The sum of first three terms of an arithmetic series is 21. If the sum of the first two terms is subtracted from the third term then it would be 9. find the three terms of the series. The first and last bra​

Answers

Answer 1

Answer:

The terms are - 1, 7 and 15.

Step-by-step explanation:

Let the terms be a-d, a, a+d.

ATQ, a-d+a+a+d=21, a=7 and a+d-(a-d+a)=9. 2d-a=9, d=8. The terms are - 1, 7 and 15.

Answer 2

The first three terms will be :   -1, 7, 15

We have sum of first three terms of an arithmetic series is 21. It is given that if the sum of the first two terms is subtracted from the third term then it would be 9.

We have to find the three terms of the series.

What is Arithmetic progression or sequence?

An arithmetic progression or sequence with common difference [tex]d[/tex] is given as -

a, a + d, a + 2d, a + 3d .....

According to the question -

a + (a + d) + (a + 2d) = 21

3a + 3d = 21

3(a + d)=21

a + d = 7                             (Eqn. 1)

(a + 2d) - (a + a + d) = 9

a + 2d - a - a - d = 9

d - a = 9

a = d - 9

Substituting the value of 'a' in Eqn. 1, we get -

d - 9 + d = 7

2d - 9 = 7

2d = 16

d = 8

Therefore -

a = 8 - 9

a = -1

The three terms are -

a = -1

a + d = -1 + 8 = 7

a + 2d = -1 + 2 x 8 = 15

Hence, the first three terms will be - -1, 7, 15

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Related Questions

multiply
0.105 x 0.7=

Answers

Answer:

0.0735 got it right

Step-by-step explanation:

got it right

Solve the equation | 7x + 5| = |3x - 13|​

Answers

I 7X + 5 I = I 3X- 13I

7×+5 = 3x +13

7X-3x = 13-5

4x = 8

X= 8/4

X=2

The Vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).Find the length of each diagonal.Show me with the steps Please!​

Answers

Answer:

13 and 17 units

Step-by-step explanation:

explaination is in pic.

The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.

What is the length between two points in a plane?

The length between two given points (x₁, y₁) and (x₂, y₂) will be:

√[(x₂ - x₁)² + (y₂ - y₁)²] units

Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).

Therefore, the diagonals of the quadrilateral will be AC and BD.

The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).

Now, the length of the diagonal AC will be:

= √[(-8 - 4)² + (2 - (- 3))²] units

= √[(- 12)² + (5)²] units

= √[144 + 25] units

= √(169) units

= 13 units                                  (length can't be negative)

Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).

Now, the length of the diagonal BD will be:

= √[(-1 - 7)² + (- 5 - 10)²] units

= √[(- 8)² + (- 15)²] units

= √[64 + 225] units

= √(289) units

= 17 units                                  (length can't be negative)

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i don’t know what it is can someone help

Answers

Answer:

b

Step-by-step explanation:

One year ago, the ratio of Honey and Piyush ages was 2:3 respectively. After five years from now, this ratio becomes 4:5. How old is Piyush now?

Answers

Answer:

eşnatto eşmatoroorlfld

Answer:

Now , Piyush age =3+Honey age

Step-by-step explanation:

Honey age=x

Piyush age=y

1 year ago,Honey age=x-1

Piyush age=y-1

the ratio of Honey and Piyush age=2:3

x-1:y-1=2:3

x-1/y-1=2/3

3(x-1)=2(y-1)

3x-3=2y-2

3x-2y= -2+3

3x-2y=1 eq _1

after 5 years from now,

Honey age=x+5

Piyush age=y+5

the ratio of them=4:5

x+5/y+5=4/5

5(x+5) =4(y+5)

5x+25=4y+20

5x-4y=20-25

5x-4y=-5 _eq2

eq1and 2_

5x-4y= -5

3x-2y= 1

-

2x-2y=-6

x-y =-3

-y=-3-x

y=3+x

Sitting on a park bench, you see a swing that is 100 feet away and a slide that
is 60 feet away. The angle between them is 30°.
distance between the swing and the slide?
What is the approximate

Answers

Answer:

50

Step-by-step explanation:

Answer:

The approximate between the swing and slide is 56.21 feet.

Step-by-step explanation:

Find the inverse of the given function. f(x) = 7x – 4​

Answers

Hi there!

[tex]\large\boxed{y = \frac{x + 4}{7}}[/tex]

f(x) = 7x - 4

Rewrite f(x) with y:

y = 7x - 4

Swap the x and y variables:

x = 7y - 4

Solve for y:

x + 4 = 7y

y = (x + 4)/7

f(x) =-x^2+x+13
find f(9)

Answers

Answer:

f(9) = - 59

Step-by-step explanation:

Substitute x = 9 into f(x) , that is

f(9) = - (9)² + 9 + 13

     = - 81 + 22

    = - 59

Answer:

-59

Step-by-step explanation:

f(x) =-x^2+x+13

Let x = 9

f(9) = - (9)^2 +9+13

       = -81 +9+13

      = -59

Choose the congruence theorem that you would use to prove the triangles congruent

Answers

Answer:

It would be the HL theorum.

Step-by-step explanation:

The answer would be the HL theorum by just considering the name.  "HL" stands for Hypotenuse-leg.  The problem tells you that both triangles share the same length of their hypotenuse (The Hypotenuse is the line with one dash in it, or the one opposite of the 90 degree angle) and one of the legs (The legs are the lines that connect to make the 90 degree angle).  This makes the triangle congruent because if 2 sides of a triangle are the same it means that the third one is congruent as well.

I need help, please come answer this

Answers

10

Work:
PEMDAS
8 • 15/5 - (5 + 9)
8 • 3 - 14
24 - 14
10

Answer:

[tex]8 \times \frac{15}{5} - (5 + 9) \\8 \times 3 - (14) \\ 24 - 14 \\ = 10[/tex]

I hope I helped you^_^

solve the inequality and graph the solution

-5-7x < -40

Answers

Answer:

x > 5

Step-by-step explanation:

-5-7x < -40

Add 5 to each side

-5+5-7x < -40+5

-7x < -35

Divide by -7, remembering to flip the inequality

-7x/-7 > -35/-7

x > 5

Open circle at 5, going to the right

Which of the following numbers are solutions of the sentence x-3 < 2?
I -3
II 0
III 2
IV 5

O ll only
O III only
O I and III only
O I, II, and III only
O I, II, III, and IV​

Answers

Answer:

O I, II, and III only

Step-by-step explanation:

x-3 < 2

Add 3 to each side

x-3+3< 2+5

x<5

-3 is less than 5

0 is less than 5

2 is less than 5

5 is not less than 5

I , II , II are true

Here are two fractions 3/10 and 5/7 work out which one is closer to a 1/2

Answers

Answer:

Therefore 3/10 is closer to ½

Step-by-step explanation:

We've to get the difference:

» with 3/10 :

[tex] \frac{1}{2} - \frac{3}{10} = { \boxed{\frac{1}{5} }}[/tex]

» with 5/7

[tex] | \frac{1}{2} - \frac{5}{7} | = { \boxed{ \frac{3}{14} }}[/tex]

but:

[tex] \frac{3}{14} > \frac{1}{5} [/tex]

Among both the given fractions, the one that is closer to a ½ is 3/10.

What is a fraction?

A number that is stated as a quotient in mathematics, when the numerator and denominator are split in half. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction.

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

A fraction is a number that represents a portion of a whole. In order to evaluate it, a whole is divided into a number of components.  A correct fraction has a numerator that is lower than its denominator.

Required calculations are done with both the fractions,

1/2 - 3/10 = 1/5

1/2 - 5/7 = 3/14

3/14 ≥ 1/5

Therefore, among both the given fractions, the one that is closer to a ½ is 3/10.

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Simplify
1)a³b⁴/ ab³
2)2 (x³ )²
3)3x*2x³ y²

Answers

Answer:

1) a³b⁴/ ab³ = a²b

2)2 (x³ )² = 2x^6

3)3x*2x³ y² = 6x⁴y²

What is the solution set of { x | x <-5} n { x | x >5 }? Help needed!

Answers

Answer:

The Empty set............

Answer:

There is no solution for the intersection of these two sets, as they do not intersect! They don't have any numbers in common and thus form an empty set. The correct answer choice is option D. the empty set.

Step-by-step explanation:

The solution for { x | x <-5} is ---> x < -5

The solution for { x | x >5 } is ---> x > 5

If you placed the two sets on a number line close to each other, you would see that they do not intersect. Thus there is no solution for the intersection of set A and set B as defined in the given problem.

See the graph for better understanding. You see how there's an empty space or area between -5 and 5? Yeah, this is called the empty set which is option D from your answer choices.

Find the value of a. A. 57 B. 104 C. 26 D. 52​

Answers

Answer:

Option D, 52

Answered by GAUTHMATH

The conjecture "if n is a whole number then 3n+1 is a prime number" is disapproved by which statement

Answers

Answer:

D

Step-by-step explanation:

Simply because 25 is divisible by 5.

Which of the following is true about the quotient -2/0?
A.
The quotient is equal to -2.
B.
The quotient is undefined because the denominator is zero.
C.
The quotient is undefined because the numerator is negative.
D.
The quotient is equal to 0.

Answers

Answer:

B.The quotient is undefined because the denominator is zero.

Step-by-step explanation:

You cannot divide by zero.  Take a piece of paper and divide into zero pieces.  It cannot be done as we know it.  That is undefined.

The quotient is undefined because the denominator is zero.

Option (B) is the correct answer.

Round 4746.13662611 to the nearest whole number.

Answers

Answer:

4746

Step-by-step explanation:

4746 is the answer. since 1(the first number after the point) is less then 5 so we dont need to round the last number (before the point)

25 points, choices in photo
Which of the following accurately shows the first step when solving the following system of equations by substitution?

Answers

I would go with C as a first step

The correct answer is C (that is equating f(x) and g(x))

How to solve a quadratic and linear equation?

A quadratic polynomial has highest degree 2 and a linear polynomial has highest degree 1.

In geometric sense, solving them means finding the point of intersection of curves:

In X-Y plane, these polynomials can be written as:

[tex]y=-x^{2} +2x+3\\y=-2x+3[/tex]

Taking the value of y from second equation and substituting it in first equation we get,

[tex]-x^{2} +2x+3=-2x+3[/tex]

Therefore, with the above procedure, we got the first step of solving the equations with the help of substitution.

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Create a triangle ABC of your choice. Using GeoGebra tools, construct the angle bisectors of ∠A and ∠B. Mark the intersection point of the angle bisectors, and label it point D.
Create a line through point D perpendicular to .
Find the intersection of line segment and the perpendicular line, and label it point E. With point D as the center, create a circle passing through point E.
Measure and label the radius of the inscribed circle of ΔABC on the diagram.
Take a screenshot of your result, and paste it below.

Answers

The steps to create attached screenshot of the inscribed circle of triangle ΔABC using GeoGebra tools includes;

1) Clicking on the Geometry link, under Powerful Math Apps group

2) On the opened Geometry page click on the Polygon icon and follow the instructions that come up, which is Select all vertices and then the first vertex (selected) again (a second time)

3) Once the triangle is created, select the Angle Bisector icon, under the Construct group; A message will appear, asking to Select three points or two lines, select three vertex, of the triangle created with a mouse click, with the vertex A in the center, such as BAC, or CAB a straight line representing the angle bisector of angle ∠A is created

4) Repeat the above to create the angle bisector of angle ∠B

5) Click on the Point button under the Basic Tools group, then click on the intersection of the two angle bisectors created above, the point will be automatically labelled point D

6) Click on the Perpendicular Line, icon under the Construct group, then click on point D, and then the line AB to draw the perpendicular from D to AB

7) Click on the point Point icon and then the intersection point of the perpendicular from D and AB to label the point E

8) Click on the Circle with Center basic tool and then points D and E above, to create the inscribed circle of triangle ΔABC

9) Select the Segment tool, then select the center of the circle and a point

on the circumference. Click on the label, from the pop up options, select

the label option AA then change the label of the segment created to Radius

and select Show Label and Show Value. The inscribed circle of ΔABC created with GeoGebra tools is attached

Learn more about GeoGebra hear;

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Answer:

Step-by-step explanation: from edmentum


What will be the first term of a geometric series which has its sum 280, common ratio 3 and the last term 189 ?

Answers

Answer:

b1=7

Step-by-step explanation:

If we deal with geometric series, we should use the formulas for it. If there is the last term, it is not infinite geometric series. The sum of geometric series which isn't infinite is equal to b1(r^n-1)/(r-1)   where b1 is the first term and r is the common ratio.

So 280= b1(3^n-1)/(3-1)

560= b1(3^n-1)

560= b1*3^n-b1

Then express bn=b1*r^(n-1)

189= b1*3^(n-1)

189= b1*3^n*1/3

567= b1*3^n when

560= b1*3^n-b1

560=567-b1

b1=7

The Ramirez family and the Stewart family each used their sprinklers last summer. The water output rate for the Ramirez family's sprinkler was 40 L per hour.
The water output rate for the Stewart family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total
water output of 1575 L. How long was each sprinkler used?

Answers

Answer:

15.5

Step-by-step explanation:

Yes

Warren is on vacation and needs to arrange transportation. A rental car costs 40 dollars per day plus a one-time cost of 14 dollars for insurance. Construct a function C(x) that gives the total cost of renting a car for x days. C(x)=________.
If Warren has budgeted 254 dollars for the rental, how many days can he afford?

Answers

Answer:

C(x)=40x+14, 6 days

Step-by-step explanation:

C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.

C(x)=254=40x+14, 40x=240, x=6

Is 3584 a term of the series 7+14+28+56........?
(please answer if you know; this is the question from geometric series:- General progression)
(full steps and process required)
(No spam answers or else you'll be reported )​

Answers

Answer:

yes it is the 10th term in the series

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{14}{7}[/tex] = 2 , then

[tex]a_{n}[/tex] = 7 [tex](2)^{n-1}[/tex]

Equate [tex]a_{n}[/tex] to 3584 and solve for n

7 [tex](2)^{n-1}[/tex] = 3584 ( divide both sides by 7 )

[tex]2^{n-1}[/tex] = 512 , that is

[tex]2^{n-1}[/tex] = [tex]2^{9}[/tex]

Since the bases on both sides are equal, both 2 , then equate the exponents

n - 1 = 9 ( add 1 to both sides )

n = 10

3584 is the 10th term in the series

ABCD is a rectangle. AB = 3x+5, AC = 7x-9, BC = 2y+5, BD = 2x+62. Solve for x. (Round your answer to one decimal place, if necessary.)

Answers

Answer:

x=14.2

Step-by-step explanation:

AC = BD

The diagonals of a rectangle are equal

7x-9 =  2x+62

Subtract 2x from each side

7x-9-2x = 2x+62-2x

5x-9 = 62

Add 9 to each side

5x-9+9 = 62+9

5x= 71

Divide by 5

5x/5 = 71/5

x=14.2

ITS TIMED HELP!!!
Assuming x and y are two odd numbers and x/y is an integer. Which of the following statements are true?
1: x + y is odd.
2: xy is odd.
3: x/y is odd.
4: x-y is odd.

A: 1 and 2 only.
B: 1 and 3 only.
C: 2 and 3 only.
D: 2, 3, and 4 only.
E: 2 and 4 only.​

Answers

Answer:

C

Step-by-step explanation:

1: x + y is even. Try it. 3 + 5 = 8. 2x + 1 + 2y + 1 = 2x +2x + 2. That's even no matter what 2 odd numbers you use.

2: xy is again try it 3 * 5 = 15 which is odd. (2x + 1)(2y + 1) = 4xy + 2x + 2y + 1. The first 3 terms are even. The last one is odd. So xy is odd.

3. 9/3 = 3. Three should be true. The numerator is greater than the denominator. And x/y is given as an integer. So the statement should be true.

4. x - y is This can't be right. 2x + 1 - 2y - 1 = 2x + 2y. The result is even.

2 and 3 only

I need help plz anyone I don't understand this at all.

Answers

Answer:

jejejjejejr

Step-by-step explanation:

uejejjejejjsjs

1/4x-2= -6+ 5/12x1/4x-5/12x= -6+23x-5x/12 = -43x-5x= -4×122x= -48x= -48/2x= -24

Kristian spends 45% of his $ 75 on a game. What is the price of the game​

Answers

Answer:

The price of the game is 33.75

Step-by-step explanation:

45% of 75

.45 * 75

33.75

The price of the game is 33.75

How I solve equations like these is by multiplying the percent (45) by the whole (75) and dividing the product ( 3375) by 100. In this case 75 is equal to 100 because 75 is the whole.

What is the slope of a line that passes through the points (-2, 4) and (-6, 12)?

Answers

Here’s the answer to your question
Hope you understand it!,

Answer:-3\2

Step-by-step explanation:

slope is difference y axis by x axis

4-12/-2+6=-6/4=-3\2

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