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4 years ago

Factor completely, then place the factors in the proper location on the grid. x^2n + 10x^n + 16

Mathematics

1 answer:

postnew [5]4 years ago

7 0

Answer:

$(x^n + 2)(x^n + 8)$

Step-by-step explanation:

The polynomial $x^{2n}+10x^n + 16$ can be factored exactly the same as the polynomial $x^2 + 10x + 16$ . Here it factors into two numbers which multiply to 16 but add to 8. These factors are 8 and 2. So it factors into the expression (x+8)(x+2).

For the polynomial $x^{2n}+10x^n + 16$ it factors into the same factors except x ^n is used instead. The factors are $(x^n + 2)(x^n + 8)$

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Solve the system of equations by graphing. {y=x+1<br> y=2x

lawyer [7]

Answer:

x=1, y=2

Step-by-step explanation:

8 0

3 years ago

Find all polar coordinates of point P where P = ordered pair 3 comma negative pi divided by 3 .

jek_recluse [69]

Answer:

The all polar coordinates of P are:

(3 , -π/3) , (3 , 5π/3) , (-3 , 2π/3) , (-3 , -4π/3)

Step-by-step explanation:

* Lets study the polar coordinates of a point

- In polar coordinates there is an infinite number of coordinates

for a given point.

- The polar coordinates of a point (x , y) is (r , θ), where

r = √ ( x2 + y2 )

θ = tan-1 ( y / x )

# Ex: the following four points are all coordinates for the same point.

* (5 , π/3) = (5 , −5π/3) = (−5 , 4π/3) =(−5 , −2π/3)

- These four points only represent the coordinates of the point without

rotating more than once

- So the point (r,θ) can be represented by any of the following

coordinate pairs (r , θ + 2π n) and (−r , θ + (2n + 1) π), where n is

any integer.

* Now lets solve the problem

∵ P = (3 , -π/3)

∵ (r , θ + 2πn)

∴ r = 3 an d Ф = -π/3

- let n = 1

∴ P = (3 , -π/3 + 2π)

∴ P = (3 , 5π/3)

∵ P =(3 , -π/3)

∵ P = (-r , θ + (2n + 1) π)

Let n = 0

∴ P = (-3 , -π/3 + (2×0 + 1) π)

∴ P = (-3 , -π/3 + (0 + 1) π)

∴ P = (-3 , -π/3 + π)

∴ P = (-3 , 2π/3)

∵ P =(3 , -π/3)

∵ P = (-r , θ + (2n + 1) π)

Let n = -1

∴ P = (-3 , -π/3 + (2(-1) + 1) π)

∴ P = (-3 , -π/3 + (-2 + 1) π)

∴ P = (-3 , -π/3 + -π) = (-3 , -4π/3)

∴ P = (-3 , -4π/3)

5 0

3 years ago

BRAILIEST !!!!!!

Stells [14]

Option a: multiply $\frac{2}{5}$ by 4.

Explanation:

The expression is $\frac{2}{5} \div \frac{1}{4}$

Dividing the two fractions which is the same as multiplying the first fraction by the reciprocal value of the second fraction.

Hence, it can be written as

$\frac{2}{5} \times \frac{4}{1}=\frac{8}{5}$

Hence, $\frac{8}{5}$ is the quotient.

Option a: multiply $\frac{2}{5}$ by 4.

To determine the quotient, let us multiply the term $\frac{2}{5}$ by 4, we get,

$\frac{2}{5} \times 4=\frac{8}{5}$

Hence, $\frac{8}{5}$ is the quotient.

Thus, Option a is the correct answer.

Option b: multiply $\frac{2}{5}$ by $\frac{1}{4}$

To determine the quotient, let us multiply the term $\frac{2}{5}$ by 4, we get,

$\frac{2}{5} \times \frac{1}{4}=\frac{1}{10}$

$\frac{1}{10}$ is not the quotient. Since, the quotient is $\frac{1}{10}$ which is not equivalent to $\frac{8}{5}$ and hence we cannot multiply $\frac{2}{5}$ by $\frac{1}{4}$

Hence, Option b is not the correct answer.

Option c: multiply $\frac{5}{2}$ by $\frac{1}{4}$

To determine the quotient, let us multiply the term $\frac{5}{2}$ by $\frac{1}{4}$ , we get,

$\frac{5}{2} \times\frac{1}{4}=\frac{5}{8}$

$\frac{5}{8}$ is not the quotient. Since, the quotient is $\frac{5}{8}$ which is not equivalent to $\frac{8}{5}$ and hence we cannot multiply $\frac{5}{2}$ by $\frac{1}{4}$