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WINSTONCH [101]
3 years ago
6

Find the missing expressions... (6+4n) - (8+3n) =? And (4+6n) - (3+8n)=?

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
5 0
(6+4n)-(8+3n)= 7n-2
(4+6n)-(3+8n)= 14n+1

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Use the Distributive Property to multiply. 2(b – 7)
mr Goodwill [35]

Answer:

2b - 14

Step-by-step explanation:

2(b – 7)

2b - 14

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3 years ago
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His triangle has a perimeter of 48 feet. The second side is 5 feet longer than the first side. The third side is 3 feet longer t
kotegsom [21]

Answer:

The length of the second side is 22.5 feet.

Step-by-step explanation:

7 0
3 years ago
Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

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3 years ago
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Ivenika [448]
When x=0, y=-8, so that is the y-intercept.

When x increases by 1, y decreases by 2, so the slope is -2.

The equation of the function is
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zaharov [31]

Answer:

a-x

b-/

Step-by-step explanation:

64/4x4=64

625x25/25=625

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