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3 years ago

Factor completely x3 + 7x2 − 2x − 14.

Mathematics

2 answers:

Lapatulllka [165]3 years ago

8 0

Answer:

(x+7)(x^2-2)

Step-by-step explanation:

x^3 + 7x^2 − 2x − 14

We will factor by grouping

Take x^2 out of the first two terms and -2 out of the last 2 terms

x^2(x+7) -2(x+7)

Now we can factor out (x+7)

(x+7)(x^2-2)

frutty [35]3 years ago

3 0

Answer:

the factors of x3 + 7x2 − 2x − 14. are (x^2-2)(x+7)....

Step-by-step explanation:

x3 + 7x2 − 2x − 14.

We will group the terms.

Make pairs of the terms:

(x3 + 7x2 ) - (2x + 14.)

Now find the common factor of each pair

x^2(x+7)-2(x+7)

(x^2-2)(x+7)

Thus the factors of x3 + 7x2 − 2x − 14. are (x^2-2)(x+7)....

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Solve the system using the substitution method<br> 6x - 2y = -4<br> y= 3x + 2

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Answer:

Step-by-step explanation:

6x - 2y = -4

y= 3x + 2

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6x - 2(3x +2) = -4

Now usually we'd we simply solve for X.

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4 years ago

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A rectangle's length is 3 feet longer than its width. its perimeter is 62 feet

DanielleElmas [232]

Hi!

<h3>The perimeter is equal to </h3>

<h3>The length is 3 feet longer than the width so...</h3>

<h3>Simplify</h3>

4w + 6 - 6 = 62 - 6

4w = 56

4w/4 = 56/4

<h2>The width is 14 and the length is 17. </h2>

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3 years ago

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4 years ago

Transform each polar equation to an equation in rectangular coordinates and identify its shape.

Gemiola [76]

Answer:

(a) $x ^ 2 + y ^ 2 = 6 ^ 2$

(b) $(x-1) ^ 2 + y ^ 2 = 1$

Step-by-step explanation:

Remember that to convert from polar to rectangular coordinates you must use the relationship:

$x = rcos(\theta)$

$y = rsin(\theta)$

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

In this case we have the following equations in polar coordinates.

(a) $r = 6$ .

Note that in this equation the radius is constant, it does not depend on $\theta$ .

As $r ^ 2 = x ^ 2 + y ^ 2$

Then we replace the value of the radius in the equation and we have to::

$x ^ 2 + y ^ 2 = 6 ^ 2$

Then $r = 6$ in rectangular coordinates is a circle centered on the point (0,0) and with a constant radius $r = 6$ .

(b) $r = 2cos(\theta)$

The radius is not constant, the radius depends on $\theta$ .

To convert this equation to rectangular coordinates we write

$r = 2cos(\theta)$ <em>Multiply both sides of the equality by </em><em>r</em>.

$r ^ 2 = 2 *rcos(\theta)$ <em>remember that</em> $x = rcos(\theta)$ , <em>then: </em>

$r ^ 2 = 2x$ <em>remember that </em> $x ^ 2 + y ^ 2 = r ^ 2$ , <em>then:</em>

$x ^ 2 + y ^ 2 = 2x$ <em>Simplify the expression. </em>

$x ^ 2 -2x + y ^ 2 = 0$ <em>Complete the square. </em>

$x ^ 2 -2x + 1 + y ^ 2 = 1$

$(x-1) ^ 2 + y ^ 2 = 1$ <em>It is a circle centered on the point (1, 0) and with radio $r=1$ </em>

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3 years ago