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

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

Answers

american deli and honey hot

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

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

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

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

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:

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

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.

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.

how to write this numbers in word 30.659

Answers

Answer:

thirty and six hundred fifty-nine thousandths

Step-by-step explanation:

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

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.

Help me on this please

Answers

Answer:

answer d

Step-by-step explanation:

negative exponents need to be put into the denom

Using the protractor, find the angle measure.

Answers

Which angle i need to see

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

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

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

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:

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 to 15x+9 when x=−1.

Answers

Answer:

The answer is -6.

Step-by-step explanation:

Can someone help I will brainlest

Answers

Your answer will be 2.4

2.4 I think. (Hope it’s right)

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.

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

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!

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

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]

I need help with this

Answers

Answer:

y=-1/3x+2

Step-by-step explanation:

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

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 :)

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:

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:

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