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

PLEASE ANSWER BOTH QUICK

Answers

Answer:

1.C

2.A

Step-by-step explanation:

dude trust me

What is the formula for calculating slope? Explain it in full.

Answers

Answer:

Use slope formula

Step-by-step explanation:

To calculate the slope, you can use the slope formula which is the change in the height compared to the change in the width. Using ordered pairs, this is the change in the y-values divided by the change in the x-values or the rise divided by the run.

If 6 is an element in the domain of f(x) = 9x-25/5, what is the corresponding element in the range?

Answers

Answer:

Step-by-step explanation:

f(x) = 9x - 25/5

f(x) = 9x - 5

f(6) = 9*6 - 5

f(6) = 54 - 5

f(6) = 49

=================

You might mean

f(x) = (9x - 25)/5

f(6) = (9*6 - 25) / 5

f(6) = (54 - 25) / 5

f(6) = 29/5

f(6) = 5.8

Moral: please use brackets to clarify the question.

3. Samuel tiene 11 cajas con mosaicos cuadrados de 20 cm por
lado y quiere cubrir una pared que mide 3 m de largo y 2 m
de alto. Si en cada caja hay 14 mosaicos, éserá necesario que
compre más cajas?
Matemáticas

Answers

Answer:

Primero veamos el área de la pared, es decir, el área total que Samuel debe cubrir.

La pared es de 3m por 2m.

Entonces el area es:

A = 3m*¨2m = 6m^2.

Ahora veamos los mosaicos.

Cada mosaico es un cuadrado de 20cm por 20cm.

El primer paso sería cambiar las unidades para tener metros aca también.

1cm = 0.01m

entonces.

20cm = 20*0.01m = 0.2m.

Entonces cada mosaico es:

0.2m por 0.2m

El área de cada mosaico es:

a = 0.2m*0.2m = 0.04m^2.

En una caja de mosaicos hay 14 mosaicos, entonces con una caja Samuel puede cubrir 14 veces a, o:

14*0.04m^2 = 0.56m^2.

Y Samuel tiene 11 cajas, entonces tenemos 11 veces lo de arriba:

11*0.56m^2 = 6.16m^2.

Y el área de la pared es 6m^2.

6.16m^2 > 6m^2

Entonces con las 11 cajas de mosaicos podemos cubrir completamente esa pared, y vamos a tener algunos mosaicos sobrantes.

Entonces Samuel no debe comprar mas cajas.

Each digit 8 in the number 8.888 has a different value placed on its place in the place-value chart. Each 8 is multiplied by its place value. I've made up a song to help you remember this. What is the rule that this is referring to? Write the rule below.

Answers

Answer:

The value of every digit in a decimal figure is given by its position in that figure.

Step-by-step explanation:

The Rule:

The value of every digit in a decimal figure is given by its position in that figure.

For the figure 8.888, from left to right,

The first 8 is in units

The second 8 is in tenth (this means 8/10 = 0.8)

The third 8 is in hundreth (this means 8/100 = 0.08)

The fourth 8 is in thousandth (this means 8/1000 = 0.008)

The sum of the place values of the digits after the decimal point = 0.888

when the unit 8 is added, you then get 8.888

Which equation below represents a horizontal line?


x = 4


y = x – 0


y = x + 0


y = 4

Answers

Answer:

x=4

Step-by-step explanation:

this should be the answer hope it helps

Y= 4 hope this helps

Harvy claims that he can map rectangle ABCD to rectangle EFGH. Select all the transformations or series of transformations that support his claim.

Answers

Answer:

Option (B) and (D)

Step-by-step explanation:

To understand the relation between rectangle ABCD and EFGH take a point A from rectangle ABCD which is at E of rectangle EFGH after the series of  transformations.

Horizontal distance between A and E = 2 - (-10) = 12 units

Vertical distance between A and E = 4 - 2 = 2 units

If the point A is shifted 12 units right and 2 units up we will find the point E.

Therefore, A translation of 12 right and 2 units up has been done.

Rule for the translation,

(x, y) → (x + 12, y +2)

Moreover this,

If rectangle ABCD is reflected over x = -1 and translated 2 units up, rectangle ABCD will overlap the rectangle EFGH.

Therefore, Options (B) and (D) will be the answer.

A rectangular tank has a length of 12 feet, width of 8 feet, and height of 5 feet. Frankie filled the tank with water at a rate of 4 cubic feet per minute. At this rate, how long will it take Frankie to completely fill the tank without overflowing it?

Answers

Answer:120 minutes.

Step-by-step explanation:

look, 12x8x5=480, and 480/4-120

Polygons ABCD and A′B′C′D′ are shown on the coordinate grid: A coordinate plane is shown with two polygons represented. Polygon ABCD has vertices A at 2 comma 2, B at 2 comma 4, C at 3 comma 5 and D at 3 comma 1. Polygon A prime B prime C prime D prime has vertices A at negative 1 comma negative 2, B at negative 1 comma negative 4, C at negative 2 comma negative 5, and D at negative 2 comma negative 1. What set of transformations is performed on ABCD to form A′B′C′D′? (4 points) a A translation 1 unit to the left followed by a 180-degree counterclockwise rotation about the origin b A translation 1 unit to the right followed by a 180-degree counterclockwise rotation about the origin c A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right d A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

Answers

Answer:

Answer is A. I get it right. :3

Answer:

a

Step-by-step explanation:

Six less than 2/3 of a
number is eighteen.

Answers

Answer:

36

Step-by-step explanation:

i think

The number must be 33
Hope this helps and a Brainliest would be appreciated

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper how many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper

Answers

Given :

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper.

To Find :

How many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper.

Solution :

Mass of copper in 50 gm alloy = [tex]50\times 0.12 = 6\ gram[/tex].

Mass of copper in 78 gm alloy = [tex]78\times 0.98 = 76.44\ gram[/tex].

Total mass of copper, ( 6 + 76.44 ) gm = 82.44 gram.

Percentage of copper in resulting mixture :

[tex]\%=\dfrac{82.44}{50+78}\\\\\%=64.4\ \%[/tex]

Hence, this is the required solution.

Find the missing terms in the sequence:
18, -72, 288,

Answers

Answer:

-1,152

Step-by-step explanation:

18 · (-4) = -72

-72 · (-4) = 288

288 · (-4) = -1,152

Type your response in the box. We each have a different level of health, and that level of health depends on many factors, including our lifestyles and habits. Some factors, however, might be outside our control. In your opinion, which is the biggest factor in determining how healthy you are? your level of physical activity your diet your level of stress factors outside your control, such as heredity Font Sizes

Answers

Answer:

Diet

Step-by-step explanation:

Health & fitness level has multiple factors. Some internal choice factors, some externally ascribed factors. Eg(s) - Diet, Excercise & Heredity, pollution respectively.

In my opinion, biggest factor affecting health is : Diet. As, it can affects health positively & negatively, by major extent. It can also help overcoming other health detrimental factors - eg lack of excercise, heredity issues, pollution related issues etc.

8+($6)+6
Simplify and solve this expression:

Answers

Answer:

6+8=14

14 times 6 is 84

I got 54
Mutiply 8 by 6 = 48
Add 48 and 6 =54
Answer =54

which expression is equivalent to 0.17w + 0.77 + w? -0.77 + 1.17w
-0.17w + 1.77
-1.94w
-1.6w

Answers

Answer:

113.29w +1.77

Step-by-step explanation:

At 9 pm the temperature was -2°C.
By midnight the temperature had gone down by 7 °C.
(b) Write down the temperature at midnight.​

Answers

Answer:

-9°C.

Step-by-step explanation:

Simple -2°C - 7°C.

Mercury is the closest planet to the Sun, with an average distance of 35,000,000 miles. It takes light about 3 minutes to travel from the Sun to Mercury. Neptune is the farthest, with an average distance of 2.8 x 109 miles from the Sun. How many times farther from the Sun is Neptune than Mercury? How long does it take light to reach Neptune? Follow the steps to find out. 1. Write the distance from the Sun to Mercury in scientific notation. Include units with your answer.​

Answers

Answer:

1.

[tex]2765000000 \: or \: 2.765 \times {10}^{9} [/tex]

2.

[tex]273 \: seconds[/tex]

3.

[tex]3.5 \times {10}^{7} [/tex]

Aubrey's dinner cost $85 She tips the waitstaff 30% for excellent service

Answers

Answer:

The total amount she paid would be $105.50.

Answer:

25.5 is the tip -- 110.50 is the total bill.

Step-by-step explanation:

You would calculate .30 (move the decimal over twice to switch from a percentage to a decimale) multiplied with 85 and this gives you 25.5.

85 * .3 = 25.5

Depending on the rest of the question, I added the tip to the amount of the dinner cost to obtain the total bill. You will need to see what the rest of the question is in order to verify which answer you are looking for.

what is a frequency table

Answers

Answer: its a method or organizing your info while displaying it

Step-by-step explanation:

Which one?
A. B. C. Or D.​

Answers

Answer:

A)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I think..

The equation P=$3.90+$0.10x represents the hourly pay(P) a worker receives for loading x number of boxes onto a truck. What is the slope of the line represented by the given equation?

Answers

Answer:

The slope of the line is 0.1.

NEED HELP PLEASE BEGGING PLEASE!!!!

Answers

Answer:

-54

Step-by-step explanation:

[tex]8(-9) - 6(-3)\\[/tex]

Multiply 8 by -9 and 6 by -3

[tex]-72 - (-18)[/tex]

Subtract[tex]Value = -54[/tex]

Hope this helps

plz mark brainliest

simplify the expression 6(x+4)+1=​

Answers

6x+25 should be the answer. we have no = value so the x is separate

Write your answer as a whole number and remainder.
73 : 8= R

Answers

Answer:

9 R 1

Step-by-step explanation:

73/8 = 9 R 1

we know 8x 9 = 72 so we know we have a remainder of 1

7) Compare the ratios of the corresponding sides to prove or disprove that the polygons are similar.

Answers

Answer:um thers no picture

Step-by-step explanation:

8. A sequence can be generated by using 2n - 11. What are the first four terms in
the sequence?

Answers

Answer:

              [tex]\bold{a_1=-9\,,\quad a_2=-7\,,\quad a_2=-5\,,\quad a_4=-3}[/tex]

Step-by-step explanation:

[tex]a_n=2n-11\\\\a_1=2(1)-11=2-11=-9\\\\a_2=2(2)-11=4-11=-7\\\\a_3=2(3)-11=6-11=-5\\\\a_4=2(4)-11=8-11=-3[/tex]

Which of the following is r^2 + 4s evaluated for r = 4 and s = 1.5?
14
30
38
22

Answers

Answer:

22

Step-by-step explanation:

Once you fill in the variables your equation will look like this::4^2+4(1.5)::you will the go multiply both parts of the equation leaving you with 16+6 and when you add those together you get 22.

Hope This Helps!

There are many cylinders with a volume of cubic inches. The height in inches of one of these cylinders is a function of its radius in inches where . What is the height of one of these cylinders if its radius is 2 inches? What is the height of one of these cylinders if its radius is 3 inches? What is the height of one of these cylinders if its radius is 6 inches?

Answers

Answer:

1. If its radius is 2 inches, the height is 36 inches.

2. If its radius is 2 inches, the height is 16 inches.

3. If its radius is 2 inches, the height is 4 inches.

Step-by-step explanation:

Here is the complete question:

There are many cylinders with a volume of 144[tex]\pi[/tex] cubic inches. The height [tex]h(r)[/tex] in inches of one of these cylinders is a function of its radius [tex]r[/tex] in inches where [tex]h(r) =\frac{144}{r^{2} }[/tex] .

1. What is the height of one of these cylinders if its radius is 2 inches?

2. What is the height of one of these cylinders if its radius is 3 inches?

3. What is the height of one of these cylinders if its radius is 6 inches?

Step-by-step explanation:

1. To determine the height of one of the cylinders if its radius is 2 inches,

From the question,

Since height [tex]h(r)[/tex] of one of these cylinders is a function of its radius [tex]r[/tex], and

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 2 inches

[tex]h(r) =\frac{144}{2^{2} }[/tex]

[tex]h(r) =\frac{144}{4 }[/tex]

[tex]h(r) = 36 inches[/tex]

Hence, the height is 36 inches

2. To determine the height of one of the cylinders if its radius is 3 inches,

Again,

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 3 inches

[tex]h(r) =\frac{144}{3^{2} }[/tex]

[tex]h(r) =\frac{144}{9 }[/tex]

[tex]h(r) = 16 inches[/tex]

Hence, the height is 16 inches

3. To determine the height of one of the cylinders if its radius is 6 inches,

Again,

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 6 inches

[tex]h(r) =\frac{144}{6^{2} }[/tex]

[tex]h(r) =\frac{144}{36 }[/tex]

[tex]h(r) = 4 inches[/tex]

Hence, the height is 4 inches.

x - 13 = 22 linear equations

Answers

Answer:

x = 35

Step-by-step explanation:

x - 13 = 22

Add 13 to each side

x - 13+13 = 22+13

x = 35

See attachment for math work and answer.

you are selling tickets to a school play. students tickets cost 5.00 dollars and adults tickets cost 7.00. you sell a total of 125 tickets and collect 775.00 dollars. how many of each type of ticket did you sell? PLZ HELP SHOW WORK

Answers

Answer:adult tickets - 75 and student tickets - 50

Step-by-step explanation:

75x7=525 and 50x5=250, therefore 525+250=775

hope this helps

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