Mathematics High School

Find the number of terms, n, in the arithmetic series whose first term is 13, the common difference is 7, and the sum is 2613.
A26
B27
C23
D32

Answers

Answer 1

Answer:

A

Step-by-step explanation:

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{n}{2}\left(a + x_n\right)[/tex]

Where n is the number of terms, a is the first term, and x_n is the last term.

We know that the initial term a is 13, the common difference is 7, and the total sum is 2613. Since we want to find the number of terms, we want to find n.

First, find the last term. Recall that the direct formula for an arithmetic sequence is given by:

[tex]x_n=a+d(n-1)[/tex]

Since the initial term is 13 and the common difference is 7:

[tex]x_n=13+7(n-1)[/tex]

Substitute:

[tex]\displaystyle S = \frac{n}{2}\left(a + (13+7(n-1)\right)[/tex]

We are given that the initial term is 13 and the sum is 2613. Substitute:

[tex]\displaystyle (2613)=\frac{n}{2}((13)+(13+7(n-1)))[/tex]

Solve for n. Multiply both sides by two and combine like terms:

[tex]5226 = n(26+7(n-1))[/tex]

Distribute:

[tex]5226 = n (26+7n-7)[/tex]

Simplify:

[tex]5226 = 7n^2+19n[/tex]

Isolate the equation:

[tex]7n^2+19n-5226=0[/tex]

We can use the quadratic formula:

[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 7, b = 19, and c = -5226. Substitute:

[tex]\displaystyle x =\frac{-(19)\pm\sqrt{(19)^2-4(7)(-5226)}}{2(7)}[/tex]

Evaluate:

[tex]\displaystyle x = \frac{-19\pm\sqrt{146689}}{14} = \frac{-19\pm 383}{14}[/tex]

Evaluate for each case:

[tex]\displaystyle x _ 1 = \frac{-19+383}{14} = 26\text{ or } x _ 2 = \frac{-19-383}{14}=-\frac{201}{7}[/tex]

We can ignore the second solution since it is negative and non-natural.

Therefore, there are 26 terms in the arithmetic series.

Our answer is A.

Related Questions

IF ANYONE CAN ANSWER THESE 2 QUESTIONS I WILL GIVE YOU BRAINLIEST AND LOVE YOU FOREVER. SERIOUSLY, ILL NEVER FORGET U <3

Answers

Answer:

3. 314 student and 226 adult

4. x = 6.5, y = -0.5

Step-by-step explanation:

3. First we will take our information and make a system of equations:

[tex]2.4a+1.25s=934.9[/tex]

[tex]a+s=540[/tex]

[tex]a[/tex] is the number of adult tickets sold and [tex]s[/tex] is the number of student tickets sold.

From the second equation we can rearange it to be:

[tex]a=540-s[/tex]

Then we can plug in our new value of [tex]a[/tex] to our first equation

[tex]2.4(540-s)+1.25s=934.9[/tex]

[tex]1296-2.4s+1.25s=934.9[/tex]

[tex]1.15s=361.1[/tex]

[tex]s=314[/tex]

We can then find [tex]a[/tex] by plugging in s to our second equation

[tex]a+314=540[/tex]

[tex]a=226[/tex]

4. It is mostly solved already. We can take the value of y from the first equation and plug it into the second to get:

[tex]3x -5(-5x+32)=22[/tex]

[tex]3x+25x-160=22[/tex]

[tex]28x=182[/tex]

[tex]x=6.5[/tex]

Then plug our value of x into the first equation to get:

[tex]3(6.5)-5y=22[/tex]

[tex]19.5-5y=22[/tex]

[tex]5y=-2.5[/tex]

[tex]y=-0.5[/tex]

Divide 120ml into the ratio 3:7

Answers

Answer:

Step-by-step explanation:

sum of ratio=3+7=10

total=120 ml

first part=3/10×120=36 ml

second part=7/10×120=84 ml

Which table represents a linear function?

Answers

Answer:

First Graph (1-5 2-10)

Step-by-step explanation:

10÷2=5

3÷15=5

4÷20=5

5÷25=5

4. Match these equation balancing steps with the description of what was done in each step.
Step 1:
12x−6 =10 6x−3 =5
Step 2:
6x−3 =5 6x =8
Step 3:
6x =8 x =43
Descriptions to match with each step:
A: Add 3 to both sides
B: Multiply both sides by 16
C: Divide both sides by 2

Answers

Answer:

step 1 - C.

step 2 - A.

step 3 - B.

3x^3-4x^2-28x-16 divided by 3x+2

Answers

Answer: x^2 - 2x - 8

a large bottle of juice contains 500 milliliters of juice. a medium bottle contains 70% as much juice as the large bottle. how many milliliters of juice are in the medium bottle.(can you include a number line? thanks!)

Answers

Answer:

350 millilitres

Step-by-step explanation:

70/100×500=350

Evaluate the determinate:

I 5 3 3 I
I -4 -5 1 I
I 5 3 0 I
Please show work... I will give Brainliest.!

Answers

Answer:

39

Step-by-step explanation:

detailed explanation showed in the diagram above

Help me on 5 and 6 plssssss

Answers

For number 5, you just plug -2 into x. We now have g(-2)=3(-2)+1. This gives us g(-2)=-5.

This is the same for 6. h(-6)=-3(-6)-2. This gives us h(-6)=16.

The answer is g(-2)=-5. The other answer is h(-6)=16.

how much would it cost for a 9-hour repair

Answers

it would depend on what someone would be repairing wether it be a computer repair, car repair, plumbing etc.
regardless 9 hours is a very long time so i would not expect it to be too cheap.
hope this helps

please help me !!! omaths student see the attached question​

Answers

Answer:

34.64m

Step-by-step explanation:

Tan30= x(height) /60

x=60tan30

=34.64m

write an expression describing all the angles that are coterminal with 266°

Answers

Answer:

-814°, -454°, -94°, 266°, 626°. Did you mean like that?

Sara is saving up to purchase a small T.V.
She has saved $80, which is 64% of the total
cost of the television. How much does the
television cost?

Answers

Answer:

You got this just keep trying

Step-by-step explanation:

Answer:

It might be 80

Step-by-step explanation:

first you put 64% and $80 as a fraction. 64%/$80. Then next to the fraction, you put x/100. Then you cross multiply. 64 times 100 is 6400. 6400 divided by 80 is 80. Therefore, the answer is 80. Hope this helps!

what is the number of terms for 1000z + 800y​

Answers

Answer:

2 terms

Step-by-step explanation:

hope this helps! :D

have a MIRACULOUS day!! <3

What are two equivalent fractions for 1/2 ?

Answers

The fractions which are equivalent to 1/2 are 2/4, 3/6, 4/8, 6/12 etc. Equivalent fractions have same value in reduced form.

How is the key event in this paragraph illustrated?

Answers

I think C because it dose seem to be showing sometime of an historical event. But of course I could be wrong.

Find the unknown number in the equation 16 x 7 = 28 x n. 4 7 8 10

Answers

Answer:

the answer is 4

Step-by-step explanation:

16×7= 112

112÷28=4

(4+14) divided by 9 ???????

Answers

Answer:

2

Step-by-step explanation:

4+14=18

18/9=2

The answer is 2, 14+4=18 and 18 divided by 9 is 2.

Help help help help help

Answers

10pi is the circumference

The area of a square depends on the length of its sides. This can be written in function notation as a(s). What is the best interpretation of a(4) = 16?

A. The area of a square is always one-fourth of the side length.

B. The area of a square is always four times the side length.

C. A square with sides 4 units long has an area of 16 square units.

D. A square with sides 16 units long has an area of 4 square units.​

Answers

Answer:

option d is the right answer

Given the probabilities below, for what P(A) are events A and B independent? P(B)=0.5 P(A and B)=0.25.

A) 0.75
B) 0.5
C) 0.25
D) 0

Answers

the answer is 0.75, ive had this before

You have to show work​

Answers

Answer:

your answer is right -2/3

Step-by-step explanation:

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{10 - 4}{ - 6 - 3} = \frac{6}{ - 9} = - \frac{2}{3} [/tex]

(Topic: Vectors) - Prove that ADE is a straight line

Answers

Answer:

Because the angle is a 180 degree angle.

Step-by-step explanation:

Answer:

If it looks straight, well then i would guess that it would be straight. You can also put it against a ruler and see if it matches up. if it does not then it is not a line.

Step-by-step explanation:

hope this helps

pls brainliest

In the diagram below, TU is parallel to Q R. If
RU = 12, TU = 25, and QR = 40, find the length of
SU. Figures are not necessarily drawn to scale. State
your answer in simplest radical form, if necessary.

Answers

Given that ΔQSR and ΔTSU are similar triangles, therefore, the length of SU is: 20.

Recall:

When two triangles are similar, the ratio of their corresponding side lengths are equal.

Thus, given the figure attached below, ΔQSR and ΔTSU are similar to each other.

Therefore:

SR/SU = QR/TU

SR = RU + SU = 12 + SU

SU = ?

QR = 40

TU = 25

Plug in the values

[tex]\frac{12 + SU}{SU} = \frac{40}{25}[/tex]

Cross multiply

[tex](12 + SU)25 = 40(SU)\\\\300 + 25SU = 40SU\\\\300 = 40SU - 25SU\\\\300 = 15SU\\\\\mathbf{SU = 20}[/tex]

Learn more about similar triangles on:

https://brainly.com/question/11850540

is the change of rate always constant

Answers

In mathematics, a constant rate of change is a rate of change that stays the same and does not change.

Ok here’s another question

Answers

Answer:

20 necklaces

Step-by-step explanation:

If Elizebeth is starting off w/10 necklaces we can find on the graph that $10 buys an additional 10 necklaces. Now knowing that information we can add 10 necklaces to our original necklaces and get 20 necklaces. We can also find that our unit rate of change is 10 dollars : 10 necklaces or 1 dollar : 1 necklace. Knowing this can help us solve future problems like how many necklaces can Elizebeth get for x dollars.

hellp plsssss

I would love it if you did!

Answers

Answer:

1050

Step-by-step explanation:

bylon 3 x 68 =204

wool (3x3) x 94 =846

204 + 846 = 1050

he spent 1050 $ on materials

Answer:

$846

Step-by-step explanation:

I think it is sry if u got it wrong

HELP PLEASE. The product of the roots of the equation ax^2+x-24=0 is equal to -2 2/5. Find the value of a in the equation.

Answers

The value of a in the equation is 10

The root of the equation is determined using the equation shown below:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Given the quadratic equation ax^2+x-24=0;

a = ab = 1c = -24

The product of the quadratic equation is c/a

Product = c/a

- 2 2/5 = -24/a

-12/5 = -24/a

-12a = 5 * -24

-12a = -120

a = 10

Hence the value of a in the equation is 10

Learn more about quadratic equation here: https://brainly.com/question/17210919

Compare to ax^2+bx+c

b=1c=-24a=a

Product of roots=c/a

ATQ

[tex]\\ \tt\hookrightarrow \dfrac{c}{a}=-2\dfrac{2}{5}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{-24}{a}=\dfrac{-12}{5}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{24}{a}=\dfrac{12}{5}[/tex]

[tex]\\ \tt\hookrightarrow 12a=120[/tex]

[tex]\\ \tt\hookrightarrow a=10[/tex]

what is y-2=4(x+1) in slope intercept form​

Answers

Answer: y=4x+3

Step-by-step explanation: First, lets clean this expression up.

y - 2 = 4(x+1)

Multiply 4 times x and 4 x 1.

y-2=4x+1

add 2 to both sides.

Finally, you get y=4x+3.

Remember that 4 is your m (slope), and b (y-intercept). If you were graph this, it would increase to the right. You graph your intercept 3 on the positive y-axis at (0,3) and since your slope is 4x, you go 4 units up and 1 unit to the right and from there, you get the graph of the given equation.

Hope this explanation helps.

Karen's mother gets a restaurant bill for $25 she has a coupon for 15% off after the discount is applied she adds 20% as a tip what is the total after the discount and tax

Answers

$25.50

step by step explanation: 15% means u can multiply it by .85

so .85x25
= $21.25

the next step is to find the tip

to do this you do

$21.25+ (21.25x .2)

final: $25.50

hope this helps

Answer:

$25.50

Step-by-step explanation:

with a 15% off coupon she is paying 85% of the $25 bill, which is:

.85 x 25 = 21.25

if she adds a 20% tip on 21.25 then we can do the following:

1.2 x 21.25 to get the total after the discount and with tax:

$25.50

4000 families were randomly selected for a survey. 50% of them read the newspaper in nepali language, 45% read it in English language and 25% read in neither of these languages. How many families read the newspaper in both the languages? Also find the number of families who read exactly one of these papers.​

Answers

Answer:

2000 families read the newspaper in the Nepali language.

1800 families read it in the English language.

3800 families read the newspaper in both.

Step-by-step explanation:

#1. individual

convert % to decimal ( x ÷ 100 )

0.5 x 4000 = 2000

0.45 x 4000 = 1800

#2. together

2000 + 1800 = 3800

OR

50 + 45 = 95

95 ÷ 100 = 0.95

0.95 x 4000 = 3800

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