how many terms of the AP: 24,21,18 must be taken so that thier sum is 78?

Answers

Answer 1

First term, a = 24
common difference, d = 21-24 = -3
let the number of terms to get sum 78 is n.

S_n=78\\ \\ \Rightarrow \frac{n}{2}(2a+(n-1)d)=78\\ \\ \Rightarrow \frac{n}{2}(2 \times 24+(n-1)(-3))=78\\ \\ \Rightarrow n(48-3n+3)=78 \times 2\\ \\ \Rightarrow -3n^2+51n-156=0\\ \\ \Rightarrow 3n^2-51n+156=0

Solving the quadratic equation, we get n=4 and n=13.
So you can take either 4 terms or 13 terms to get the sum 78.

Related Questions

Nel salone di un rivenditore di automobili, il 20% delle macchine sono SUV, il 35% sono monovolume e 27 sono berline. Calcola il numero di SUV.

Answers

Answer: 12

Step-by-step explanation: 27 sedanes son 45% (de 100 - (35 + 25)) es necesario hacer 27/45 para averiguar la tasa unitaria, multiplicar la tasa unitaria por porcentaje para averiguar la respuesta

the graph shows the solution to which inequality
y>2/3x+1

Answers

Answer:

The graph shows the solution to which inequality y>2/3x+1.

Step-by-step explanation:

hope that helps

Find the slope of the line y = –5x − 1

Answers

Answer:

-5

Step-by-step explanation:

The function follows y = mx + b form where m is the slope.

m = -5

The slope is -5

Answer:

-5

Step-by-step explanation:

the equation is written in form y = mx + b

The m is the slope and the b is the y intercept.

So the m in the equation is -5.

Question 3
~ True or false?

Answers

Answer:

It is true

Step-by-step explanation:

20/-7 is ~2.56

-2.8 (8 repeating) is -2.8......

So it is true

Hope this helps!

Answer:

True

Step-by-step explanation:

???????????????????????

Answers

Multiply by -2 to get rid of fraction.
But I don’t see it there

Answer:

I can't see the yellow..... but it should be subtract 10 from both sides!

So the answer is cyan or light blue (2nd one)

Step-by-step explanation:

Hope this helps! Mark as Brainliest!

It S.P. =Rs810, loss percent=10% find C.p

Answers

Answer:

x=900

Step-by-step explanation:

100-10=90

90/100=0.9

x*0.9=810

x=810/0.9

x=900:)

hope it helps!!

Have a great day

Which temperature during the week is the closest to 0? Explain how you decided this using absolute value.

A -3.5 F
B 5 F
C 1.5 F
D -0.5
E -2 F
the rest of the choices 2.5 and -4

Answers

Answer: I would have to go with e because it is the closest because it is -2 and if it were to get to zero it wouldn't take that long.

Step-by-step explanation:

Tell whether the rates form a proportion

28 points in 3 games; 112 points in 12 games
Yes
No

Answers

Answer: yes

Step-by-step explanation: the answer is yes

hellllpppppp meeeeeee please

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{7x}{2} <5\\7x<10\\x<\frac{10}{7}[/tex]

What is your favorite place to get wings and what type of wings do you like?

Answers

american deli and honey hot

The number 0 is a solution to which of the following inequalities? Select all that apply. x – 5 ≤ -3

Answers

Answer:

The number 0 is a solution to that specific inequality

Step-by-step explanation:

0-5 <- -3

-5 <- -3

-3 is greater than -5

what is the answer for 7(x+2) = 6(x+1)

Answers

Answer:

x= -8

Step-by-step explanation:

Simple math

Answer: x = -8

7(x + 2) = 6(x + 1)

⇔ 7x + 14 = 6x + 6

⇔ 7x - 6x = 6 - 14

⇔ x = -8

Step-by-step explanation:

Help me on this please

Answers

Answer:

answer d

Step-by-step explanation:

negative exponents need to be put into the denom

A rectangular cartoon is 80 cm x60 cm x40 cm .then, how many packets of shops can each of 10 cm x 5cm x 4 cm be kept inside the cartoon

Answers

Answer:

Step-by-step explanation:

10 x 5 x 4

Multiply everything by 8

80 x 40 x 32

You can't go over that because 80 is at it's limit.

Explicación paso a paso:

10 x 5 x 4

Multiplica todo por 8

80 x 40 x 32

No se puede pasar de eso porque 80 está en su límite.

espero te sirva

Can someone help I will brainlest

Answers

Your answer will be 2.4

2.4 I think. (Hope it’s right)

I need help with this

Answers

Answer:

y=-1/3x+2

Step-by-step explanation:

A store donated 2 1/4 cases of crayons to a daycare center. Each case holds 24 boxes of crayons; each box holds 8 crayons. How many crayons did the center receive?

Answers

Answer:

432 crayons

Step-by-step explanation:

convert 2 1/4 to 9/4

1 case=24 boxes=8 crayon in each box

24*8=192 for 1 case

9/4*192=432

The center received 432 crayons

The length of a rectangle is the sum of the width and 2. The area of the rectangle is 48 units. What is the length, in units, of the rectangle? please hurry

Answers

Answer:

The answer is 48 divided by 2= 24.

Hope I helped.

What is the answer to 15x+9 when x=−1.

Answers

Answer:

The answer is -6.

Step-by-step explanation:

Please help!!!!!!!!!

Answers

Answer:

ascending order:

angle KLM

angle KML

angle LKM

Step-by-step explanation:

angle opposite to the largest side is the largest angle:

largest angle = angle LKM

angle opposite to the smallestest side is the smallest angle:

smallest angle = angle KLM

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks the players to run from one corner to the other corner across the middle of the field.

Answers

Answer:

And the question is???

Answer:

Step-by-step explanation:

use the pythagorean therom:

a^2 + b^2 = c^2

substitute in your values

90^2 +120^2=c^2

multiply

8100+14400=c^2

add

22500=c^2

take the square root of both sides

c= 150 meters :)

Classify this polynomial.
2n

A:Liner
B:quadratic
C:cubic
D:none of these

Answers

Answer:

Step-by-step explanation:

this polynomial is to thhe first degree 2[tex]n^{1}[/tex] so is a linear one

I NEED HELP ASAP, WILL MARK BRAINLIEST Find the value of y. Round to the nearest tenths place.

Answers

Answer:

Side a = 1

Side b = 0.5

Side c = 0.86603 = √3/2

Nearest tenths is 0.9

Step-by-step explanation:

The following is one way to perform the calculation. It may not be the best way.

Calculates 2 sides based on 3 given angles and 1 side.

b = a·sin(B)/sin(A) = 0.5

c = a·sin(C)/sin(A) = 0.86603 = √3/2

Area =

ab·sin(C)

= 0.21651

Perimeter p = a + b + c = 2.36603

Semiperimeter s =

a + b +c

= 1.18301

Height ha =

2×Area

= 0.43301

Height hb =

2×Area

= 0.86603

Height hc =

2×Area

= 0.5

Median ma = √(a/2)2 + c2 - ac·cos(B) = 0.5

Median mb = √(b/2)2 + a2 - ab·cos(C) = 0.90139

Median mc = √(c/2)2 + b2 - bc·cos(A) = 0.66144

Inradius r =

Area

= 0.18301

Circumradius R =

2sin(A)

= 0.5

0.86 is more than 0.85 so the nearest tenths place has to be 0.9

I will also post questions and you please answer them

You are at a parade looking up at a large balloon floating directly above the street. You are 60 feet from a point on the street directly beneath the baloon. To see the top of the baloon, you look up at an angle of 53°. To see the bottom of the ballon you look up at an an angle of 29°. Estiamte the height, h, of the balloon to the nearest foot. Answer with only the numeric value

Answers

Answer:

The height of the balloon is 46 feet.

Step-by-step explanation:

Let the height from the ground to the top of the balloon be represented by x. Applying the appropriate trigonometric function, we have;

Looking at the top of the balloon,

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 53° = [tex]\frac{x}{60}[/tex]

x = 60 x Tan 53°

= 79.6227

x = 79.62 feet

Looking at the bottom of the balloon, let the height from the ground to the bottom of the balloon be represented by y.

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 29° = [tex]\frac{y}{60}[/tex]

y = 60 x Tan 29°

= 33.2585

y = 33.26 feet

The height of the balloon = x - y

= 79.6227 - 33.2585

= 46.3642

The height of the balloon is 46 feet.

A manufacturer is considering building a new and better mousetrap. She estimates the probability that the new mousetrap will be successful is . If it is successful, it would be able to make $120,000. Of course, she would make nothing if it were unsuccessful. The development costs for the mousetrap are $98,000. What is the expected value?

Answers

Answer:

$22,000 if successful

Step-by-step explanation:

So if She is able to make $120,000 on the trap, but it cost$98,000, just subtract $98,000 from $120,000 and you get $22,000 if she is successful she can expect that much

Answer:

22,000

Step-by-step explanation:

how to write this numbers in word 30.659

Answers

Answer:

thirty and six hundred fifty-nine thousandths

Step-by-step explanation:

Acme is selling a 6 pound turkey for $25.50.
Write the rate
What is the unit rate

Answers

Answer:

$4.25 each pound

Step-by-step explanation:

To find the unit rate you want to divide the price by the pound

25.50 / 6 = 4.25

Therefore it's $4.25 each pound which is the unit rate

Write the equation of the line that passes through the point (-4, -9) and has a slope of 1/2

Answers

Y = 1/2x + b
Plug in the point :)
-9 = 1/2(-4) + b
-9 = -2 + b
b = -7
Y = 1/2 -7

Answer:

The answer is y=1/2x-7

Step-by-step explanation:

y-y=m(x-x¹)

y-(-9)=1/2(x-(-4)

y+9=1/2x+2

-9 -9

y=1/2x-7

PLZ HELP I SUCK AT MATH :( JUST LIKE MY USERNAME SAYS :(
Which of the following equations have exactly one solution?
Choose all answers that apply:

(Choice A)
-19x + 18 = -19x + 18

(Choice B)

-19x -18 = -19x + 18

(Choice C)

19x + 18 = -19x + 18

(Choice D)

19x - 18 = -19x + 18

Answers

Answer:

Option C and Option D have exactly one solution.

Step-by-step explanation:

The equation will have exactly one solution when it completely solves and we get value of x.

Checking all choices

(Choice A)

-19x + 18 = -19x + 18

-19x+19x=18-18

0=0

(infinite solutions)

(Choice B)

-19x -18 = -19x + 18

-19x+19x=18+18

0≠36

(no solution)

(Choice C)

19x + 18 = -19x + 18

19x+19x=18-18

38x=0

x=0

(One solution)

(Choice D)

19x - 18 = -19x + 18

19x+19x=18+18

38x=36

x=36/38

x=18/19

(One solution)

So, Option C and Option D have exactly one solution.

Using the protractor, find the angle measure.

Answers

Which angle i need to see

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