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3 years ago

8

What is the equation of the line whose Y intercept of three and So what is the equation of the line whose Y-intercept is 3 and s

lope is 1?

1 answer:

viva [34]3 years ago

3 0

Answer:

y = x + 3

Step-by-step explanation:

the equation ofa line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = 1 and c = 3, hence

y = x + 3 ← is the equation of the line

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Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.

Flura [38]

Answer:

The inequality that you have is $5^{n}>2^{2n+1}+100,\,n>4$ . You can use mathematical induction as follows:

Step-by-step explanation:

For $n=5$ we have:

$5^{5}=3125$

$2^{(2(5)+1)}+100=2148$

Hence, we have that $5^{5}>2^{(2(5)+1)}+100.$

Now suppose that the inequality holds for $n=k$ and let's proof that the same holds for $n=k+1$ . In fact,

$5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.$

Where the last inequality holds by the induction hypothesis.Then,

$5^{k+1}>(2^{2k+1}+100)\cdot (4+1)$

$5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100$

$5^{k+1}>2^{2k+3}+100\cdot 4$

$5^{k+1}>2^{2(k+1)+1}+100$

Then, the inequality is True whenever $n>4$ .

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3 years ago

Julie is digging a square area in her backyard a for a vegtable garden. If the area is 52 square feet, what is the approximate l

AURORKA [14]

Answer:

<em>The correct option will be: (b) 7 feet.</em>

Step-by-step explanation:

Suppose, the length of the garden is $x$ feet.

As the <u>shape of the garden is like a square, then the area of the garden</u> will be: $(length)^2 = x^2$ feet²

Given that, the <u>area is 52 square feet</u>. So, the equation will be.......

$x^2= 52\\ \\ x=\sqrt{52} = 7.211.... \approx 7$

So, the approximate length of the garden will be 7 feet.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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