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3 years ago

Factor completely x³ - 7x² + 2x + 40 given x = -2 is a root.

Mathematics

1 answer:

klemol [59]3 years ago

6 0

Answer:

(x +2)(x -4)(x -5)

Step-by-step explanation:

When you divide the cubic by (x +2), the factor that has -2 as a root, you get a quadratic with roots 4 and 5. Thus the factors are ...

(x +2)(x -4)(x -5)

___

In the attachment, we have done the division using a graphing calculator. You can also do it by polynomial long division or by synthetic division. The resulting quadratic is ...

x^2 -9x +20 = (x -4)(x -5) . . . . . factor the quadratic

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An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in sh

larisa86 [58]

The amount of rim needed for each window is 141.4 in

<h3>How to find the length of the outer rim?</h3>

Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.

An arc is part of section of the circumference of a circle

<h3>What is the length of an arc?</h3>

So, length of arc, L = Ф/360 × 2πR where

Ф = central angle of arc and
R = radius of circle.

Gven that for the window rim

Ф = angle of the rim = 270° and
R = radius of the rim = 30 in

Substituting the values of the variables into the equation for L, we have

L = Ф/360 × 2πR

L = 270°/360° × 2π × 30 in

L = 3/4 × 2π × 30 in

L = 3/2 × π × 30 in

L = 3 × π × 15 in

L = 45π in

L = 141.37 in

L ≅ 141.4 in

So, the amount of rim needed for each window is 141.4 in

Learn more about length of an arc here:

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2 years ago

ANswer please! Brainliest!!

andreyandreev [35.5K]

Answer:

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Step-by-step explanation:

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3 years ago

WILL GIVE 30 points. The GRE is an entrance exam that many students are required to take in order to apply to graduate school. I

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Answer:

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3 years ago

Read 2 more answers

In triangle MPN, angle P is a right angle. If cos N= 3/5 which of the following statements is true

Bezzdna [24]

Answer: Sin N = $\frac{4}{5}$

Step-by-step explanation:

Since we have given that

In triangle MPN, ∠P=90°

$\cos N=\frac{3}{5}$

As we know the formula for "Trigonometric Ratios":

$\cos N=\frac{Base}{Hypotenuse}=\frac{3}{5}$

By Pythagorus theorem , we get

$H^2=B^2+P^2\\\\5^2=3^2+P^2\\\\25=9+P^2\\\\25-9=P^2\\\\16=P^2\\\\P=\sqrt{16}\\\\P=4\ units$

So, we get,

$\sin N=\frac{Perpendicular}{Hypotenuse}=\frac{4}{5}$

Hence, Sin N = $\frac{4}{5}$

3 0

3 years ago

A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as

mamaluj [8]

Answer:

The farmer have at first <u>202</u> chickens.

Step-by-step explanation:

Given:

A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as ducks left.

Now, to find the chickens farmer have at first.

Let the chickens be $x.$

And, the ducks be $y.$

<em>As, the farmer had twice as many chickens as ducks on his farm.</em>

So, $x=2y$ ......(1)

<em>As, given the farmer after selling 166 chickens and ducks, he had half as many chickens as ducks left.</em>

According to question:

$x-166=(y-29)\times \frac{1}{2}$

$x-166=\frac{y-29}{2}$

Substituting the value of $x$ from equation (1) we get:

$2y-166=\frac{y-29}{2}$

<em>By cross multiplying we get:</em>

$4y-332=y-29$

<em>Adding both sides 332 we get:</em>

$4y=y+303$

<em>Subtracting both sides by </em> $y$ <em> we get:</em>

$3y=303$

<em>Dividing both sides by 3 we get:</em>

$y=101.$

Now, to get the number of chickens substituting the value of $y$ in equation (1):

$x=2y\\\\x=2\times 101\\\\x=202.$

Therefore, the farmer have at first 202 chickens.

7 0

3 years ago