The first term of an AP is -7 and the ratio of the eight term to the third term is 7:1 calculate the common difference

Answers

Answer 1

Answer:

the common difference is 6.

Step-by-step explanation:

Given;

first term of an AP, a = -7

let the common difference = d

The third term is written as;

T₃ = a + 2d

The eight term is written as;

T₈ = a + 7d

The ratio of the eight term to third term = 7:1

[tex]\frac{T_8}{T_3} = \frac{7}{1} = \frac{a+ 7d}{a + 2d} \\\\7 = \frac{a+ 7d}{a + 2d}\\\\Recall, a = -7\\\\7 = \frac{-7+ 7d}{-7 + 2d}\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = \frac{42}{7} \\\\d = 6[/tex]

Therefore, the common difference is 6.


Related Questions

G
100%
Calculate the area of the parallelogram, in mề.
40 m
15 m
25 m
10 m
30 m
A. 250 m2
B. 450 m2
OC. 600 m²
OD. 900 m²
O E. 1000 m​

Answers

Answer:

C. 600 m²

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides and four angles) with two pairs of parallel sides. Opposite sides and angles of a parallelogram are equal to each other. Also, the diagonals are equal.

The area of a parallelogram is the product of its base and its height. It is given by the formula:

Area = base * height

We can see that for this parallelogram, the height = 15 m, the base = 40 m, hence:

Area = base * height = 40 m * 15 m = 600 m²

What is the perimeter of the house is c=5


I’m marking brainliest.

Answers

Answer:

132

Step-by-step explanation:

C=5

3c - 2 = 13

2c = 10

4c + 1 = 21

4c + 2 = 22

length = (3c- 2) + (4c + 1)

length = 13 + 21

length = 34

width = (4c + 2) + (2c)

width = 22 + 10

width = 32

Perimeter

p = 2l + 2w

p = 2*34 + 2*32

p = 68 + 64

p = 132

What are the solutions to the system of equations?
y=4x^2+6x−3
y=2x−3
Enter your answers in the boxes.
(_,_) and (_,_)

Answers

Answer:

(0, - 3 ) and (- 1, - 5 )

Step-by-step explanation:

Given the 2 equations

y = 4x² + 6x - 3 → (1)

y = 2x - 3 → (2)

Substitute y = 4x² + 6x - 3 into (2)

4x² + 6x - 3 = 2x - 3 ( subtract 2x - 3 from both sides )

4x² + 4x = 0 ← factor out 4x from each term

4x(x + 1) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = 0 : y = 2(0) - 3 = 0 - 3 = - 3 ⇒ (0, - 3 )

x = - 1 : y = 2(- 1) - 3 = - 2 - 3 = - 5 ⇒ (- 1, - 5 )

shira was riding the screamer when it broke down. her seat was 53 jorizontal feet from the central support pole. What was her seat's angle of rtation. Is there more tahn one possible solutions

Answers

Answer:

The possible solutions are 58 degree, 122 degrees, 302 degrees and 238 degrees

Step-by-step explanation:

Please see the attachment

From the figure, it is evident that

cos AOB = OB/OA = 53/100 = 0.53

Thus, cos-1 (0.53) = 58 degrees

AOB = 58 degree

Also, there are can be other values depending on the quadrants

COB = 180 -58 = 122 degrees

FOB = 360 -58 = 302 degrees

EOB = 180 + 58 = 238 degrees

A television shop sold a set for $799. It made a profit of $ 245.25. How much did the shop buy the television for ?

Answers

Answer:

the shop originally bought the television for $553.75

Step-by-step explanation:

this is because if they sold it for $799 and made a profit of $245.25 then you would subtract the profit from the price the TV sold for and you get $553.75

Minus $799 with $245.25 then you will get the answer.

Draw a box-and-whisker plot of the data. 37, 34, 26, 33, 38, 36, 30

Answers

I’m sorry this is messy but I hope this is right!! <3

I need help

An amount of $16,000 is borrowed for 8 years at 7.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Answers

Answer:

$28009.05

Step-by-step explanation:

Let us use the formula A = P(1 + r/n)^(nt)

Step 1: Convert 7.25 to decimal

[tex]7.25\% = 0.0725[/tex] in decimal form

Step 1: Percent means 'per 100'. So, 7.25% means 7.25 per 100 or simply 7.25 over 100. [tex]7.25 \div 100\\\\= \frac{7.25}{100}\\\\= 0.0725[/tex] If you divide 7.25 by 100, you'll get 0.0725 (a decimal number).

Step 2: Solve with the formula

[tex]A = 16000(1 + 0.0725)^8\\\\A= 28009.05[/tex]

Step 1: Add the numbers: [tex]1+0.0725=1.0725[/tex][tex]=16000\cdot \:1.0725^8[/tex][tex]=16000\cdot \:1.75056[/tex]Step2: Multiply[tex]=28009.05068[/tex]

A cylinder and its dimensions are shown below.
5 in.
3.5 in.
Benton is painting the lateral surface of this cylinder. Which expression will give him
the number of square inches that he will be painting?

Answers

Answer: 2π(1.75)(5)

Step-by-step explanation:

Hoped this helped

How many blocks with dimensions of a 3x1x1 can fit in a unit cube?
2
3
6
9

Answers

3 , hope this helps you

Which of the following shows an example of an arithmetic sequence?
5, 15, 45, 135, 405
-5, 0, 0, 0, 0
Olololo
-10, -19, -28, -37,-46
0,1,1,2,2
Determine the common difference:

Answers

Answer:

C) -10, -19, -28, -37, -46

Common difference: -9

Step-by-step explanation:

A) 5, 15, 45, 135, 405 is an example of a geometric sequence because each subsequent term is being multiplied by 3, which is the common ratio.

B) -5, 0, 0, 0, 0 is an example of a geometric sequence with a common ratio of 0 because each subsequent term is being multiplied by 0.

C) -10, -19, -28, -37, -46 is an example of an arithmetic sequence because each subsequent term is subtracted by 9, which is the common difference.

D) 0, 1, 1, 2, 2 is neither a geometric nor arithmetic sequence because the sequence shows no pattern that follows that of the two possible sequences.

Solve the equation. x/3=15 Shown work.

Answers

Answer:

45

Step-by-step explanation:

x/3=15

Mutiply each side by 3

x=45

[tex]\boxed{x\:=\:45}[/tex] ✅

Step-by-step explanation:

[tex] \frac{x}{3} = 15 \\ ✒ \: x = 15 \times 3 \\ ✒ \: x = 45[/tex]

To verify:-

[tex] \frac{x}{3} = 15 \\ ✒ \: \frac{45}{3} = 15 \\ ✒ \: 15 = 15 \\ ✒ \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

find the length of the diagonals of rectangle QRST

Answers

Answer: 11: 26

12: 111

Step-by-step explanation:

Answer:

11:

since diagonal are equal of rectangle

QS=RT

4x+6=6x-4

6+4=6x-4x

2x=10

x=10/2

x=5

now

diagonal :4x+6=4*5+6=26

12.

again

QS=RT

9x+12=11x-10

12+10=11x-9x

2x=22

x=11

now

diagonal=9*11+12=99+12=111

Evaluate (2x + 3) + ( x- 5) show answer pls

Answers

Step-by-step explanation:

2x +3 +x-5

3x+3+(-5)

3x +(-2)

x= -2÷3

x=-6

HOPE IT HELPED

What would be the surface area?

Answers

Answer:

7&2 = 49

49 x 3.14 x 2(there are two circles) = 307.72

Now we find the lateral surface area, we need to find circumference first:

2 x 3.14 x 7 = 43.96

Now we need to multiply by the height:

43.96 x 11 = 483.56

Now lets add our areas:

483.56 + 307.72 = 791.28 m^2 is your answer.

What is the length of the missing leg?

Answers

Answer:

a = 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a leg b is another leg c is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

a = a

b = 8

c = 10

Step 2: Solve for a

Substitute in variables [Pythagorean Theorem]:                                            a² + 8² = 10²Evaluate exponents:                                                                                         a² + 64 = 100[Subtraction Property of Equality] Subtract 64 on both sides:                      a² = 36[Equality Property] Square root both sides:                                                    a = 6

Santiago buys a new television for $989.76. If
the sales tax rate is 8.75%, what is the total cost
of the television?

Answers

Answer:

$1076.36

Step-by-step explanation:

The full price before tax can be represented by 1.00($989.76), and the 8.75% tax by                                                                       0.0875($989.76)

which can be combined to obtain the total cost:  (1.0875)($989.76) = $1076.36

Nine chips numbered 1 through 9 are placed in a box and mixed. Margie selected one chip from the box. What is the probability that Margie selected a chip that is a multiple of three?
6/3
b.) 1/2
c.) 2/3
d.) 1/3

Answers

Answer:

1/3

Step-by-step explanation:

3 is a multiple of 3 itself so that's 1. 6 is also a multiple of 3 so that's 2 out of 6 in other terms 2/6. 2/6 simplified is 1/3 so he also has 1/3 of a chance of rolling a digit that is a multiple of 3.

If a function is defined by the equation y=-5x+1 and the domain is the set {-2,0,2,4},
which set below represents the range of the function?
(1) {11, 12, 13, 14}
(3) {-10, -1,9,19)
(2) {-19, -9,1,10)
(4) {51, 53, 55, 57)

Answers

A

Identify the input values.

Since there is an even root, exclude any real numbers that result in a negative number in the radicand

The solution(s) are the domain of the function.

Mark Me Brainest

I don’t know how to do this

Answers

Answer:

x-10

Step-by-step explanation:

help plzzzz i need to find the volume of the cone

Answers

Answer:

2h3-r5

Step-by-step explanation:

first 3-2=5

then 2h3-r=2h3-r5

finally 2h3-r5

Answer:

3.28653¯V7h

Step-by-step explanation:

Here’s the revenue and expenses for the month. Calculate whether Mia had a profit or loss

Answers

Answer:

300

Step-by-step explanation:

subract costs from revenue

Suppose the cost of electricity is $0.03 for each kilowatt-hour. Carlos's house runs on 11.14 kilowatt-hours a day. Find the cost of electricity for Carlos's house in one day.

Answers

Answer: I think the answer is $33.42

Explanation: If it’s $0.03 for every hour and there is only 11.14 hours used a day just multiply 11.14 by .03 and you get .3342 then you move the decimal over 2 spaces to get 33.42

Please help what’s 6,7,8.

Answers

Answer: 7 is 1/8, 8 is 2/8 or 1/4

Step-by-step explanation:

Learning task 1.
Look around inside your house, illustrate five (5) thigs which represents a circle

i will make you brainlest if u answer this properly

Answers

Plate, bowl, pan, pot, cup

How do I do this please help

Answers

Answer:

C) 4,0

Step-by-step explanation:

Basically to find zeros you set up the expression equal to zero.

First pair is (0,0) they derived this by setting the leftmost x to 0 so x=0, this meant that when x was plugged back into the equation y = x(x-4) the y value we got out was 0 because y = 0 (0-4) = 0, thus the pair (0,0).

For second pair, we set up x-4= 0, solve this to get x = 4 (add 4 to both sides). Now plug this back into full equation y= 4 (4-4)= 0, you get y=0 and your ordered pair is (4,0) which is the second pair of zero.

Zero are x-intercept where y is zero which is the main reason why we setup x=0 or x-4=0 to start with.

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[answer]  

»»————- ★ ————-««  

Here’s why:  

According to the question, the factored form of the given quadradic expression is: [tex]x(x-4)[/tex].I have graphed this on a graphing program.

⸻⸻⸻⸻

When graphed, the parabola passes the points (0,0) and (4,0). They are the zeros.

⸻⸻⸻⸻

Option C (4,0) would be the other 'zero'.

⸻⸻⸻⸻

See graph attached.

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

1/2 divided by 4 =__

Answers

Answer: 0.125
1/2 dived by 4 = 0.125

Answer:

1/2 divided by 4 = 1/8 or 0.125

Step-by-step explanation:

1/2 divided by 4

(1/2) ÷ 4

= 1/2 × 1/4

= 1/8 or 0.125

There are 250 students in a class the ratio of boys to girls is 3:2 how many boys are there?

Answers

Answer:

total no of children = 250

let no.of boys be = 3x

let no.of girls be = 2x

equation = 3x+2x= 250

              = 5x= 250

             = x= 250\5

             = x= 50

so, no,of boys = 3x = 3x50 = 150

and no,of boys = 2x = 2x50 = 100

heres ur ans ,

hope it does help u !

if so plz mrk the brainliestt !!!!!

Find the value of x.

Answers

Answer:

70.86 degrees

Step-by-step explanation:

cos x = adjacent side / hypotenuse

= 2/6.1 = 0.32787

x = 70.86.

Answer:

x ≈ 70.9°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2}{6.1}[/tex] , then

x = [tex]cos^{-1}[/tex] ([tex]\frac{2}{6.1}[/tex] ) ≈ 70.9° ( to 1 dec. place )

PLS HELP ME!!!!!!!!!!

Answers

Answer:

1)  yes, SAS

2)  yes, AAS

3)  yes, SAS

4)  not enough information to know

Step-by-step explanation:

Factor and find the zeros of the relation.
(c.) y = 30x^2 + 44x + 16
(d.) y = 10x^2 +60x + 80

Answers

Answer:

Step-by-step explanation:

c.

y= 30x² +44x +16

factor

y= 2 (15x² +22x +8)

find zeros

15x²+22x+8=0

ax²+bx+c=0

x= (-b±√(b²-4ac))/2a

x= -22±√484-480/30 = -22±2/30 = -11±1/15

there are 2 zeros x= -10/15 ; x= -12/15

d.

y= 10x² +60x +80

factor

y= 10(x²+6x+8) = 10( x+2)(x+4)

finding zeros

x+2 =0 so x= -2

x+4 =0 so x= -4

there are 2 zeros x= -2; x= -4

Other Questions
An average of 20 pears were sold from Monday to Friday. After the sales on Saturday and Sunday, the average pears sold per day were increased to 25. How many pears were sold on Saturday and Sunday? Select the correct answer.All of the following are questions to research when evaluating supplements except:A. How was exercise performance or changes in body composition evaluated?B. Was a placebo used?C. Do other bodybuilders use this supplement?D. Were the subjects randomly assigned to the treatments? simile, metaphor or personification we are all dressed in down jackets and vests, so we collide and roll like bumper cars at the state fair 18. The effect of the diction of jimmy Carters speech is to make the audience feel that they should _____. A. Feel reassured B. Take action C. Ignore the crisis D. Not worryE. Mourn HELP FAST PLEASEEEEE Situation 1 Booum !!Mathieu et Anita sont fans de football et notamment de l'quipe lyonnaise. Ce soir ilsregardent un match qui oppose leur equipe preferee a l'quipe de Montpellier. Ils sonttous les deux trs excits surtout depuis que leurequipe mene 2 buts a 0 Au momentde la mi-temps, ils sont certains de la victoire de leurs champions. Ils profitent de cetteinterruption pour discuter du match mais sont surpris par une violente deflagrationLa television neuve d'Anita vient d'exploser. Les dommages sont importants. Ils onttous les deux des morceaux de verres incrusts dans le visage et sur les brasrexplosion a endommag le mur qui separait le salon de la cuisine et le home cinemaest pulverise. Ils sont dsempares Que faire ? Comment obtenir reparation ? Peuventils demander reparation au fabricant de la television?Rappelez et qualifiez juridiquement les faitsIdentifiez les pretentions des partiesPresentez l'argumentation juridique que pourraient mobiliser Mathieu et Anita d'unepart, le fabricant d'autre partJustifiez l'intert du regime special de responsabilit concernant les produitsdefectueux pour les consommateurs Plz help me well mark brainliest if correct!!.. Ali bought his mom 2 dozen (24) of roses. 1/3 of them are red and the rest are pink. How many are pink I WILL REWARD BRAINLIEST Can someone PLEASE help me with this? I will give brainliest The costs and revenues associated with two alternatives are listed below: Alternative 1 Alternative 2 Projected revenue $ 100,000 $ 125,000 Unit-level costs 20,000 30,000 Batch-level costs 20,000 25,000 Product-level costs 15,000 15,000 Facility-level costs 10,000 10,000 Which alternative should be selected based on this information What is the 18th term of the arithmeticsequence 2,-2.-6.-10....?F-72H -68WG -70J -66 2 Find the circumference and area of the pizza. Use 3.14 for pi. Round your answer to the nearest hundredth 13 in. The circumference of the pizza is Whats is the theme of road not taken by Robert frost n whats details in the text develop this theme Which of the following components are part of the complete blood count assay? Discuss how Edwin Arlington Robinson's use of language and imagery affects the meaning of "AuntImogen." Cite evidence from the poem to support your position. Your response should be at least twohundred words.Click here to access the text of the poem. ---------- control sets the price below the market equilibrium in order to make products more affordable. Geometry/// find the surface area of the square pyramid if the height of each triangular face is 20 m and the length of each side of the base is 19 m Find what is x for that angle? 12(x-2) + 3x = 1/3(x+12) + 10x step by step solve plz