Mathematics High School

3. The sum of the second term and the ninth term of an arithmetic sequence is -5. The sum of the third and fourth terms of the same sequence is 7. Find the first term of the sequence.
​

Answers

Answer 1

Answer:

First term of the sequence is [tex]11[/tex]

Step-by-step explanation:

Let [tex]a[/tex] be the first term and [tex]d[/tex] be the common difference

We have

The sum of the second term and the ninth term of an arithmetic sequence is [tex]-5[/tex]

[tex]a+(2-1)d+a+(9-1)d=-5\\\\2a+9d=-5---eqn1[/tex]

The sum of the third and fourth terms of the same sequence is [tex]7[/tex]

[tex]a+(3-1)d+a+(4-1)d=7\\\\2a+5d=7---eqn2[/tex]

eqn 1 - eq2

[tex]4d=-12\\\\d=-3[/tex]

Substituting in eqn 1

[tex]2a+9\times -3=-5\\\\2a=22\\\\a=11[/tex]

First term of the sequence is [tex]11[/tex]

Related Questions

The number of students in a chess club decreased from 19 to 16. What is the percent decrease? Round your answer to the nearest percent. [The percent decrease is ___%.​]​

Answers

Answer:

it it went down 16%

Step-by-step explanation:

if you calculate it, 16 out of 19 points is 84%. this means that it went down 16%.

Answer:  16%

Explanation:

The decrease is 3 since 19-16 = 3. Divide this decrease value by the original count: 3/19 = 0.1579 = 15.79% = 16% approximately

How many problems of each point value are on the test? 10 problems worth 5 points and 25 problems worth 2 points 14 problems worth 5 points and 15 problems worth 2 points 16 problems worth 5 points and 13 problems worth 2 points 15 problems worth 5 points and 13 problems worth 2 points.

Answers

The question is an illustration of system of equations

There are 14 problems worth 5 points and 15 problems worth 2 points

The system of equations is given as:

[tex]x + y = 29[/tex]

[tex]5x + 2y = 100[/tex]

Make x the subject in [tex]x + y = 29[/tex]

[tex]x = 29 - y[/tex]

Substitute 29 - y for x in [tex]5x + 2y = 100[/tex]

[tex]5(29 - y) + 2y = 100[/tex]

Open brackets

[tex]145 - 5y + 2y = 100[/tex]

Evaluate like terms

[tex]145 - 3y = 100[/tex]

Collect like terms

[tex]- 3y = 100-145[/tex]

Evaluate like terms

[tex]- 3y = -45[/tex]

Divide both sides by -3

[tex]y = 15[/tex]

Substitute 15 for y in [tex]x = 29 - y[/tex]

[tex]x = 29 - 15[/tex]

[tex]x = 14[/tex]

This means that there are 14 problems worth 5 points and 15 problems worth 2 points

Read more about system of equations at:

https://brainly.com/question/14323743

(7−2)3×(24−11)? cause im in 6th grade lol

Answers

Answer:

(7−2)(3)(24−11)

=(5)(3)(24−11)

=15(24−11)

=(15)(13)

=195

Step-by-step explanation:

find the value of x ​

Answers

Can you give more details and whats the equation?

PLEASE HELP ASAP! I WILL GIVE BRAINLIEST JUST PLEASE HELP

Answers

Answer:

38cm squared

Step-by-step explanation:

What is the function of the line with a slope of 1/5
that goes through the point (-1,5)

Answers

Y= Mx+c

Y= 1/5x + c

Now you can find see by simply just replacing with the given points

5=1/5(-1)+c

C= 26/5

Final answer:

Y= 1/5x+26/5

Bella is training for a marathon. She can run 19 miles in 150 minutes. How many miles can she run in 5 hours?

Answers

Answer:

Step-by-step explanation:

The answer is 38 miles

A recipe requires 2 eggs for every 5 dozen cookies. At this rate, how many eggs are required for 30 dozen​

Answers

6 eggs (i think)







5x12=60 cookies require 2 eggs
30x12=360
360 divided by 60= 6

so six eggs

Answer:

12

Step-by-step explanation:

Theres 6 5's in 30. ( 5,10,15,20,25 and 30.)

There is 2 eggs in every 5 dozen cookies, ( 5d, 2, 10d, 4, 15d, 6, 20d, 8, 25d, 10, 30d, 12.) The d means dozen by the way...

I am so sorry if you use this and get it wrong!! I am not good at math!! And i am sorry, this is probably confusing >-<

5(x-2)-3= 5x-13
help me plz​

Answers

X has infinity solutions.

Can you help me answer this question?
Increase £184 by 3%

Answers

Answer:

189.52

Step-by-step explanation:

184 x 0.03

5.52

184 + 5.52

189.52

Answer:

184*1.03 = £189.52

Step-by-step explanation:

28 less than twice a number is equal to 6 . Find the number.

Answers

28 less than twice a number is equal to 6.Let the number be x.Therefore, by the problem[tex]2x - 28 = 6 \\ = > 2x = 6 + 28 \\ = > 2x = 34 \\ = > x = \frac{34}{2} \\ = > x = 17[/tex]

Answer:

x = 17

Hope you could get an idea from here.

Doubt clarification - use comment section.

How many fifths are there in the fraction 21/5?

Answers

Answer:

21

Step-by-step explanation:

1/5 x 21 = 21/5

4square plus 2power of xdivide by 2 equal to 16 what is the answer of this question​

Answers

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

We can solve this question by understanding what is first says. The expression tells us 4 square which is 16 plus to to the power of x and all that divided by two: [tex]16+2^{x} / 2 = 16[/tex]

Now we can solve for x:

1.  [tex]16 + 2^{x} = 32[/tex]

2. [tex]2^{x}=16[/tex]

3. [tex]x=4[/tex]

There are 222 red marbles in a box. Amit takes out 6 red marbles and replaces them with 12 blue
marbles. He continues doing this till all the red marbles are replaced with blue marbles.
Which of the following expressions gives the total number of blue marbles he put in the box?
A (222 + 6) = 12 B (222 - 6) + 12 C (222 - 6) + 12 D (222 + 6) x 12

Answers

Answer:

(222 - 6) + 12

Step-by-step explanation:

You put B and C as the same thing but the correct option is this because first you take away 6 (subtract 6) from the 222 marbles then you replace them with 12 (add 12).

What is the value of X?

Answers

Answer: It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable

PLEASE help


xº
520
38°
220°
X = degrees

Answers

Step-by-step explanation:

by complete angle

x+38+52+220=360

x+310=360

x=360-310

x=50

The ratio of the radii of two circles is 2:3. Find the ratio of their areas. If the area of the bigger circle is 3123 sq. cm, find the area of the smaller circle.​

Answers

Answer:

Your answer .

Step-by-step explanation:

PLEASE HELP!! the polynomial expression x(2x^2+15)(4x^2+5x+3 where x is in inches can be used to model the number of cubic inches of cement that will be needed for a new porch. The cement contractor used 2 for the value of x. Determine the dimensions in inches of the cement needed for the porch. Height(shortest length side) width(medium length side) and length(longest length side)

Answers

Answer:

height 2 incheswidth 23 incheslength 29 inches

Step-by-step explanation:

For x=2, the dimensions are ...

  height = x = 2 inches

  width = 2x² +15 = 2(2²) +15 = 8 +15 = 23 inches

  length = 4x² +5x +3 = (4x +5)x +3 = (4·2 +5)2 +3 = 29 inches

HELP PLZ I NEED THIS DONE ASAP

Answers

Answer:

Step-by-step explanation:

The answer would be -19

Given, y = -2[tex] {y}^{2} + 9y + 3 \\ = {( - 2)}^{2} + 9( - 2) + 3 \\ = 4 - 18 + 3 \\ = 7 - 18 \\ = - 11[/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

a video game system was on sale for $350. if the discount was 10% off, how much money did they take off the price?

Answers

Answer:

they took off 35$

Step-by-step explanation:

hope this helps

Answer:

$35

Step-by-step explanation:

10 divided by 350 = $35

PLEASE ANSWER QUICKLY 100 POINTS!!!! Simplify the expression below. (See picture below) What is the numerator of the simplified expression?

Answers

Answer:

13N+26/9n-26/3

Step-by-step explanation:

Answer:

13N+26/9n-26/3

Step-by-step explanation:

Mark as brainliest

C.J can shoot 36 shots in 3 minutes enter the number of shots C.J can shoot in 1 minute

Answers

Answer:

he can shoot 12 shots in 1minute

Step-by-step explanation:

3minutes = 36 shots

1 minute= 36 divided by 3 which is equal to 12

Suppose your family buys a "movie card" from a DVD

store that entitles you to rent 25 movies. You rent 3

movies per week.

Model the situation with a linear function.

Answers

y = 3x + 25, because I’m assuming that that you start by renting 25 movies.

The function that models this given situation is 3x = 25.

What is a function?

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, my family bought a movie card from a DVD store that entitles you to rent 25 movies.

Assuming no. of weeks to be x, therefore i can watch movies for

3x = 25 weeks at 3 movies rented each week.

learn more about functions here :

https://brainly.com/question/12431044

#SPJ5

I need help asap pls

Answers

Answer:

d? Kerana ianya tidak sama kaki

A line passes through the point ( -1,2 ) and has a slope of 6. Write an equation for this line.

Answers

Answer:

y = 6x+8

Step-by-step explanation:

y = mx+b

y = 6x + b

2 = 6(-1)+b

2 = -6+b

8 = b

y = 6x+8

What is 1/4 + 10/16?

Answers

I’m pretty sure ur answer would be 0.875

Answer:

[tex]\frac{7}{8}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}\ + \frac{10}{16}\[/tex]

[tex]= \frac{4}{16}\ + \frac{10}{16}\\[/tex]

[tex]= \frac{14}{16} \\[/tex]

[tex]= \frac{7}{8}[/tex]

hope it helps :)

mark brainliest!

Mike makes and sells skateboards. If he has a cost of $6,200 per year plus a cost of $15 per skateboard, how many skateboards must he sell in order to make a profit if each skateboard sells for $35?

Answers

Answer: 310

Step-by-step explanation:

35-15= 20

6200 / 20 = 310

Answer:310

Step-by-step explanation:divide 6200 by 20 and it gives you 310

Combine the like terms to create an equivalent expression
−4q-(-8p)+10

Answers

Answer:

Step-by-step explanation:

−4q-(-8p)+10

= -4q + 8p + 10.

(There are no like terms).


Solve the equation below for q.
V=1/4xq

Answers

Answer:

q=4v/x

Step-by-step explanation:

Select “Rational” or “Irrational” to classify each number.

Answers

1. rational 2. irrational 3. irrational 4. rational
Other Questions
What is the perimeter of the square? A. 17 ft B. 34 ft C. 48 ft. D. 68 ft. Hello People Look At The Image And Tell Me Is This True Or Not A56. Put in a right order1 2 3 4 5 6 7 8people some after famous name their children people.a) 2-1-5-6-7-3-4-8 b) 2-1-4-8-7-3-5-6c) 4-8-2-1-3-5-6-7 d) 2-4-1-5-7-8-6-357. Put in a right order1 2 3 4 5 6 names have some a meaning speciala) 3-1-2-4-6-5 b) 2-1-4-3-5-6c) 3-1-5-6-4-2d) 3-2-1-4-5-6 58. Make this sentence negativeI like British pop musica) I dont like British pop musicb) I like not British pop musicc) I like to not British pop musicd) I doesnt like British pop music59. Make this sentence negativeI am reading a good book at the momenta) I am not reading a good book at the momentb) I not am reading a good book at the momentc) I dont reading a good book at the momentd) I doesnt reading a good book at the moment60. Make this sentence negativea) I am going to have coffee after the lesson b) I am to not going to have coffee after the lesson c) I am not going to have coffee after the lesson d) I am going not to have coffee after the lesson 61. Make this sentence negativeI went out last night a) I went not out last night b) I not went out last night c) I didnt went out last night d) I didnt go out last night 62. Where you go for your last holiday?a) did b) were c) dod) have63. Find the odd wordJune- July -month -August Septembera) monthb) Junec) Julyd) September64. Find the opposite verb of arrivea) borrowb) lendc) leaved) go away65. Find the opposite verb of lend a) loseb) owec) borrowd) pass66. Find the opposite verb of repair a) mendb) breakc) crashd) fix 67. Find the opposite verb of missa) pullb) receive c) mendd) catch68. Find the opposite verb of pusha) pullb) putc) turnd) offer69. Give the synonym to the word appearancea) lookb) headc) disappeard) fashion70. Find the odd word 1 2 3 4 5Intelligent- banker- friendly-young-stresseda)1b)2c)3d)4e)5 How far will the snail be from the rock after 9 minutes? what do people do when they scared Which characteristics did early Japanese, Chinese, and Korean civilizations share?They were friendly nations that shared culture and customs.They were nations at war that shared a common religion.They were neighboring countries that shared a common history.They were countries with dissimilar culture and customs. LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given) Wildcat Pizza, Inc. is trying to decide whether to revise its target capital structure. Currently, it targets a 50-50% mix of debt and equity, but it is considering a target capital structure with 70% debt. Wildcat currently has 6% after-tax cost of debt and a 12% cost of common stock. The company does not have any preferred stock outstanding Can someone help me make sense of the problem. Provide an explanation and answer if at all possible The article Saving the Ganges contains both facts and opinions. Facts are statements that can be proved or verified to be true. Opinions are statements of belief or judgment that cannot be proved and that differ among people.List five facts the article tells you about the Ganges. For each fact, suggest some possible sources where the information might be found and verified. Loquan has 2 pieces of fabric, each measuring 3 & 1/4 feet long. How many feet of fabric does Loquan have in total? Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights come on at the same time Which of the following statements does NOT describe a river delta? A. sediment that builds up where a river meets a larger body of waterB. some are muddy and unstable; others are so big crops can grow on themC. earth scooped out that can form a lake or deep valleyD.where a flowing river empties its load at the mouth of a river Write the formula for the volume of a cone V=1/3 r^2 h in terms of h. Find the height h of a cone with volume V= 32 cm^3 and a radius r= 4cm PLEAS HELPA scuba diver descends in the water at a rate of 2312 feet per minute for 2.6 minutes. He immediately changes course when he sees a large fish and ascends at a rate of 28 feet per minute for 2 minutes.What is the scuba diver's position relative to sea level after the 4.6 minutes?Enter your answer as a decimal in the box. ft HELP!!! WILL MARK BRAINLIEST!!! +15 POINTS!! REAL ANSWERS ONLY PLEASE! Hello could someone help me I dont get this? Will name brainliest :D if correct answer please no links What is the name of the famous pass crossing the area where Kentucky, Tennessee, and Virginia meet? 4.indhomeJulio won a contest. His cash prize is given to him in the following way:On the first day, Julio will receive $0.25.For each successive day, the amount of money Julio receives doubles.a. Write an explicit formula to represent the amount of money, f (d), in dollars, Julio receives d days after the first day.b. How much money will Julio receive on the tenth day? what president was elected with an overwhelming majority of electoral votes in 1980?