Answer:

I got you with Question 3 and 4 my guy.

3) He would need 12 and it would cost 50k

4) 9% payments: $563.24, 7% payments: $494.75. Monthly savings: $69.49, 9% total repaid: $2022,764.90 , 7% total repaid: $148,423.63 , Savings: $54,341.27

The Tom will need to bring to the closing $54,341.27

He would need 12 and it would cost 50k.

We have given that,

Tom buys a condominium for $42,600.

He makes a down payment of 15% and pays these closing costs to survey $225.

What is the meaning of a down payment?

The meaning down payment is a part of the full price paid at the time of purchase or delivery with the balance to be paid later.

Inspection, $110; mortgage fee, $852; legal fees, $450; title insurance, $286

9% payments: $563.24

7% payments: $494.75.

Monthly savings: $69.49

9% total repaid: $2022,764.90  

7% total repaid: $148,423.63

Savings: $54,341.27

To learn more about the savings visit:

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If m(arc RU) = (16x – 13)° , m(arc SU) = (11x – 24)°, and m∠STU = (3x + 1)°, find m(arc SU).​

Answers

Answer: 75 degrees

Step-by-step explanation:

The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges $2 for the first time they service your lawn, and the price will multiply by a factor of 0. 85 every week thereafter. Green Thumbs charges $350 for the first time they service your lawn, and then charges an additional $30 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?

Answers

The cost-savings if the Yert Family chooses the cheaper company is: $450.50

How do you determine the cheaper company?

First, we determine the cost of the service of each company. Comparing that will give us an idea of the company whose service is cheaper.

Second, we subtract the lower sum from the higher. This gives us the cost savings by the Yert Family.

Step 1

Expressing the payment plan for Green Lawns, we have:

First week= $2
Second week = (2 + (2*0.85) )  = 3.7

Third week= (3.7 + (2*0.85) ) = 5.4

Using the above cumulative method, we arrive at the series of payments due per week

The series of payment are given as follows:
2 + 3.7 + 5.4+7.1+8.8+10.5+12.2+13.9+15.6+17.3+19+20.7+22.4+24.1+25.8+27.5+29.2+30.9+32.6+34.3+36.0+37.7+39.4+41.1+42.8+44.5+46.2+47.9+49.6

= $799.50

Step 2

Expressing the payment plan for Green Thumbs, we have:

350 + (30*30) = $1,250



Step 3

Hence (assuming they go for Green Lawns) the cost savings will be:

$1,250.00 - $799.50 = $450.50

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What do we do to both sides of this equation to solve?

x−10=8
Question 2 options:

Subtract 10 from both sides


Add 10 to both sides


Multiply both sides by 10


Divide both sides by 10

Answers

Add 10 to both sides

Step-by-step explanation:

x-10 = 8

x - 10 + 10 = 8+ 10

x = 18

Step-by-step explanation:

Add 10 to both sides

or,x-10+10=8+10

or,x=18

Please answer this question.

Answers

Answer:

B

Step-by-step explanation:

given that x and y vary inversely then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition y is 24 when x is 8 , then

24 = [tex]\frac{k}{8}[/tex] ( multiply both sides by 8 to clear the fraction )

192 = k

y = [tex]\frac{192}{x}[/tex] ← equation of variation

when y = 18 , then

18 = [tex]\frac{192}{x}[/tex] ( multiply both sides by x )

18x = 192 ( divide both sides by 18 )

x = [tex]\frac{192}{18}[/tex] = [tex]\frac{32}{3}[/tex]

Answer:

Step-by-step explanation:

Write the inverse variation

y = k/x

Solve for k

y = 24

x = 8

y = k/x           Substitute the givens into this equation

24 = k/8        Multiply both sides by 8

8*24 = k

k = 192

Solve for x  when y = 18

y = k/x            Multiply both sides by x

xy = k             Divide by y

x = k/y

x = 192/18

x = 10 2/3       The answer is given as an improper fraction.

x = (10*3 + 2)/3

Answer: x = 32/3

help?
Alyssa is getting gas for her car. Her car’s 15-gallon tank has 1/5 a tank of gas left. If gas costs $2.699 per gallon, how much will she pay for gas, rounded to the nearest cent?

Answers

Answer:

$32.39

Step-by-step explanation:

She has a 15-gallon tank and it has 1/5 a tank of gas left (so about 3/15)

Because she needs to refill it and already has 1/5, she'll only need to pay for 4/5 a tank of gas (12/15).

So the equation should be 12 times $2.699.

12 × 2.699 = 32.388

Then, round to the nearest cent.

32.388 = $32.39

Hope this helped !

What is the value of x?
What is the value of y?

Answers

Answer:

Step-by-step explanation:

Use Pythagorean's theorem. The two shorter sides (6+x) and 20 are apart of a right triangles of a hypotenuse of (18+6). Therefore:

[tex](6+x)^2+20^2} =(18+6)^2[/tex]

[tex](6+x)^2+400 =576[/tex]

[tex](6+x)^2=176[/tex]

Take the square root of both sides:

[tex]6+x=\sqrt{176}[/tex]

[tex]x=\sqrt{176} -6[/tex]

Moving on to the smaller triangle, we can find the value of 'y' to be:

[tex]6^2+y^2=18^2[/tex]

[tex]y^2+36=324[/tex]

[tex]y^2=288[/tex]

[tex]y=\sqrt{288}[/tex]

I don’t understand this subject at all if you wold answer that would be a big help

Answers

Answer:

d is about 8.6 feet.

Step-by-step explanation:

We have similar triangles, so we can set up and then solve this proportion:

[tex] \frac{d}{10} = \frac{6}{7} [/tex]

[tex]7d = 60[/tex]

[tex]d = 8.6[/tex]

The admission fee at an amusement park is $ 1.75 $1.75 for children and $ 6.20 $6.20 for adults. On a certain day, 301 301 people entered the park, and the admission fees collected totaled $ 1350 $1350 . How many children and how many adults were admitted

Answers

Answer: I would say that you have to divide the children's cost and the total amount of money. you would do the same for the adults as well

1,350/1.75= 780 Children

1,350/6.20= 220 Adults

determine the oreadred pair for (-10,3) whenitn it has been reflected over the y-axis

Answers

Answer:

I determined it's cherry pie because the typical slice size allows 10 slices and that is enough for 10 people to enjoy it's goodness quite amazing

Given the following construction, which of the following can you now create?

Select ALL that apply.


options:

square


equilateral triangle


rhombus


the midpoint of segment AB


perpendicular bisector of segment AB

Answers

square is the correct answer

Yummy Cookies just opened a brand new cookie bakery, and sales are increasing every month!
In January, the baker made 10 chocolate chip cookies. In February, the baker doubled the January order, took 6 cookies home to his family, and sold the rest. If the baker continues to double the full amount and then brings 6 cookies home to his family, how many cookies will the baker sell in March and April?
Will mark Brainliest to the first answer!

Answers

Answer:

In March the baker will sell 34 chocolate chip cookies. In April he will sell 74 cookies.

Step-by-step explanation:

So first, we end up doubling the original amount of cookies from January for February which gets us 20 cookies, he takes 6 homes leaving us with 14. He continues to double the FULL amount so he doubles 20 for March which gets us 40, then we again take 6 away leaving us with 34. We do the same thing for April. Double 40 getting 80, take away 6 you get 74. Done.

20*2-6=34 40*2-6=74
March-34
April-74
I think this is it

What is 85% of 21?
I need to know for school because we're doing this project.

Answers

Answer:

85% of 21 is 17.85.

3 of 5
Find the midpoint of the line segment with end coordinates of:
(-3,-1) and (-4, 2)
Give coordinates as decimals where appropriate.

Answers

Answer:

(-3.5, 0.5)

Step-by-step explanation:

Midpoint Formula

M (x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)

Solving

M (x, y) = (-3 - 4 / 2, 2 - 1 / 2)M (x, y) = (-7/2, 1/2)M = (-3.5, 0.5)

Select the THREE expressions that are equivalent to 6x+ 1 - (3x - 1)

Answers

Se

please elaborate 9638x
3x + 26x + 1 + -3x - -16x + -3x + 1 + 1

please need help on = 0.35+0.6+____= 1

Answers

Answer:

0.59

Step-by-step explanation:

0.59 I think if I'm wrong correct me.

Which statement was made by the negative to indicate a bias in the survey data presented by the affirmative?
The survey did not ask for the students' opinions regarding their freedom of expression.
The survey was conducted by a uniform manufacturer that profits from schools requiring school uniforms.
The survey was performed in elementary schools, not in high school environments.
The survey only asked female school officials for their opinions, not male school officials.

answer B

Answers

Answer:

The survey was conducted by a uniform manufacturer that profits from schools requiring school uniforms.

Step-by-step explanation:

She can choose from 7 pairs of pants, 6 t-shirts, 7 sweaters or hoodies, and 2 pairs of shoes. How many different outfits does Kaylee have to choose from?

Answers

Answer:

So, there are seven choices, etc, so the equation is

7x6x7x2

because there are multiple ways

so, 588

Can someone explain how to get the answer, please? Thanks!

Answers

The mean is 10,

The median is 10,

And there is no mode.



The mean of a set of numbers is the sum divided by the number of terms,

7+15+12+6+10=50

There are 5 numbers in the set,

50/5=10.
10 is the mean.



Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers,

6, 7, 10, 12, 15,

10 is in the middle so it is the median.



The mode is the element that occurs most in the data set. In this case, all elements occur only once, so there is no mode.




Just so you don’t confuse the data with the group sets,

The actual data set is 7, 15, 12, 6, and 10

This data paired with score column or group set means that,

10 people got a score of 1-10
6 people got a score of 11-20
12 people got a score of 21-30
15 people got a score of 31-40
And 7 people got a score of 41-50 :)

The line graphed below has a slope of ____.

Answers

To find the slope, we must have two points

   --> Two points: (-3,1) and (-1, -5)

The slope's formula is -->  [tex]\frac{y2-y1}{x2-x1}[/tex]

(x1, y1) --> (-3,1)(x2, y2) --> (-1, -5)

So the slope = [tex]\frac{-5-1}{-1--3} =\frac{-6}{2} =-3[/tex]

The line graphed below has a slope of -3

Hope that helped!

What is the value of x? Your answer may be exact or rounded to the
nearest tenth.

Answers

91 because the one on the left tip and top equal the outside always!!! hope this helps!!

The value of x in the given figure is 91 degrees.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

We need to find the value of x in the given figure.

To find x, firstly we need to find the unknown interior angle.

By Angle sum property the sum of three angles of a triangle is 180 degrees.

a+54+37=180

a+91=180

Now subtract 91 from both sides

a=180-91

a=89 degrees.

Now let us find the value of x which is adjacent to 89 degrees.

The sum should be 180 degrees

a+x=180

89+x=180

Subtract 89 from both sides

x=91 degrees

Hence, the value of x in the given figure is 91 degrees.

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An account statement has a balance of 109 dollars and 75 cents. carl is balancing his checking account. after comparing the bank statement to his register, he notices an outstanding debit of $58.00. which shows the correct amount in carl’s checking account? $51.75 $109.75 $167.75 $221.87

Answers

The correct amount in carl’s checking account will be $51.75. Then the correct option is A.

What is subtraction?

It simply means to deduct something from the object or number of group, place, etc. Subtraction means to take away from the group or a number of objects.

An account statement has a balance of 109 dollars and 75 cents.

Carl is balancing his checking account.

After comparing the bank statement to his register, he notices an outstanding debit of $58.00.

Then the correct amount in carl’s checking account will be

→ 109.75 - 58 = $ 51.75

More about the subtraction link is given below.

https://brainly.com/question/4319655

Answer:

Step-by-step explanation:

a

order 130 inches, 4 yards, 10 feet from greatest to least

Answers

Answer:

Step-by-step explanation:

Before comparison can take place, these three measurements must be expressed in the same unit of measurement:

130 inches becomes 130/12 feet, or 10.83 ft;

4 yards becomes 4*3 feet, or 12 feet; qne

10 feet stays as is.  

It becomes obvious that the greatest measurement is 12 feet, followed by 10.83 feet, followed by 10 feet.

The ordered list from greatest to least is 4 yards, 130 inches, 10 feet.

What is Unit of Measurement ?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

First, we need to convert all the units to a common unit before we can compare them.

Let's convert them all to inches:

4 yards = 12 feet × 4 = 48 feet = 48× 12 inches = 576 inches

10 feet = 10 × 12 inches = 120 inches

Now we have: 130 inches, 576 inches, 120 inches

Ordering from greatest to least, we get:

576 inches, 130 inches, 120 inches

4 yards, 130 inches, 10 feet

Therefore, the ordered list from greatest to least is 4 yards, 130 inches, 10 feet.

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Sage borrowed $4500 from her parents to buy a new car. So far she has repaid $2740. If sage repays her parents $110 a month, how much time will it take her to pay back the full amount of the loan?

Answers

Answer:

16 months

Step-by-step explanation:

Hey there!

This would be the correct answer because first you need to subtract the amount she paid from the amount she owes.

[tex]4500-2740[/tex]

[tex]=1760[/tex]

After that divide that answer from 110

This is because she will be paying 110 each month

[tex]1760/110[/tex]

Once you calculate that you will get 16.

you leave your house and drive 7 miles north, then turn left and drive 24 miles west. how far are you from your house?

Answers

Now this question is a candidate for the Pythagorean Theorem :

According to the question (assuming that you're x miles away from your house) --

[tex]\implies{7}^{2} + {24}^{2} = {x}^{2} \\\implies625 = {x}^{2} \\\implies x = \sqrt{625} \\ \boxed{x = 25} [/tex]

(Rejecting x= - 25 because distance cannot be negative(atleast hypothetically))

What type of triangle is defined by the following set of side lengths
12, 8, 16
Question 3 options
Acute
Obtuse
Right
Not a triangle

Answers

The type of triangle defined by the following set of side lengths is an obtuse triangle

Properties of a triangle.

Triangles are 2-dimensional shapes with 3 sides and angles.

The triangle with the sides 12, 8 and 16 is considered a triangle since the sum of two of its sides is greater than the third.

The triangle is not right angle since the sum of its longest side is not equal to the sum of the square of other two sides.

This shows that the triaangle can either be acute or obtuse. Since one of the sides differes from the other by 8 units, hence one of its angles will be greater than 90 degrees.

This shows that the type of triangle defined by the following set of side lengths is an obtuse triangle

Learn more on obtuse triangle here: https://brainly.com/question/5023725

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