The seventh term of an arithmetic progression is equal to twice the fifth term. The sum
of the first seven terms is 84. Find the first term.

Answers

Answer 1

Answer:

a₁ = - 24

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₇ = 2a₅ , then

a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )

- a₁ - 2d = 0 → (1)

The sum to n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

Given [tex]S_{7}[/tex] = 84 , then

[tex]\frac{7}{2}[/tex] (2a₁ + 6d) = 84

3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )

2a₁ + 6d = 24 → (2)

Thus we have 2 equations

- a₁ - 2d = 0 → (1)

2a₁ + 6d = 24 → (2)

Multiplying (1) by 3 and adding to (2) will eliminate d

- 3a₁ - 6d = 0 → (3)

Add (2) and (3) term by term to eliminate d

- a₁ = 24 ( multiply both sides by - 1 )

a₁ = - 24


Related Questions

Are ratios 8:16 and 1:2 equal? Why?

Answers

Because 8/8=1 and 16/8= 2

Answer:

Yes, 8:16 and 1:2 are equal

Step-by-step explanation:

They are both equal to 1/2.

8/16 simplified is 1/2

You can multiply the numerator and denominator to get 8 / 16

1 x 8 = 8

2 x 8 = 16

8/16

find the area of a Semicircle whose radius is 3.5 cm (take pi as 22/7

Answers

Answer:

TSA=115.5cm²

Step-by-step explanation:

T.S.A=3πr²

Given r=3.5cm

eq.

3×22/7×3.5×3.5

=3×22×0.5×3.5

=115.5cm²

Answer:

[tex]19.25cm^{2} \\[/tex]

Step-by-step explanation:

Formula

[tex]\frac{\pi r^{2} }{2}[/tex]

Solve

[tex]\frac{(\frac{22}{7} )(3.5cm)^{2}}{2}= \frac{(\frac{22}{7} )(3.5cm)(3.5cm)}{2}=\frac{((\frac{22}{7} )(3.5cm))(3.5cm)}{2}=\frac{(\frac{77}{7}cm)(3.5cm) }{2}[/tex]=

[tex]\frac{(11cm)(3.5cm)}{2}=\frac{38.5cm^{2}}{2}=19.25cm^{2}[/tex]

What Is the value of p? 33°

Answers

Answer:

90 - 33 = 57 57is the answer

Step-by-step explanation:

Answer:

p=57 degrees

Step-by-step explanation:

P and 33 are complementary we know this because of the right angle so set up this equation:

90=angle + angle

sub in the numbers

90=33+P

Substract both sides by 33 to get p alone.

p=57

pleas solve this for me
y=x^2-x

Answers

Answer:

there i tried :)

Step-by-step explanation:

i don’t know if this is what your looking for but i if it is i hope this helped

WHAT IS THE SLOPE OF THE LINE???
I NEED HELP ASAP PLEASE

Answers

Answer:

(-3, 1)

Step-by-step explanation:

The line goes down 3 (-3) and to the right 1

(-3, 1)

(Sorry if I am wrong. Please don't get mad)

Hope I helped :)

The slope of the line is -3/1 due to rise over run.

Write 3x3x4x4x3x4 using exponents
I NEED IT NOW

Answers

Answer: 3^3 x 4^3

Here you go!

3^3 x 4^3

ok brainly is asking me to put more characters in my answer so yeah im doing that

Peter says there are two distances for which he and Maria charge the same amount. To prove Peter is not correct, Maria graphs a line for her delivery charges and a line for Peter’s delivery charges. Each line represents the relationship between the amount (y), in dollars, each person charges for a delivery and the distance (x), in miles, each drives for the delivery. Without showing the graph, explain how Maria’s graph of the two lines proves Peter is not correct.

Answers

.................look at the picture below

You have a box that measures 11
inches on each side. What is the
volume of that box

Answers

Answer:

1,331in^3

Step-by-step explanation:

The water level in a bathtub is directly proportional to the time that the water has been running. If the water level is 4 inches after 5 minutes, what is the water level after 9 minutes? O A. 10 inches O B. 7.2 inches O C. 8 inches OD. 11.25 inches​

Answers

Answer:

i think its 8

Step-by-step explanation:

becuse 4/5 its equal to 8/9 so thats why.

denada✌

16. A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain. (2 points

Answers

Answer:

yes

Step-by-step explanation:

10x10=6x6 + 8x8

100= 36 + 64

Pythagoras theorem

Solve: (step by step please)
x^2+9x+9=0

Answers

Answer:

[tex]x=\frac{-9\pm3\sqrt{5} }{2}[/tex]

Step-by-step explanation:

Standard Form: ax² + bx + c = 0

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

Step 1: Write equation

x² + 9x + 9 = 0

Since we cannot factor the expression, we will have to use the quadratic formula.

Step 2: Define

a = 1

b = 9

c = 9

Step 3: Solve for x

Substitute: [tex]x=\frac{-9\pm\sqrt{9^2-4(1)(9)} }{2(1)}[/tex]Evaluate: [tex]x=\frac{-9\pm\sqrt{81-36} }{2}[/tex]Evaluate: [tex]x=\frac{-9\pm\sqrt{45} }{2}[/tex]Simplify: [tex]x=\frac{-9\pm3\sqrt{5} }{2}[/tex]

Answer:

 X1= -9-3[tex]\sqrt5[/tex]  over 2    X2= -9+3[tex]\sqrt5[/tex] over 2  (draw a line under the -9 to the 5

                                                                         and put a 2 under like a fraction

                                                                          i cant get the line all the way

                                                                          across on here   sorry

Step by step explanation:

x= -9 [tex]\sqrt9^2 -4x1x9[/tex]    Over (draw a line under that) Put all that under sq root

             2 x 1                        also

x= -9+ [tex]\sqrt81-36[/tex]         Over 2

           2

x= -9 + [tex]\sqrt45[/tex]                 Over 2

         2

x=-9 +3[tex]\sqrt5[/tex]                   Over 2

        2

separate solutions    gives your answer above  

Also ......note ..... put a line under each  + sign  ok I worked hard getting this all down best i can


Solve the inequality 3(k-9) > 3k + 6.

Answers

Answer:

No solution

Step-by-step explanation:

Solving inequalities is similar to solving equations. First let's distribute the 3 with (k-9)

[tex]3(k - 9) > 3k + 6[/tex]

[tex]3k - 27 > 3k + 6[/tex]

(Subtract 3k from both sides)

[tex] - 27 > 6[/tex]

[tex] - 33 > 0[/tex]

(Subtract 6 from both sides. You can also add 27 to both sides. You will get the same answer.)

This inequality is invalid. There are no values of k that make the inequality true.

Answer:

No solution

Step-by-step explanation:

Pleas help me complete this question
The answer should be —-students

Answers

Answer:

1.1 × 10^ 4

Step-by-step explanation:

Answer:

2.7*10^4 - 3.7*10^3

=10^3[2.7*10-3.7]

=10^3 [27-3.7]

=10^3 *23.3

=2.33*10^4

Hope this helps!!

A checking account is set up with an initial balance of $5400, and $300 is removed from the account each month for rent (no other transactions occur on the account).

Write an equation that can be solved to find the number of months, m, it takes for the account balance to reach $1800.

Answers

Answer:

$1800 xm^2= 68658

Step-by-step explanation:

1. The video store rented 42 videotapes on
Monday, 35 on Tuesday, 51 on
Wednesday, and 32 on Thursday. What
was the average number of videotapes
initially rented per day from Monday to
Thursday if all were one-day rentals?
A. 37
B. 38
C. 40
E. 54

Answers

Answer:

C. 40

Step-by-step explanation:

average = (42 + 35 + 51 + 32)/4 = 40

Answer: C. 40

Write the word sentence as an equation. Then solve.

10 more than a number c is 3.

Answers

Answer:

10+c=3

Step-by-step explanation:

to solve this you would then subtract 10 from both sides, to get c by itself.

3-10= -7

Your answer would be -7 and the equation would be 10+c=3.

What is the range of the function f(x) = 3/4|x|- 3

Answers

Answer:

[-3,∞)

Step-by-step explanation:

f(x) = x + 7
and
g(x) = x^2
What is f( g( -7))

Answers

I THINK IT IS

X-49x^2

Factor the expression completely.

18 x − 21 18x−21

Answers

Answer:

3( 6x-7)

Step-by-step explanation:

18 x − 21

Factor a 3 out of each term

3*6x - 3*7

3( 6x-7)

Answer:

Factor 18x−21

18x−21

=3(6x−7)

Answer:

3(6x−7)

Step-by-step explanation:

3) Consider the following linear equations:
y = x - 4 and -8y = 8x - 32

What are the intercepts of the line y=x-4 ?

x-value of x-intercept _____
y- value of y-intercept _____

Answers

X intercept is 4 and y intercept is -4

3/4 divided by 1/8 show work pls

Answers

Answer:

7

Step-by-step explanation:

a fraction divided by a fraction can be multiplied by the reciprocal. so...

instead of 3/4 ÷ 1/8, you do

3/4 * 8/1 which equals

24/4 which equals

6

Answer:

6

Step-by-step explanation:

3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 =6

*8×3=24 *4×1=4

*24÷4=6

47 426 round to the nearest thousands​

Answers

Answer:

47 000

I hope this helps

do positive numbers have negative square roots?

Answers

Yes. They have two square roots. Both have the same absolute value but one is positive while the other is negative.

Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.

Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?

HELP PLS

Answers

Answer:

Sample Response: To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.

Hope this helps. :)

Solve the equation using inverse operations. show your work

-x^2=-36

Answers

Answer:

x = 6, -6

Step-by-step explanation:

-x^2 = -36

~Take the square root of both sides

x = ±6

Best of Luck!

Which of the relations below is a function?

{(2,3), (3,4), (5,1), (6,2), (2,4)}

{(2,3), (3,4), (5,1), (6,2), (3,3)}

{(2,3), (3,4), (5,1), (6,2), (7,3)}

Answers

Answer:

{(2,3), (3,4), (5,1), (6,2), (7,3)}

Step-by-step explanation:

A relation may or may not represent a function.

The relation that is a function is (c) {(2,3), (3,4), (5,1), (6,2), (7,3)}

Relations and functions

For a relation to be considered a function, then the x values must point to different y-values.

The above condition is true for the relation (3).

This is so because all x values in this relation point to different y-values.

Hence, the relation that is a function is (c) {(2,3), (3,4), (5,1), (6,2), (7,3)}

Read more about relations and functions at:

https://brainly.com/question/10283950

I need help with the fraction thing I’m doing

Answers

Answer:

12

/ \

2 6

/ \

2 3

Step-by-step explanation:

This is the answer

Answer:

      12

2             6

        2            3

Step-by-step explanation:

Because reasons.

Can someone help me plz

Answers

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)

What is 3 x 3 1/4?

Please help

Answers

Answer:

3 times 3 1/4 is 13 times 3 which is 39

Step-by-step explanation:

Solve: x3 = 27

A) X = 3

B) X= 3 and x = -3

C) X = 9

D) X = 9 and x = -9

Answers

Answer:

C

Step-by-step explanation:

27/3=9

Just do cube root of 27.

x has to equal 3 because -3 cubed is -27, 9 cubed is 729, and -9 cubed is -729.

X = 3, The answer is choice A.

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