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3 years ago

What is (128 +7x- 12) = (4x - 3)?

Mathematics

1 answer:

podryga [215]3 years ago

4 0

Answer:

x = -119/3 = -39 2/3

Step-by-step explanation:

(128 +7x- 12) = (4x - 3)

Combine like terms

(116 +7x) = (4x - 3)

Subtract 4x from each side

116 +7x-4x=4x-4x-3

116 +3x = -3

Subtract 116 from each side

116-116 +3x = -3-116

3x = -119

Divide each side by 3

3x/3 = -119/3

x = -119/3

x = -39 2/3

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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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$216 = 6^{4x+ 11}$

$6^3 = 6^{4x+ 11}$

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$x = -2$

Answer: (c) x = -2

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3 years ago

Which of the following is a counterexample for this conditional statement?If an appliance is used for cooling, then it is a refr

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Explanation

We are asked to give a counter-example for the given statement

A counter-example is an example that opposes or contradicts an idea or statement.

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we have that

Statement: If an appliance is used for cooling

Conclusion: then it is a refrigerator

Then, the option that contradicts this, will be a clothes dryer

Because a dryer doesn't cool

Hence, the answer is a cloth dryer

option D

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8 months ago

What is (128 +7x- 12) = (4x - 3)?​

What is (128 +7x- 12) = (4x - 3)?