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3 years ago

11

Solve the equation for x.

1 answer:

yarga [219]3 years ago

6 0

Answer:

-90

Step-by-step explanation:

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Use the law of syllogism to form a conclusion from the given premises. Premise 1: If a polygon was translated to the right, then

Pachacha [2.7K]

<span>Premise 1: If a polygon was translated to the right, then its image is congruent to its pre-image.

In symbols: p => q

Premise 2: If an image is congruent to its pre-image, then a rigid transformation was performed.

In symbols: q => r

By the law of silogism

(p => q) and (q => r) => q => r

So, the conclusion is that </span><span>if a polygon was translated to the right, then a rigid transformation was performed. <---- answer</span>

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3 years ago

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-5(-3)(-3) what the product

sukhopar [10]

Answer:

Step-by-step explanation:

(-5) * (-3) * (-3) = -5 * -3 * -3 = 15 * -3 = -45

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3 years ago

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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

A water tank that holds 30 gallons of water when full is leaking 3/4 gallon of water every hour. If no one notices and stops the

viva [34]

It will take 40 hours for the water tank to become empty.

Explanation:
Divide 30 by 0.75 (equivalent to 3/4).

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3 years ago

Solve the equation for x. x/3 = -4 <br><br><br><br>A. -12<br>B.-7<br>C.7 <br>D.12

UNO [17]

-12 divided by 3 equals -4

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3 years ago

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