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4 years ago

Write an equation of the line in slope-intercept form f(0)=2,f(2)=4

Mathematics

1 answer:

emmainna [20.7K]4 years ago

3 0

Answer: y=2x-2

Step-by-step explanation: First you plot those two points and make a line, then find the rest below. Slope formula is y=mx+b. M is the slope, rise over run, which is 2, and b is the y-intercept, where it meets the y-axis, which is -2.

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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.

6 0

3 years ago

so uh i have a question about STEAM the app ik this is a math website but uh my question is lets say your playing roblox or mine

yawa3891 [41]

Answer:

Step-by-step explanation:

First off, steam isn't a math website.

On discord, it doesn't show steam specifically, but if you're playing a game THROUGH steam then yes, it will show.

To hide this, go to options -> game activity -> and disable "Display currently running game as a status message" on discord.

If you want to hide your status on steam, just put your status to invisible :)

5 0

4 years ago

Read 2 more answers

Glenn rode his bike for 2 hours

Natali5045456 [20]

Cool. I rode mine for 1.

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3 years ago

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Drag each equation to the correct location on the table.

Ket [755]

Answer:

Hi! I hope this is correct please inform me if this is incorrect :)

a = 1 will have.

2a + 3 < 9 - 3a.

2a + 3 > 10 -3a.

3a - 2a + 1>2.

a = 2 will have

ANY others I did not include in a = 1 :)

Please once again tell me if this is incorrect.

Step-by-step explanation:

4 0

3 years ago

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If 2n + 3(2- 2n) = 14 what is the value of n? (Please give the correct answer, I will give brainliest)

allochka39001 [22]

Answer:

n = -2

Step-by-step explanation:

Eliminating parentheses, you have ...

2n +6 -6n = 14

Combining terms and subtracting 6, you get ...

-4n = 8

Dividing by the coefficient of n gives ...

n = -2

_____

<em><u>Check</u></em>

2(-2) +3(2 -2(-2)) = 14

-4 +3(2+4) = 14

-4 +3(6) = 14

-4 +18 = 14 . . . . answer checks OK

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3 years ago