The sum of two numbers is 91. If twice the smaller number is subtracted from the larger number, the result is 4. Find the two numbers

Answers

Answer 1

Answer:

Answer:

the 2 numbers are 29 and 62

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the first four terms of an arithmetic sequence are 2,a-b, 2a+b+7 and a - 3b, where a and b are constants. Find a and b

Answers

Arithmetic Sequence

The values of a and b is a = 2 and b=3

Step-by-step explanation:

Given the terms of the arithmetic sequence are

2 , a - b , 2a + b + 7, a - 3b

Let the common difference be D

Therefore,

The difference between the first two consecutive terms is

(a – b) – 2 = D ------------------------------( 1 )

The difference between the next two consecutive terms is

D = (2a + b+7) – ( a - b ) ---------------------(2 )

Equating equation 1 and equation 2

⇒ (a – b) -2 =(2a+b+7)-(a-b)

⇒ a – b – 2 = a + 2b +7

⇒ 3b = -9

⇒ b = -3

Similarly

The difference between the next two consecutive terms is

D = (a-3b)-(2a+b+7) ------- (3)

⇒ (a-3b)-(2a+b+7)=(2a+b+7)-(a-b)

⇒ a-3b)-(2a+b+7) -a - 4b -7 === a+2b+7

⇒ 2a = - ( 14 + 6b)

⇒ a = -( 7 + 3b)

⇒ a = - ( 7 – 3*3 )

Thus the value of a = 2

Hence , the values of a and b is a = 2 and b=3

Final answer:

To find the values of a and b in an arithmetic sequence, we can set up a system of equations using the given terms. Solving the system will give us the values of a and b.

Explanation:

Let's use the information given to find the values of a and b. We can set up a system of equations using the first four terms of the arithmetic sequence.

The first term is 2, so we know that: a-b = 2.
The second term is a-b, so we can write: a-b + d = 2a+b+7, where d represents the common difference.
The third term is 2a+b+7, so we have: a-b + 2d = 2a+b+7 + d.
The fourth term is a-3b, so we get: a-b + 3d = a-3b + 2d.

We can solve this system of equations to find the values of a and b.

After simplifying and solving the system, we find that a = 10 and b = 8.

Learn more about Arithmetic sequence here:

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How do you create an equation that represents a proportional table?

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All you have to do is find the what happens to the x and then do f(x) = whatever function that makes y

Deb had a board that measures 5 feet in length. How many 1/4-foot long pieces can deb cut from the board?

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To do this, divide 5 by 1/4

You can also divide 5 by 0.25

And you get 20

Therefore, Deb can cut 20 pieces!

Hope this helped!

Which point is on the graph of the equation y = 2x - 5?(3, -1)
(2, -5)
(4, 2)
(2, -1)

Answers

The x in this equation is the first number in the brackets, and the result of the equation is the second number in the brackets. So all that needs to be done is to substitute x for 3, 2 and 4 and see which one has the correct answer.
3 X 2 = 6. 6 - 5 = 1 (3, 1)
2 X 2 = 4. 4 - 5 = -1 (2, -1)
4 X 2 = 8. 8 - 5 = 3 (4, 3)

The only one of those coordinates that are the same as any of the given answers are (2, -1). Therefore, that is the answer.

Answer:

(2,-1)

Im right because I got it right on my math quiz

The six faces of a fair cube are numbered 1 through 6. If the cube is rolled 300 times, what is the expected number of times a 5 will land face-up?