3 years ago

Geometry Find a: Fill in the blank

Mathematics

1 answer:

Nataly_w [17]3 years ago

3 0

Answer:

a=15

Step-by-step explanation:

$a^{2} =9*25\\a^{2} =225\\\\\sqrt{a} =\sqrt{222\\a=15$

Hope it helps

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Sladkaya [172]

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3 years ago

Jon invests $4,100 into an account that pays 5 percent simple interest each year. What is the total balance in the account after

NemiM [27]

Y=.05x +4100
Y=.05(3)+4100
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4 years ago

A recipe calls for 1/6 teaspoon of oregano and 1 1/4 teaspoon of pepper. What is the ratio of oregano to pepper

ikadub [295]

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b. 2:15

Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

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Prove that x-1 is a factor of x^n-1 for any positive integer n.

PolarNik [594]

Answer:

$x-1$ is a factor of $x^n - 1$

Step-by-step explanation:

$x-1$ is a factor of $x^n - 1$

We will prove this with the help of principal of mathematical induction.

For n = 1, $x-1$ is a factor $x-1$ , which is true.

Let the given statement be true for n = k that is $x-1$ is a factor of $x^k - 1$ .

Thus, $x^k - 1$ can be written equal to $y(x-1)$ , where y is an integer.

Now, we will prove that the given statement is true for n = k+1

$x^{k+1} - 1\\=(x-1)x^k + x^k - 1\\=(x-1)x^k + y(x-1)\\(x-1)(x^k + y)$

Thus, $x^k - 1$ is divisible by $x-1$ .

Hence, by principle of mathematical induction, the given statement is true for all natural numbers,n.

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3 years ago