terms are there. Divide 51 into three parts in AP so that the largest exceeds the smallest by 10.​

Answers

Answer 1

The first three terms of the Arithmetic Progression are 12, 17 and 22.

For an ARITHMETIC PROGRESSION, AP ;

First term = a

Second term = a + d

Third term = a + 2d

Where, d = common difference ;

If third term exceeds smallest by 10 ;

Third term - first term

a + 2d - a = 10

2d = 10

d = 10/2

d = 5

Sum of the three terms :

a + (a + d) + a + 2d = 51

3a + 3d = 51

d = 5

3a + 3(5) = 51

3a + 15 = 51

3a = 51 - 15

3a = 36

a = 12

The AP would be:

First term, a = 12

Second term, a + d = 12 + 5 = 17

Third term = a + 2(d) = 12 + 10 = 22

Therefore , the first three terms of the AP are :

12, 17 and 22

Learn more about ARITHMETIC PROGRESSION :

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Related Questions

Find the missing segment in the image below

Answers

Answer:

4

Step-by-step explanation:

First, we can take two triangles -- one with 2 as a side and the big one. Literally every side of the triangle with the 2 in it is parallel to its corresponding side the big triangle. Therefore, we can say that the two triangles are similar.

In similar triangles, we can say that the ratios of corresponding sides are the same. Let's say that the bottom side of the big triangle is x, and the question mark is y. Therefore, the hypotenuse of the big triangle is 6+y. Furthermore, the ratio of corresponding sides ((6+y)/y and x/2) are equal, so

(6+y)/y = x/2

Since x is clearly made up of 3 and 2, we can say 3+2=x=5

(6+y)/y = 5/2

multiply both sides by y to remove a denominator

6+y = 5*y/2

multiply both sides by 2 to remove the other denominator

12+2y = 5*y

subtract both sides by 2y to isolate the y and its coefficient

12 = 3y

divide both sides by 3 to isolate the y

y=4

41. A pair of shoes was originally priced at
$90. After two successive discounts of
10% and 5%, what was the final price?
(1) $72.90
(2) $75.00
(3) $76.95
(4) $78.25
(5) $80.40
of 30 and a pe-

Answers

Answer:

Step-by-step explanation:

First discount

90/100 * 90 = 81 dollars

Second discount.

Be careful. This is usually a discount from the price in part are.

5% of 81 = 5/100 * 81 = 4.05

81 - 4.05 = 76.95

Find the domain and range of the function, f(x)=sin|x|

Answers

Answer:

[tex]Domain = (-\infty,\infty)[/tex]

[tex]Range = (0,1)\\[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \sin|x|[/tex]

Solving (a): The domain

There is no restriction on the given function because it is not a root function and doesn't have a x denominated fraction

Hence, the domain is:

[tex](-\infty,\infty)[/tex]

Solving (b): The range

The minimum of a sine function is 0

The maximum of a sine function is 1

So, the range is:

[tex](0,1)[/tex]

Find the length of the missing side

Answers

Answer:

Step-by-step explanation:

Side=AC=9[tex]\sqrt{2}[/tex]

Side AB= x

Hypotenuse =CB= y

Side AB = 9[tex]\sqrt{2}[/tex]

Hypotenuse CB = 36

Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation

Answers

The question is an illustration of a function using graphs. When a function is plotted on a graph, the x-axis represents the domain, while the y-axis represents the range of the function.

The domain and the range of the given function are:

Domain: [tex](-\infty,\infty)[/tex]

Range: [tex](3,\infty)[/tex]

From the question, we have the function to be:

[tex]g(x) = 3^x + 3[/tex]

First, we plot the graph of g(x)

To do this, we first generate values for x and g(x). The table is generated as follows:

[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]

[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]

[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]

[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]

[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]

In a tabular form, we have the following pair of values

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]

See attachment for graph

From the attached graph of g(x), we can observe that the curve stretches through the x-axis and there are no visible endpoints.

This means that the curve starts from - infinity to +infinity

Hence, the domain is: [tex](-\infty,\infty)[/tex]

Also, from the same graph, we can observe that the curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction.

This means that the curve of g(x) is greater than 3 on the y-axis.

Hence, the range is: [tex](3,\infty)[/tex]

Read more at:

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If Y / 4 - 12 = 3.5, what is the value of y?

Answers

The answer to your question is 62

Find the value of x.
X 9 9 7 x = [?]

Answers

Due to the 2 lines being equal length from the center, the two outer lines are the same, the on is shown as 7, and another 7 bc of the lines that say they’re the same. Answer is 14

7 There are five women and six men in a group. From this group a committee of 4 is to be chosen. In how many different ways can a committee be formed that contain at least three women?​

Answers

Answer:

in three (3) ways a committee can formed

Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?



Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week

Answers

Answer: Megan's at 3 inches per week

Answer: D (Megan's at 2.5 inches per week)

Step-by-step explanation: Its right.

Your small business spent $40 on food and another $60 on materials. Then, you sold an item for $120, but you had to pay a $90 service fee. Finally, you were given a refund from the Internal Revenue Service (IRS) for $70. If the expression describing these transactions is the following, then how does it evaluate?

Answers

Answer:

40$+60$=100$ spent

120$sold

90$ payed

70$ refund

120 (sold) -90 (payed) =30+70 (refund) =100$ (profit)

Step-by-step explanation:

You spent 100$

And you sold and got 120 but you payed 90$ from 120$ money left is 30$

Then they refunded you (pay back the money (give you the money ))

So the money that your left with is 30$ and the refund money is 70$

So add the money that your left with is gives you 100$

A large cable company reports that 42% of its customers subscribe to its Internet service, 32% subscribe to its phone service and 23% subscribe to both its Internet service and phone service.
a) What is the probability that a randomly selected customer subscribes to the Internet service or the phone service?
b) What percent of customers subscribe to neither the Internet service nor the phone service?

Answers

9514 1404 393

Answer:

  a) 51%

  b) 49%

Step-by-step explanation:

a) P(A∪B) = P(A) +P(B) - P(A∩B)

  P(A∪B) = 42% +32% -23% = 74% -23% = 51%

51% subscribe to one or the other.

__

b) P(¬A∩¬B) = P(¬(A∪B)) = 1 -P(A∪B) = 1 -51% = 49%

49% of customers subscribe to neither service.

A circle has a radius of 10 units and is centered at (-9,9). What is the equation of this circle? \sqrt{9

square root of, 98, end square write the equation of this circle.

Answers

A circle has an equation of a form,

[tex](x-a)^2+(y-b)^2=r^2[/tex]

Where [tex](a, b)[/tex] is the center and [tex]r[/tex] is the radius.

The coordinates of your circle center are [tex](a,b)=(-9,9)[/tex] and the radius is [tex]r=\sqrt{98}[/tex], so plug that in,

[tex](x-(-9))^2+(y-9)^2=\sqrt{98}^2[/tex]

and simplify to get the equation,

[tex](x+9)^2+(y-9)^2=98[/tex]

Hope this helps :)

A family is thinking about buying a new house
costing 380 000$. They must pay 110 000$ down and the rest is to
be amortized over 25 years in equal monthly payments. If money
costs 7% compounded monthly
(A)What will their monthly payment be?
(B)What will be unpaid balance after 20 years?
(C)How much total interest will be paid over the 25 years?

Answers

Answer:

a.) 1908.30

b.) 96373.15

c.)302491.15

unrounded answers below

Step-by-step explanation:

The amount that is to be loaned out is 380000-110000=270000

The effective montly rate is .07/12=.005833333

a.)

[tex]270000=x(\frac{1-(1+.005833333)^{-(25*12)}}{.005833333})=1908.303833[/tex]

b.)

use what is called the prospective method (the outstanding loan balance at time n is equal to the present value of the remaining payments)

[tex]1908.303833(\frac{1-(1+.005833333)^{-(25*12-20*12)}}{.005833333})=96373.14775[/tex]

c.)

total paid= 1908.303833*12*25=572491.1499

amount of loan: 270000

Total interest paid:

572491.1499-270000=302491.1499

Which one and what do I put in the box(s)

Answers

Answer:

Option A i the right option.

First blank is 110-[tex]10\sqrt{61}[/tex] or 10(11-[tex]\sqrt{61}[/tex])

Second blank is 31.898

Let me know if anything didn't make sense.  

Step-by-step explanation:

So a diagonal through a rectangle makes two triangles.  The question wants to know how much walking is saved walking down the diagonal  vs walking along two sides that make the diagonal.  in this case the two non diagonal sides walked are 60 paces and 50 paces.

A diagonal through a rectangle specifically makes a right triangle, so to find the diagonal we can use the pythagorean theorem.  

c^2 = 60^2 + 50^2

c = [tex]\sqrt{60^2 + 50^2}[/tex]

c = [tex]\sqrt{6100} = 10\sqrt{61}[/tex]

if you don't get how to simplify a radical like that let me know.

Anyway, looking at the answers you can see right away the second option says no approximation is necessary.  Well, you need to approximate square root of 61, so we can say the second answer is not right.  So now we need to know what to fill in for option 1.

it wants the distance saved, well we know the distance of the diagonal is [tex]10\sqrt{61}[/tex]  Hopefully you can see the disctance walking the two other sides is just adding them up so 50+60=110.

Now, to find the difference, that is subtraction.  So subtract the smaller number from the larger number.  You do need to remember with a right triangle, the sum of the to non diagonal (hypotenuse) sides are always longer than said hypotenuse.  so that's 110-[tex]10\sqrt{61}[/tex].  That is the exact form.  Or you could use 10(11-[tex]\sqrt{61}[/tex])  They are the same.

Then just plug that into a calculator for a decimal approximation.

If f (x) = 8X, then f (3) =
O 24
O 64
O 512
O 4,096

Answers

Answer: 24
Explanation:
F(x)= 8x
F(3)= 8*3
F(3)=24

3. In A PQR, MZP=(4x-5),
m2Q=(8x-50), and MZR=(3x+10).
Which of the following best describes
APQR?
® Right triangle
® Isosceles triangle
© Equlateral triangle
Scalene triangle

Answers

Answer:

B

Step-by-step explanation:

The sum of all of them will result in 180. 15x-45=180. x=15. P=55, Q=70 and R=55. It's an isosceles triangle

Answer:

b

Step-by-step explanation:

its b

If you multiply the sum of 546 and 1711 by zero, what will be your result?​

Answers

Answer:

0

Step-by-step explanation:

any numbers multiply by zero always equals to zero

The carpet in the school library needs to be replaced. The dimensions of the library floor or shell each square foot of cart bit cost $1.25. What is the total cost of the new carpet for the library

Answers

To find the cost, we must:

First, find the area of the carper. It can be found dividing the carper into a rectangle and a right triangle.Then, with the area, in square foot, we have the cost per square foot, which makes it possible to find the total cost.

Doing this, we get that the cost is: $3,815, and the correct option is B.

Carpet:

The carpet can be divided into:

A rectangle of dimensions 56 ft and 38 ft.A right triangle of legs 71 - 38 = 33 ft and 56 ft.

----------------------------------------------

Area of the rectangle:

The area of a rectangle of dimensions l and w is given by:

[tex]A_r = lw[/tex]

In this question, the dimensions are l = 56 ft, w = 38 ft, so the area, in square feet, is:

[tex]A_r = 56*38 = 2128[/tex]

-------------------------------------------

Area of a right triangle:

The area of a right triangle of legs a and b is given by:

[tex]A_t = \frac{ab}{2}[/tex]

In this question, the legs are a = 56, b = 38, so the area, in square feet, is:

[tex]A_t = \frac{56(33)}{2} = 924[/tex]

----------------------------

Total area:

The total area is the sum of the area of the rectangle with the area of the right triangle, thus:

[tex]A = A_r + A_t = 2128 + 924 = 3052[/tex]

-------------------------

Cost:

Each square foot costs $1.25.

There are 3,052 square feet. So, the cost is:

[tex]C = 1.25*3052 = 3815[/tex]

Thus, the cost is $3,815, and the correct option is B.

A similar question is found at https://brainly.com/question/13209573

Mr. Cole packed 20 pounds into a suitcase, and Mrs. Cole packed 23 pounds into the same suitcase. They then had to remove 8 pounds because it was too heavy. How many pounds was their suitcase after making it lighter?

Answers

Answer:

35 lbs is the final weight

Step-by-step explanation:

20 +23 = 43 lbs

Then they had to remove 8 lbs

43 - 8 =35

35 lbs is the final weight

help with summer school

Answers

Answer:

19

Step-by-step explanation:

3a -2^3 ÷b

Let a = 7 and b = 4

3*7 -2^3 ÷4

PEMDAS says exponents first

3*7 -8 ÷4

Multiply and divide from left to right

21 - 2

Subtract

19

find the value of the trigonometric ratio​

Answers

Answer:

3/5

Step-by-step explanation:

sinA = opposite/hypotenuse = BC/AC = 21/35 = 3/5

There are 3 red marbles and 8 blue marbles in a bag. (a) What is the ratio of all marbles in the bag to blue marbles? (b) What is the ratio of red marbles to all marbles in the bag?​

Answers

Answer:

a.) 11:8

b.) 3:11

Step-by-step explanation:

a)

Add all marbles

8 + 3 = 11

Blue marbles = 8

So, the ratio will be 11:8

b)

Red marbles = 3

All marbles = 11

So, the ratio will be 3:11

Hope this helps.

Answer:

Step-by-step explanation:

A washer and a dryer cost $858 combined. The washer costs $92 less than the dryer. What is the cost of the dryer?

Answers

Answer:

383

Step-by-step explanation:

Let dryer be d.

(d + 92) + d = 858

2d + 92 = 858

      -92 =  -92

---------------------

    2d = 766

    ----    ------

     2        2

       d = 383

The dryer is $383

Hope this helped.

Answer:

$475

Step-by-step explanation:

The dryer costs x.

Since the washer costs $92 less than the dryer, then the dryer costs x - 92.

Combined, they cost $858.

x + x - 92 = 858

2x - 92 = 858

2x = 950

x = 475

Answer: $475

Ashley has a rectangle made out of paper that is 8 cm by12 cm. She folds it in half twice, first vertically and then horizontally. The new rectangle looks just like the original rectangle but smaller. What is the area of the new smaller rectangle in square cm

Answers

Answer:

[tex]Area =24cm^2[/tex]

Step-by-step explanation:

Given

[tex]L = 8cm[/tex]

[tex]W = 12cm[/tex]

[tex]r = 2[/tex] -- folded twice

Required

The area of the new rectangle

When the length was folder, the new length is:

[tex]l = L/2 = 8cm/2 = 4cm[/tex]

When the width was folder, the new width is:

[tex]w = W/2 = 12cm/2 = 6cm[/tex]

So, the new area is:

[tex]Area =l * w[/tex]

[tex]Area =4cm * 6cm[/tex]

[tex]Area =24cm^2[/tex]

An airplane started at 0 feet. It rose 21,000 feet at takeoff. It then descended 4,329 feet because of clouds. An oncoming plane was approaching, so it rose 6,333 feet. After the oncoming plane passed, it descended 8,453 feet, at what altitude was the plane flying?

Answers

14551 feet use a calculator

if PQR measures 75° , what is the measure of SQR

Answers

Answer:

PQR+SQR=180°(angles in a triangle)

75°+SQR=180°

SQR=180°-75°

SQR=105°

Find the missing side length image below

Answers

Answer:

40

Step-by-step explanation:

Based on the Proportional Transversal Theorem, the three parallel lines hat intersects the two transversals, divides the transversal lines proportionally.

Therefore, we would have the following ratio:

28/35 = ?/50

Cross multiply

35*? = 50*28

35*? = 1,400

Divide both sides by 35

? = 1400/35

? = 40

What is 4 × 1/7 on a numberline​

Answers

Answer:

4/7

Step-by-step explanation:

When you multiply by fractions you multiply the numerators and denominators

4/1 x 1/7

Anything that doesnt have anything under it always has a 1 as its denominator

Plane P is a cross-section of the solid below. What shape is the cross section?
A. rectangle
B. not enough information
C. hexagon
D. pentagon

Answers

Answer:

C. Hexagon

Step-by-step explanation:

The answer is clearly C. Hexagon. This is because the question is referring to the shape shown on Plane P as if it were 2D. Therefore, the shape with 6 sides is a hexagon and cannot be anything else.

The shape is the cross-section is a hexagon.

What is a hexagon?

In geometry, a hexagon may be described as a closed two-dimensional polygon with six aspects. The hexagon has 6 vertices and 6 angles also. Hexa means six and gonia approach angles.

All hexagons have six facets, regardless of the sort of hexagon it is. which means that normal hexagons, irregular hexagons, concave hexagons, and convex hexagons all have six facets.

Learn more about hexagon here:-https://brainly.com/question/1615720

#SPJ2

Can u please help I got 1 minnnn lefttttt

Answers

Answer:

26 cm

Step-by-step explanation:

P = 2a + 2b

a = side

b = base

Answer:

The area=base×height

=10×4

=40cm^2

perimeter=2(length+breadth)

I think to find the height Dc you use the pythagoras theorem of

Dc^2=de^2+ce^2

=√16+9

=5

therefore the perimeter will be

p=2(5+10)

=20cm

I hope this helps and sorry if it's wrong

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