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2 years ago

Find the product. (7−x)(x−1)=

Mathematics

2 answers:

Alexxx [7]2 years ago

5 0

Answer:

-x^2 + 8x - 7

Step-by-step explanation:

(7 - x)(x - 1)

(7 * x) + (7 * -1) + (-x * x) + (-x * -1)

7x - 7 - x^2 + x

8x - 7 - x^2

-x^2 + 8x - 7

Best of Luck!

vaieri [72.5K]2 years ago

3 0

Answer:

-x² + 8x - 7

Step-by-step explanation:

Step 1: Write expression

(7 - x)(x - 1)

Step 2: FOIL (First Outside Inside Last)

7x - 7 - x² + x

Step 3: Combine like terms

-x² + 8x - 7

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2 years ago

I dont understand how to simplify an expression with exponents

Mashutka [201]

Answer:

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$\frac{a^x}{a^y}=a^{x-y}$

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2 years ago

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2 years ago

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

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3 years ago