The sum of 5 amd 8 terms of an A.P is 37 and its 11 term is 32 find the A.P

Answers

Answer 1
Given:

Sum of 5th & 8th terms of an AP = 37

11th term = 32

Find:

A.P

Solution:

We know that,

nth term of an AP – an = a + (n - 1)d

Hence,

⟹ a₅ + a₈ = 37

⟹ a + (5 - 1)d + a + (8 - 1)d = 37

⟹ 2a + 4d + 7d = 37

⟹ 2a + 11d = 37 -- equation (1)

Similarly,

⟹ a₁₁ = 32

⟹ a + (11 - 1)d = 32

⟹ a + 10d = 32

⟹ a = 32 - 10d

Substitute the value of a in equation (1).

⟹ 2(32 - 10d) + 11d = 37

⟹ 64 - 20d + 11d = 37

⟹ 64 - 37 = 20d - 11d

⟹ 27 = 9d

⟹ 27/9 = d

⟹ 3 = d

Substitute the value of d in equation (1).

⟹ 2a + 11(3) = 37

⟹ 2a + 33 = 37

⟹ 2a = 37 - 33

⟹ 2a = 4

⟹ a = 4/2

⟹ a = 2

Now,

General form of an ap = a , a + d , a + 2d...

⟶ Required AP = 2 , 2 + 3 , 2 + 2(3)...

⟶ Required AP = 2 , 5 , 2 + 6...

⟶ Required AP = 2 , 5 , 8...

I hope it will help you.

Regards.

Answer 2

Answer:

→ md - 2nd + 3md = 2 * [ a + (n - 1)d ]

→ 4md - 2nd = 2 * [ a + (n - 1)d ]

→ 2(2md - nd) = 2 * (a + nd - d)

→ 2md - nd - a + d = nd

→ 2md - nd - (md - 2nd) + d = nd

[ From equation (1) ]

→ 2md - nd - md + 2nd + d = nd

→ md + nd + d = nd

→ (m + n + 1)d = n * d

→ (m + n + 1) = n

Step-by-step explanation:


Related Questions

can someone explain to me how to do this

Answers

Answer:

x=45

Step-by-step explanation:

We know that 2y+6 and 8y-102 are vertical angles to each other. This means that 2y+6=8y-102. [tex]6y=108[/tex], which means that y=18. [tex]2\cdot(18)+6=36+6=42[/tex]. Since one line is a straight angle, it is 180 degrees we can do [tex]3x=180-45=135[/tex], so x=45.

Answer:

y = 18

x = 46

measures of the angles:

8y - 102 = 42

2y + 6 = 42

3x = 138

Step-by-step explanation:

So first remember the verticle angles theorem, which states that, when two lines intersect there will be four angles formed; the angles that are opposite from each other will be congruent, that is,  they will have the same measure.

Using this we know that opposite angles have to be congruent:

so

(2y + 6) = (8y -102)

now there is an algebra equation that can be solved by inverse operations and simplifying

2y + 6 = 8y - 102

    +102      +102

2y + 108 = 8y

-2y             -2y

108 = 6y

/6        /6

18 = y

Also, remember that two adjacent angles that form a line will add up to 180,

so

3x + (2y + 6) = 180

*note: I could have also used (8y - 102) but I choose to use (2y + 6)

so now substitute in the value of y that was found

y = 18

3x + (2 * 18 + 6) = 180

simplify

3x + ( 36 + 6) = 180

3x + 42 = 180

now use inverse operations

3x + 42 = 180

     -42     -42

3x = 138

/3      /3

x = 46

What Is The Slope Of the Line

Answers

Answer:

2/2.5 or 3/4 I pretty sure that's right

-1/10 divided by 1/6

Answers

[tex]-0.6[/tex]

For more help, Take a look at this chart.

Answer:

-3/5

Step-by-step explanation:

-1/10 divided by 1/6

-1/10 x 6/1

-6/10 the divided by 2

-3/5

A company ships 26 refrigerators in a truck Each refrigerator weighs 309 pounds. What is the total weight of the refrigerators in the truck?
O 2,472 pounds
7,884 pounds
O 8,034 pounds
O 8,294 pounds

Answers

Answer:

8034

Step-by-step explanation:

C'mon!!.... easyyyy

309x26 =8034

Megan scored 80% on a test. She got 20 questions correct. How many questions were on the test?

Answers

Answer:

25

Step-by-step explanation:

I'm writing this to get to the 20 character minimum

Answer:

26 Questions

Step-by-step explanation:

Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
If cat and dog start running away from each other how far away from each other will they be after 30 minutes?

Answers

Answer;

They will be 0.5x miles away from each other

Explanation;

Since the dog runs twice the speed of the cat

Its speed will be 2 * x = 2x mph

Now we want to know how far they will be from each other after 30 minutes

Kindly note that 30 minutes is 1/2 hour

Mathematically;

distance = speed * time

Distance of cat = x * 1/2 = 0.5x miles

Distance of dog = 2x * 0.5 = x miles

The dog is x - 0.5x miles = 0.5x miles away from the cat

They will be 0.5x miles away from each other.

Calculation of the distance:

Since Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.

So here the speed of the dog should be 2x

Now we know that

[tex]Distance = speed \times time\\\\[/tex]

Here distance of cat should be x of 30 minutes or half hour = 0.5x miles

And, Distance of dog should be 2x of 0.5 = x miles

So, the difference should be

= x - 0.5

= 0.5x miles

hence, They will be 0.5x miles away from each other.

Learn more about speed here: https://brainly.com/question/1825528

How do you write -4.50 as a mixed number

Answers

Answer:

-9/2

Step-by-step explanation:

Solve for I.
-30 = 5(x + 1)

Answers

Answer:

x or I=-7

Step-by-step explanation:

PLEASE HELP, IM NOT SURE!!!


The scale on a map reads 2 inches = 5 miles. What is the actual distance
between two cities on the map that are 6.5 inches apart?*
O A. 2.6 miles
B. 13 miles
O C.32.5 miles
D. 16.25 miles

Answers

Answer:

Step-by-step explanation:

2 inches = 5 miles.

So if you divide both sides by 2,

1 inch = 2.5 miles

To find how many miles 6.5inches is equal to, multiply 2.5 by 6.5

6.5 inches = 2.5 x 6.5 = 16.25 miles

SHCIUWU SIU SIJSJSH USIABSBNJSSJJAKJAH YUJJU

• Lawson already has $60 in his wallet but needs a total of at least $500 for his holiday. He gets
paid $30 per day for delivering newspapers. What is the least number of days he must work to
get enough money for his holiday?

Answers

Answer:

15

Step-by-step explanation:

500-60=440

440/30=14.66666667

simplify 14.66666667= 15

             

OMG Help Me !Select all the correct answers. Which tables represent constant functions? Pick 2 and show your work. No guessing.
x y
2 -1
2 0
2 1
x y
2 -3
4 -7
6 -11
x y
2 3
4 3
6 3
x y
1 3
2 12
3 27
x y
1 -1
2 -1
3 -1

Answers

Tables 1 and 2 because they move at a constant rate of change and they are linear functions with a slope.

Table 3 is not a function because there is more than one input for each output.

Table 4 is an exponential equation with the equation y = 4x^2

Table 5 is not a function for the same reason as table 3.

Answer:

Yes! The answer is A and B. Or the 1st and 2nd ones.

Step-by-step explanation:

I have 4 and 11/12 . how much do i need to add to get 6 and 1/2

Answers

Answer:

= 1 7/12

Step-by-step explanation:

6 1/2 - 4 11/12 =

6 6/12 - 4 11/12 =

5 18/12 - 4 11/12 =

=1 7/12

To check if the answer is right or wrong, you can add 1 7/12 to 4 11/12

4 11/12 + 1 7/12 = 5 18/12 = 6 6/12 = 6 1/2

Hope this helps and pls do mark me brainliest if you can:)

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements: 1. As x increases infinitely, the y-values are continually doubled for each single increase in x. 2. As x decreases infinitely, the y-values are continually halved for each single decrease in x. She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine's statements and her conclusion?

Answers

Answer:

"as x increases infinitely, the y-values are continually doubled for each single increase in x".

Step-by-step explanation:

Given the exponential equation f(x) = 2x of which Geraldine is asked to explain the limits on the range, the expression that best explains the accuracy of Geraldine's statements and her conclusion is that "as x increases infinitely, the y-values are continually doubled for each single increase in x".

for example let y = f(x) so thet y = 2x

for every va;ues of x, y will be doubled as shown;

If x = 1

y = 2(1) = 2

If x = 2

y = 2(2) = 4

If x = 3

y = 2(3) = 6

I can be seen that the value of y doubles for all values of x hence making her first statement accurate.

The second statement 'As x decreases infinitely, the y-values are continually halved for each single decrease in x'. is not totally right because the y values may not be halved for some values of x as x increases.

Her conclusion is not also right because there are  limits within the set of real numbers on the range of this exponential function. for every value of x, y will always tend to a real value.

Joey wants to save up enough money to buy a new baseball bat that costs $200. He already has $50. If Joey makes $40 per week, write an inequality that represents the number of weeks (w) until he will have enough money?

Answers

Answer:

50+40w=200

Step-by-step explanation:

200-50=150

150 divided by 40=3.75 so 3 1/2 weeks


Math
Jim baked 24 cupcakes for the upcoming bake sale. He also bought drinks.
Which sets below are factor pairs of 24?
A (3,6)
B (4.6)
C (6,8)
D (1, 24)
E (38)
Click Submit below if you want to finish the test and see the results
Save and Exit
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
26 27 28

Answers

your answer is b(4,6) explain: hajsjsjdjjshahshshsjsjsjjsjsjsjsjsjsjsjjsjsjsjs
The factor pairs are:
D (1,24)
B (4,6)
Because:
1 x 24 = 24
6 x 4 = 24

You bought 12 red apples and 15 green apples to make a pie.
What is the ratio of the number of red apples to the total number of apples?
4 over 9

Answers

Answer:

12 over 27 = 4 over 9

Step-by-step explanation:

12 over (12 + 15) = 12 over 27 = 4 over 9

What is the speed of a car that is traveling at 75,000 meters in 5,400 seconds.

Answers

Answer:

13.9

Step-by-step explanation:

Speed=distance/time

S=75,000/5,400

S=13.8 repeating OR (rounded) 13.9 m/s

HURRY!!!!
The value of a baseball card can be represented by the equation y = 3 x + 39, where x represents the number of years that Robert has owned the card and y represents the total value, in dollars, of the card. What was the value of the card when Robert originally purchased it?
$3
$13
$36
$39

Answers

The value of the card was $13 when he originally purchased it.

Answer:

mark as brainliest plz...        it is $39

Step-by-step explanation:

ayeeeeeeeeeeeeeee

Is this equation an example of a literal equation? Why?

Answers

Answer:

yes this is...,.,.,.....

If f(x) = 2x2 + 5x - 8 and f(x) = -10,
which of the following could be a
value for x?
-2

Answers

Answer:

x = -2 or x = -1/2

Step-by-step explanation:

We can just set up an equation where the quadratic is equal to -10, and then solve the equation:

[tex]2x^2+5x-8=-10\\2x^2+5x+2=0\\\\[/tex]

Now, factor:

[tex](2x+1)(x+2) = 0\\x=-2 \text{ or } x=-1/2[/tex]

Solve the equation 3x + 4y = 16 for x.
O A x V 16
B. x=3(16-4)
O c. x = 16 - 4y
O D. x. 18 AV

Answers

3x-4y=16

add 4y to both sides

3x=4y+16

divide both sides by 3

x=(4y+16)/3

Can you please answer this my homework is due ✨

Answers

2:1100
3:1650
6:3300
It is all multiplying with the number 550

Can someone please help me?

Answers

Answer:

4

Step-by-step explanation:

It is 4 because there are 4 pea pods with 3 peas in each pod.

Answer:

2

Step-by-step explanation:

Absolute value is DISTANCE. How many units a number is away from zero.

a.) 3
b.)4
C.) -3
d.) -4

Answers

I believe it is B) 4

The number line is going by .5 per space and there are 8 spaces in the red line segment. You can then do 8 x .5 and you will get 4.

Kenson and Shelly are each saving money.
• Kenson has $60 in savings and will save an additional $12 every week.
• Shelly has $85 in savings and will save an additional $7 every week.
Which equation can be used to determine w, the number of weeks it will take Kenson and Shelly to save the same amount of money?
A. 720 + 60w = 595 + 85w
B. 7w + 595 = 12w + 720
C. 60 + 7w = 85 + 12w
D. 60 + 12w = 95 + 7W

Answers

Answer:

D.

Step-by-step explanation:

D. 60 + 12w = 95 + 7W

Bill can hit a bucket of 32 golf balls in 17 hours.
How much could he hit in 23 hours

Answers

17x = 32

x = 1.882

23x = 23 x 1.882 = 43.286 = 43 balls

An electrician charges an hourly rate of $50, but also charges a fixed fee for making house calls regardless of time spend on the job. One day, the electrician earned a total of $250 for a 2 hour job. Write an equation for C,C, in terms of t,t, representing the total cost of the electrician's services if the electrician spends tt hours at the house working.

Answers

Answer:

C=50t+150

Step-by-step explanation:

From the information given, the equation will need to show that the total cost of the electrician services would be equal to 50 that is the hourly rate for the number of hours spent working plus the fixed fee:

Fixed fee=250-(50*2)=250-100=150

According to this, the equation would be:

C=50t+150, where C is the total cost of the electrician's services and t is the number of hours spent working.

What is the measure of Angle 1 in this figure?
A. 30°
B. 80°
C. 110°
D. 130°​

Answers

Answer:

A

Step-by-step explanation:

Answer will be
D. 130

Find the slope of AB through points A(1,7) and B(-1,4). m of AB=

Answers

Hi there & welcome to brainly !

Answer:

[tex] \huge{ \boxed{ \bold{ \tt{ \frac{3}{2}}}}} [/tex]

Step-by-step explanation:

Given :

A ( 1 , 7 ) , B ( - 1 , 4 )

To find :

Slope = ?

Solution :

Let A ( 1 , 7 ) ↦ ( x₁ , y₁ )

Let B ( - 1 , 4 ) ↦ ( x₂ , y₂ )

Finding the slope :

[tex] \boxed{ \tt{slope \: ( \: m)= \frac{y2 - y1}{x2 - x1} }}[/tex]

[tex] \sf{↦ \: slope = \frac{4 - 7}{ - 1 - 1}} [/tex]

[tex] \sf{↦ \: slope = \frac{ - 3}{ - 2}} [/tex]

[tex] \sf{↦ \: slope = \boxed{ \sf{ \frac{3}{2} }}}[/tex]

And we're done !

Hope I helped!

Best regards! :D

~TheAnimeGirl

I need help Type fast

Answers

yeah i can help u out on how u can get answers for math go check out m a t h w a y
Other Questions
7) Write an equation in point-slope form of the linethrough point J(-2,10) with slope - 2 How did the concert of Karma relate to the concept of reincarnation ? A single-turn circular loop of radius 9.4 cm is to produce a field at its center that will just cancel the earth's field of magnitude 0.7 G directed at 70degrees below the horizontal north direction. Find the current in the loop. Pampered Pooch charged $10 for 2 hours of doggie daycare and $20 for 4 hours. What is the unit rate? Show your work. figururative language is this Do you ever feel like a plastic bag PLEASE HELP Explain two Christian beliefs about the baptism of Jesus. What was one effect of the Peloponnesian War?Macedonia invaded Greece.Sparta allied with Macedonia.Athens took over Macedonia.Macedonia defeated the Greek navy. Hay dos nmeros naturales consecutivos y la suma del cuadrado de esos nmeros es 221cules sern esos nmeros? The lease agreement specified quarterly payments of $6,500 beginning September 30, 2021, the beginning of the lease, and each quarter (December 31, March 31, and June 30) through June 30, 2024 (three-year lease term). The florist had the option to purchase the truck on September 29, 2023, for $13,000 when it was expected to have a residual value of $19,000. The estimated useful life of the truck is four years. Mid-South Auto Leasings quarterly interest rate for determining payments was 3% (approximately 12% annually). Mid-South paid $51,000 for the truck. Both companies use straight-line depreciation or amortization. Anything Grows incremental interest rate is 12%.Required: a. Calculate the amount of selling profit that Mid-South would recognize in this sales-type lease. (Be careful to note that, although payments occur on the last calendar day of each quarter, since the first payment was at the beginning of the lease, payments represent an annuity due.) b. Prepare the appropriate entries for Anything Grows and Mid-South on September 30, 2021. c. Prepare an amortization schedule(s) describing the pattern of interest expense for Anything Grows and interest revenue for Mid- South Auto Leasing over the lease term. d. Prepare the appropriate entries for Anything Grows and Mid-South Auto Leasing on December 31, 2021. e. Prepare the appropriate entries for Anything Grows and Mid-South on September 29, 2023, assuming the purchase option was exercised on that date. The Post-It note was created when a scientist decided to try putting a new adhesive that he'd heard about on his paper bookmarks. What is this an example of? Creative thinkingScientific methodScientific lawArtistic ability In early cities, who generally managed the allocation of resources? i will mark brainlyiest Read the passage below and answer the question that follows.Imagine that youve taken a job as a city planner. Your first task is to find out how many people live in your city. Then, youre asked to find out how large of an area your city covers.If you combine these two measurements together, what information would you now have?A.your citys migration rateB.your citys level of educationC.your citys weatherD.your citys population densityPlease select the best answer from the choices provided 1. If 18 zombies eat 45 brains, then how many brains will 4 zombies eat?brains02. A machine can make 246 bolts in 6 minutes. If you run the machine for 33minutes, how many bolts can it make?T14-olC3. You can buy 78 paper clips for a dollar. How much would it cost to buy 351paper clips984. A math teacher can make 45 students cry in 180 days. At this rate, how dayswould it take to make 50 students cry? I have not been selected for a diversity visa twice and now Im planning to apply for a student visa in Australia. Can I apply? If so, what are the chances of getting a visa? How did pop artist created unique works of art? When choosing between continuing an argument and walking away, which situation supports walking away as the better option? Which best describes the role of Constantinople in the Byzantine Empire?Constantinople was a main trading center.Constantinople was a secondary trading center.Constantinople was a Greek trading center.Constantinople was a Roman trading center. A 42-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is Two inches more than seven times the length of the first piece. Find the lengths of the pieces. pleaseeee i will give you the brainliesttt! What is the reason behind increasing status of earthworms?