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2 years ago

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

Mathematics

1 answer:

masha68 [24]2 years ago

7 0

By the binomial theorem,

$7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1$

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

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The width of a rectangle is the length minus 3 units. The area of the rectangle is 54 units. What is the width, in units, of a r

saul85 [17]

Width of the rectangle is 9 units

Step-by-step explanation:

Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units

Area of the rectangle = length × width

54 = x (x - 3)

54 = x² - 3x

x² - 3x - 54 = 0

x² + 6x - 9x - 54 = 0 (Using Product Sum rule to factorize)

x(x + 6) - 9(x + 6) = 0

(x + 6)(x - 9) = 0

x = -6, 9 (negative value is neglected)

x = 9 units

4 0

2 years ago

Suppose a pyramid’s dimensions are tripled. What is the ratio of this new, larger pyramid’s volume to that of the original pyram

anzhelika [568]

Answer:

The answer is D

Step-by-step explanation

I took the quiz on ed.

4 0

2 years ago

Read 2 more answers

If ∆ABC and ∆GEF are congruent, the value of x is___? and the value of y is ___?

attashe74 [19]

Answer-

The value of y is 6 units.

Solution-

Given ∆ABC ≅ ∆GEF

If two triangles are congruent, then the corresponding sides are also congruent.

So,

EF = BC, GF = AC

Putting the values,

$\Rightarrow x-y=4$ --------------1

$\Rightarrow x-8=2$

$\Rightarrow x=10$ --------------------2

Putting the values of x in equation 1,

$\Rightarrow 10-y=4$

$\Rightarrow y=10-4=6$

Therefore, the value of y is 6 units.

7 0

2 years ago

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Explain why you would make one of the addends a tens number when solving an addition problem

leonid [27]

You refer to a multiple of ten. As a multiple of ten you can just add it to another number easier than a "ones number".

4 0

2 years ago

Identify the percent of change as increase or decrease then find the percent of change round to the nearest tenth of a percent (

morpeh [17]

Hello,

Here is the first answer:

The answer is "16.6 or 17%".

Reason:

636 x 100% = 16.6666666667%

Here is your second answer:

The answer is "50%".

Reason:

36 x 100% = 50%

Here is your third answer:

The answer is "43.3 or 43%".

Reason:

52120 x 100% = 43.3333333333%

Here is your fourth answer:

The answer is "328.5 or 329%".

Reason:

11535 x 100% = 328.5714285714%

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

7 0

2 years ago