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.
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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

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:

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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 :

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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).

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.

PLEASE HELP ASAP! I WILL GIVE BRAINLIEST JUST PLEASE HELP

Answers

Answer:

38cm squared

Step-by-step explanation:

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

Answers

Answer:

21

Step-by-step explanation:

1/5 x 21 = 21/5

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

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


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

Answers

Answer:

q=4v/x

Step-by-step explanation:

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

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

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).

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

Answers

1. rational 2. irrational 3. irrational 4. rational

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!

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

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 >-<

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

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:

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

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

I need help asap pls

Answers

Answer:

d? Kerana ianya tidak sama kaki

5(x-2)-3= 5x-13
help me plz​

Answers

X has infinity solutions.

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:

find the value of x ​

Answers

Can you give more details and whats the equation?

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

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

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

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]

(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:

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.

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