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2 years ago

Use inductive reasoning to determine the next two terms in each sequence: a) 1, 3, 7, 15, 31 ....

Mathematics

2 answers:

Shalnov [3]2 years ago

7 0

Answer:

63,127

Step-by-step explanation:

the interval between each number is multiplied by 2

such as between 1 and 3 we have 2 so 2×2=4

the 4+3=7 and so on

AysviL [449]2 years ago

6 0

Answer: 63, 127

Step-by-step explanation: 1+2=3; 3+4=7; 7+8=15; 15+16=31; 31+32=63; 63+64=127

Or, if we call the first value a1 , the sequence is given by an=2n−1

The first approach to analyzing almost any sequence is to look at the differences of successive elements. In this sequence, that’s 2, 4, 8, 16, 32. That makes the answers above pretty easy.

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Shortern this expression pls

pogonyaev

Answer:

$c =\frac{8}{3}$

Step-by-step explanation:

Given

$c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}$

Required

Shorten

We have:

$c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}$

Rationalize

$c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} + \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}$

Expand

$c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} + \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}$

$c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} + \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}$

$c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} + \sqrt{\frac{(4 - \sqrt 7)^2}{9}$

Take positive square roots

$c =\frac{4 + \sqrt 7}{3} + \frac{4 - \sqrt 7}{3}$

Take LCM

$c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}$

Collect like terms

$c =\frac{4 + 4+ \sqrt 7 - \sqrt 7}{3}$

$c =\frac{8}{3}$

4 0

2 years ago

(12,10),(-2,r), m=-4

Savatey [412]

Answer:66

Step-by-step explanation:

Y=mx+b

10=-4*12+b

10=-48+b

b=58

r=-4(-2)+58

r=66

4 0

3 years ago

Which expression is equivalent to 3(6m)+m?<br> A)19m B)21m C)7m+3 D)18m+6m(with exponent 2)

julsineya [31]

A) 19m because 3 times 6 is 18 then you add m, which would be 19m

5 0

2 years ago

A square has a side of 6.25 feet. What is the area in square feet? Round to the correct significant digits. (2 points)

soldi70 [24.7K]

Answer:

A=39.06 Sq Ft

Step-by-step explanation:

We are given with a square which has a side of 6.25 feet. We are asked to determine the area in square feet and Round to the correct significant digits.

Area of square is given as

A= side x side

Side = 6.25 ft

A=6.25 x 6.25

A= 39.0625

Rounding it to the nearest hundredth place

A=39.06 sq ft

7 0

2 years ago

Can someone else me with the answer I think that it’s 93 degrees

inna [77]

Thank you for coming to Brainly with your questions!

I believe the answer is:

93 degrees. You were correct. The interior angles all add up to 360, so you subtract each given angle to find the missing angle.

I hope this helps you! Please mark Brainliest! Let me know if I can help you with any further questions!

-Belle

7 0

3 years ago

Read 2 more answers