The sum of three terms in AP is 15. If the first two terms are each decreased by 1 and the last is increased by 1 then the resulting terms are in GP. find the numbers.​

Answers

Answer 1

Answer:

3, 5, ,7 or 9, 5, 1

Step-by-step explanation:

Let the three terms in AP be a - d, a & a + d

where a = First term and d = Common difference.

Condition 1: sum of three terms in AP is 15.

a - d + a + a + d = 15

3a = 15

a = 15/3

a = 5

Condition 2: When first two terms are each decreased by 1 and the last is increased by 1 then new terms so obtained will be as follows:

a - d - 1, a - 1, a + d + 1

These terms are in G.P.

[tex] {(a - 1)}^{2} = (a - d - 1)(a + d + 1) \\ \\ {(5 - 1)}^{2} = (5 - d - 1)(5 + d + 1) \\ \\ {(4)}^{2} = (4 - d)(6 + d) \\ \\ 16 = 24 + 4d - 6d - {d}^{2} \\ \\ 0 = 8 - 2d - {d}^{2} \\ \\ {d}^{2} + 2d - 8 = 0 \\ \\ {d}^{2} + 4d - 2d - 8 = 0 \\ \\ d(d + 4) - 2(d + 4) = 0 \\ \\ (d + 4)(d - 2) = 0 \\ \\ d + 4 = 0 \: \: or \: \: d - 2 = 0 \\ \\ d = - 4 \: \: or \: \: d = 2 \\ \\ when \: d = - 4 \\ \\ a - d = 5 - ( - 4) = 9 \\ a = 5 \\ a + d = 5 - 4 = 1 \\ \\ when \: d = 2 \\ a - d = 5 - 2 = 3 \\ a = 5 \\ a + d = 5 + 2 = 7 \\ \\ thus \: three \: terms \: in \: AP \: are: \\9, \: 5, \: 1 \: \: or \: \: 3, \: 5, \: 7[/tex]


Related Questions

Please help!! Best answer gets brainliest<3

Answers

Answer:

-5.1

Step-by-step explanation:

Since we know the starting temperature was -12.6 and the decrease was 7.5, that gives an equation.

-12.6 - 7.5.

Since we are working in temperature we need to be careful when subtracting.

-12.6 - 7.5 = -5.1

In a calculator, -12.6 - 7.5 would be 20.1 but since we are using temperature the answer is -5.1.

Hope that helps. x


Help please and thanks!

Answers

Answer:

9. x = 31°

10. m∠ABC = 62°

11. m∠BCA = 60°

Step-by-step explanation:

We are given the following values for ΔABC, and its exterior angle, ∠ACD:

In ΔABC, the two nonadjacent interior angles are:  

m∠A = 58° m∠B = 2x°

While the exterior angle, m∠ACD = (5x - 35)°.

In order to solve for questions 9 through 11, we must apply the Exterior Angle Theorem which states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent or remote interior angles.

Question 9:

In order to find the value of x, we can use the Exterior Angle Theorem:

m∠ACD = m∠A + m∠B

(5x - 35)° = 58° + 2x°

5x° - 35° = 58° + 2x°

Subtract 2x from both sides:

5x° - 2x - 35° = 58° + 2x° - 2x

3x - 35° = 58°

Next, add 35° to both sides:

3x° - 35° + 35° = 58° + 35°

3x° = 93°

Divide both sides by 3 to isolate x:

[tex]\displaystyle\mathsf{\frac{3x}{3}\:=\:\frac{93}{3} }[/tex]

x = 31°

Therefore, the value of x = 31°.

Question 10:

In order to find m∠ABC, we must first substitute the value of x into m∠B:

m∠B = 2x° = 2(31)° = 62°

Therefore, m∠ABC = 62°.

Question 11:

In order to find m∠BCA, we must first find the value of its supplement, m∠ACD, by substituting the value of x derived from question 9.

m∠ACD = 5x° - 35° = 5(31)° - 35° = 120°

Next, substitute the value of m∠ACD into the following equation:

m∠BCA + m∠ACD = 180°

m∠BCA + 120° = 180°

Subtract 120° from both sides:

m∠BCA + 120° - 120° = 180° - 120°

m∠BCA = 60°

Therefore, m∠BCA = 60°.

Verify:

In order to verify whether we have the correct values for each interior angles, we can apply the Triangle Sum Theorem which states that the sum of all interior angles of a triangle is equal to 180°.  In other words:

m∠A + m∠B + m∠C = 180°.

58° + 62° + 60° =  180°

180° =  180° (True statement).

pls help quick
plssss
plssssss

Answers

The second year would be 16.
The third year would be 20.

WILL GIVE BRAINLIEST TO

Answers

Answer: [tex]\frac{(y+2)^{2} }{4} - \frac{(x-4)^{2} }{9} =1[/tex]

Step-by-step explanation: Big brain

Approximately what portion of the circle is shaded blue?

Answers

Answer: C. (1/6)

Step-by-step explanation: If you split the circle in half horizontally, the top part would be 1/3 and the bottom part would be 3/3. 1/3 + 3/3 = 4/6 and 4/6 simplified is 1/6.

Rick's Phone Service charges $12.52 for an activation fee plus $6 for every gigabyte (g) used.

Which of the following graphs models the situation?

(Please, help me I will do everything I can to boost you.. It's been a rough night of homework.)

Answers

Answer:

d

Step-by-step explanation:

same explanation as before just replace the current values with the previous explanation

Answer:

After a quick stint of attempting to read the graphs I would speculate D

E=4i+3j A=5i finfd E.A=EAcos

Answers

Answer:

theta = 36.87

Step-by-step explanation:

E.A= (4i+3j).5i= 20

|E| |A| =

[tex] | e| |a| = \sqrt{4 ^{2} + {3}^{2} } \times 5 = 25[/tex]

[tex] \cos(theta) = \frac{e.a}{ |e ||a | } = \frac{20}{25} = \frac{4}{5} \\ theta = \cos ^{ - 1} ( {.8} ) = 36.87 [/tex]

factorize completly Mn + np + or + rt​

Answers

Answer:

n (m + p) + r (o + t)

Step-by-step explanation:

You have to split the expression in half.

First, focus on mn + np, the common factor would be n.

So the first part of the answer would be mn ÷ n and np ÷ n.

Leading to it being n(m + p).

Then you focus on the second half or + rt.

You find the common factor, which is r.

You divide both sides by r.

Hence why you get r(o + t).

Lastly, you put them together, n(m + p) + r(o + t).

Hope this helps :)


Here is an encoded message, a message that has been converted into a code.
WRGDB LYD JRRG GDB.
Can you figure out what it says in English? How was the original message encoded?

Answers

Im not sure but thank you for the points

Lumber pieces that are 1 1/2 inches thick are being piled in the bed of a truck. The bed rests at a height of 36 inches and the crew has been instructed to make sure the height of the pieces above the ground does not exceed 7 feet. What is the greatest number of pieces of lumber that can be placed in a stack ? can someone please answer <33

Answers

Answer:

Step-by-step explanation:

36 inches  = 3 ft

max height of lumber stack is 7 - 3 = 4 ft.

4 ft = 48 inches

48 inch / 1.5 inch/board = 32 boards

A rectangular prism with a volume of 101010 cubic units is filled with cubes with side lengths of \dfrac12
2
1

start fraction, 1, divided by, 2, end fraction unit.
How many \dfrac12
2
1

start fraction, 1, divided by, 2, end fraction unit cubes does it take to fill the prism?

Answers

now, we're assuming that the prism has a volume of 10³ and is filled with cubes of sides 1/2 long, Check the picture below.

now notice the bottom-right part of the picture, if we put two small cubes next to each other, they add up to 1, so to get 10 units from that, we'll need 20 of those halves, or 20/2 = 10, meaning we'll need 20 cubes side by side to make a length of 10 horizontally.

The same will be true for getting cubes to make up 10 vertically, we'll need 20, the same is true to fill up from back to front, we'll need 20 cubes.

so we can say that the rectangular prism will need 20 cubes from front to back, 20 horizontally and 20 vertically, that'll be 20*20*20 cubes, or 20³ or 8000 cubes.

mind you that we used a Cube for the prism, but the same will be true if we were to rearrange the cubes and make the prism taller or wider, same 8000 cubes will fill it in.

M - n if m= 29 and n=11

Answers

Answer:

18

Not sure though but I hope i help you ☺️❤️

29 (m) - 11 (n) = 18

use the result (a+b)²=a²+2ab+b² to find the value of 49²+98+1


pls help me
I will give brainliest​

Answers

Answer:

2500

Step-by-step explanation:

a² + 2ab + b²

49² + 98 + 1

Comparing terms

a²= 49²

a= 49

2ab = 98

2× 49 × b = 98

98b = 98

b= 98/98

b = 1

or

b²= 1

b=√1

b= 1

a=49 and b= 1

Hence (a+b)²= (49+1)²

50²= 2500

PLEASE HELP ILL GIVE BRAINLIESTTTT

Answers

Answer:

27

Step-by-step explanation:

Because OC biscts AOB, then COA=COB

Therefore AOB is twice COB

10x+4 = 2(6x-3)

10x+4 = 12x -6

2x = 10

x = 5

Therefore COA is 5x6-3 = 27

Answer:

9 degrees

Step-by-step explanation:

OK so we know that m<AOB is equal to the equation 10x+4. With this in mind, we also know that m<COB equals 6x-3. The ray OC intersects m<AOB, so this means that m<COB plus m<COA equals m<AOB.

First, we find m<COA by reversing the equation around to solve for m<COA.

m<AOB - m<COB = m<COA

Then, we Pug in the angles and solve.

m<AOB = 10x+4

m<COB = 6x-3

10x+4 - 6x-3 = 4x+1

Here is where things get interesting. See those 2 lines in each angle? That means they are equal in measure.

So what you do is simple, find what x equals in order to make this equation below true.

6x-3 = 4x+1

The answer for x is 2. So then just plug in to solve for m<COA and you're done!!

4(2)+1 =9

lil bonus: you can also get the same angle degree by plugging  2 into m<COB

Sally gets $8.00 each week for allowance. She wants to purchase a used bicycle that costs $24.00. She also wants to donate $8.00 to the food kitchen. Label your drawings with bike.

1. How much money will she have to save for both?

2. How many weeks will it take her to save for both?

3.How many weeks will she have to save if she wants to buy a newer used bicycle
that costs $32.00 and still make her $8.00 donation?

Answers

Answer:

1: $32. 2: 4 weeks. 3: 5 weeks

Step-by-step explanation:

1: 8+24=32$

2: 32/8=4=4 weeks

3: 32+8=$40

    40/8=5=5 weeks

Help...................

Answers

Step-by-step explanation:

the surface area of that object consists of

2 triangles (one left, one right)

1 rectangle at the top

1 rectangle at the bottom

1 rectangle in the back

so, we need to calculate the area of each of these 5 areas and sum them up. that's it.

the area of such a triangle is

6×8/2 = 24 m²

we have 2 such triangles, so in total they are 48 m².

the rectangle at the top

10×12 = 120 m²

the rectangle at the bottom

12×8 = 96 m²

the rectangle in the back

12×6 = 72 m²

so the total surface area is

48 + 120 + 96 + 72 = 336 m²

whats 2077-210?
its for a thing im doing.

Answers

Answer:

1867

Step-by-step explanation:

What do you need it for?

What is the value of a in this linear system?
a + b + c = 62
a - b = 12
2a + b + c = 92
O A.
14
OB.
30
OC.
18
o
c
D.
26

Answers

Answer:

Step-by-step explanation:

C

can anyone help me please? i have 14 more minutes to finish this can anyone help?

Answers

Answer:

B

Step-by-step explanation:

A is 3-2 which is 1, not 5.

C is 3(2), which is 6, not 5.

D is 6, which is not 5.

-hope it helps

Answer:

B

Step-by-step explanation:

one minus five i divided by two i

Answers

Answer:

-1.5

Step-by-step explanation:

-1.5 step by step explanation

The pool at "Splash Around" is open for 14 weeks during the summer. You can swim for $6 a session, or you can buy membership for
$100 and pay only $4 a session. Which equation would you use to determine how many sessions you must use the pool to justify
buying the membership?

Answers

Answer:

Step-by-step explanation:

if x is the number of times you go swimming

100 + 4x < 6x

Out of an 98 day season

If you attend 50 days, the cost is $300 either with or without the membership

Less than 50 days, it's less expensive to just pay the daily rate.

More than 50 days, it's less expensive to have the membership.

How do you find the Dilation of 1.5? Also how would you write the Algebraic representation? ​

Answers

Answer:

Multiply each coordinate point by 1.5, y=1.5x

Step-by-step explanation:

Over the course of 12 hours the temperature changes a tour of -16°C what is the average change in temperature in one hour

Answers

Answer:

- 1 1/3 degree

Step-by-step explanation:

- 16 / 12

Solve the equation. a+3(a−1)=3(2+1) Enter the correct answer in the box. a=

Answers

Answer:

I feel like something is wrong with the equation but the answer is a = 3

Step-by-step explanation:

a + 3a - 3 = 6 + 3 = 9

--> 4a = 12 --> a = 3

help me plssssssssssss

Answers

Answer:

x= 131⁰

Step-by-step explanation:

the angles add up to 180⁰ so 180-49=131

131+49=180

hope this helps!!

Answer:

131 degrees. since it's going through 2 parallel lines, 49 is equal to the angle to the left of x, so we subtract 49 from 180 (half of 360) and we get 131

Margit works in a factory. She receives a salary of $12 per hour and piecework pay of 12 cents per unit produced. Last week she worked 38 hours and produced 755 units. What was her piecework pay?

Answers

Based on the way the piecework pay is calculated, Margit's piecework pay will be $90.60

The piecework pay is 12 cents for every unit that is produced.

Margit was able to produce 755 units in that week so her piecework pay will be:

= Number of units produced x Pay per unit

= 755 x 0.12

= $90.60

In conclusion, Margit should get a piecework pay of $90.60

Find out more on piecework pay at https://brainly.com/question/4692318.

PLS HELP ME WITH GEOMETRY PLSAND THANK YOU

Answers

Answer:

Yes

Step-by-step explanation:

They are equal acute triangles, are congurent. Your welcom

Jasmine is scuba diving at an elevation of −68.4 feet when her friend signals to come higher. Jasmine makes three ascents, each an equal distance, to reach an elevation of −15.6 feet, where her friend is located. What was Jasmine's elevation after her first ascent? Enter your answer as a decimal in the box.

Answers

Answer:

-35.2

Step-by-step explanation:

-68.4-(-15.6)= (-52.8)

-52.8÷3=(-17.6)

-52.8-(-17.6)=-35.2

Answer:-35.2

Step-by-step explanation:

Find the equation, in standard form, of the line parallel to y=-1/5x+7 and passing through the point (-10,-3).
Show work for brainliest!

Answers

ANSWER:

y= -1/5x - 5

Since it is parallel, that means that the slope (-1/5x) is the same.

Since it is passing through the point (-10, 3), substitute the numbers in for x and y which means: -3= -1/5*(-10) + b

b stands for the new y-intercept

do the equation, and you should get the answer above!

The second side of a triangular deck is 4 feet longer than the shortest​ side, and the third side is 4 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 52 ​feet, what are the lengths of the three​ sides?

Answers

Answer:

13 ft, 17 ft, 22 ft

Step-by-step explanation:

let x be the shortest side, then second side is x + 4 and the third side is

2x - 4

sum the 3 sides and equate to 52

x + x + 4 + 2x - 4 = 52 , simplify

4x = 52 ( divide both sides by 4 )

x = 13

x + 4 = 13 + 4 = 17

2x - 4 = 2(13) - 4 = 26 - 4 = 22

lengths of 3 sides are 13 ft, 17 ft and 22 ft

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