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3 years ago

Find the length of the third side. If necessary, write in simplest radical form. 472 9

Mathematics

1 answer:

Marat540 [252]3 years ago

4 0

Answer:

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

let the third side be x , then

x² + (4 $\sqrt{2}$ )² = 9²

x² + 32 = 81 ( subtract 32 from both sides )

x² = 49 ( take the square root of both sides )

x = $\sqrt{49}$ = 7

Then the third side is 7

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The difference between two numbers is -1 and their sum is 1. Find the two numbers .

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3 years ago

Which of the following are factors of x^2+5x+4

soldier1979 [14.2K]

Answer:

(x + 4) and (x + 1)

Step-by-step explanation:

x² + 5x + 4

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x² + 5x + 4 = (x + 4)(x + 1) ← in factored form

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3 years ago

Mrs.Welch needs to buy some cat food . If each can costs $0.79 and she has a coupon for $2 off the entire purchase, how many can

allochka39001 [22]

Answer:

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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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The polynomial x^2+3x-1 is a factor of x^4+3x^3-2x^2-3x+1 true or false?

pashok25 [27]

Answer:

Yes, it is true that $x^2+3x-1$ is a factor of $x^4+3x^3-2x^2-3x+1$ .

Step-by-step explanation:

Let us try to factorize $x^4+3x^3-2x^2-3x+1$

$x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3$

Let us try to make a whole square of the given terms:

$\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\$

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Formula used above:

$a^{2} -2 \times a \times b +b^{2} = (a-b)^2$

In the above equation, we had $a = x, b = 1$ .

--------------

Further solving the above equation, taking $3x$ common out of $3x^3-3x$

$\Rightarrow (x^2-1)^2+3x(x^2-1)\\$

Taking $(x^{2} -1)$ common out of the above term:

$\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)$

So, the two factors are $(x^2-1)\ and\ (x^2+3x-1)$ .

$\therefore$ The statement that $x^2+3x-1$ is a factor of $x^4+3x^3-2x^2-3x+1$ is <em>True.</em>

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3 years ago