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3 years ago

Complete the steps to factor the polynomial by grouping.P(x) = x3 + 5x2 – x – 5

2 answers:

6 0

P(x) = x³ + 5x² – x – 5

P(x) = x²(x+5) - (x + 5)

P(x) = (x + 5)(x² - 1)

P(x) = (x + 5) (x + 1)(x -1)

valentina_108 [34]3 years ago

6 0

Answer

Find the steps to factor the polynomial by grouping.

To prove

As given the polynomial in the question

P(x) = x³ + 5x² – x – 5

P(x) = x² (x + 5) – (x + 5)

Take (x + 5) as common

P(x) = (x + 5) (x² - 1)

As using the identity

(a² - b²) = (a - b)(a + b)

P(x) = (x + 5) (x - 1)(x + 1)

Therefore the factors of the polynomial by grouping are (x + 5) and (x - 1)(x + 1) .

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In a election 210 people voted if there were 1260 possible voters what is the ratio of to nonvoters

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1260
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The ratio of voters to nonvoters is 210 to 50.

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3 years ago

Suppose z equals f (x comma y ), where x (u comma v )space equals space 2 u plus space v squared, y (u comma v )space equals spa

barxatty [35]

$z=f(x(u,v),y(u,v)),\begin{cases}x(u,v)=2u+v^2\\y(u,v)=3u-v\end{cases}$

We're given that $f_x(6,1)=3$ and $f_y(6,1)=-1$ , and want to find $\frac{\partial z}{\partial v}(1,2)$ .

By the chain rule, we have

$\dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial v}$

and

$\dfrac{\partial x}{\partial v}=2v$

$\dfrac{\partial y}{\partial v}=-1$

Then

$\dfrac{\partial z}{\partial v}(1,2)=\dfrac{\partial z}{\partial x}(6,1)\dfrac{\partial x}{\partial v}(1,2)+\dfrac{\partial z}{\partial y}(6,1)\dfrac{\partial y}{\partial v}(1,2)$

(because the point $(x,y)=(6,1)$ corresponds to $(u,v)=(1,2)$ )

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3 years ago

Regina brought 8 7/8 pound of fruit for her family . She brought 3 1/2 pound of oranges and 2 3/4 pound of peaches and some appl

butalik [34]

Answer:

Regina has bought $2\frac{5}{8}\ pounds$ of apples.

Step-by-step explanation:

Given:

Amount of fruit brought = $8\frac{7}{8}\ pounds$

Now given number is in mixed fraction we will convert into improper fraction.

To convert a mixed fraction to an improper fraction, we will Multiply the whole number part by the fraction's denominator. Add that to the numerator,Then write the result on top of the denominator.

So we can say that;

$8\frac{7}{8}\ pounds$ can be Rewritten as $\frac{71}{8}\ pounds$

Amount of fruit brought = $\frac{71}{8}\ pounds$

Also given:

Amount of oranges bought = $3\frac12\ pounds$

$3\frac12\ pounds$ can be Rewritten as $\frac{7}{2}\ pounds$

Amount of oranges bought = $\frac{7}{2}\ pounds$

Amount of peaches bought = $2 \frac34\ pounds$

$2 \frac34\ pounds$ can be Rewritten as $\frac{11}{4}\ pounds$

Amount of peaches bought = $\frac{11}{4}\ pounds$

We need to find amount of apples bought by Regina.

Solution:

Let the amount of apples bought be 'x'

Now we know that;

Amount of fruit brought is equal to sum of Amount of oranges bought and Amount of peaches bought amount of apples.

framing in equation form we get;

$\frac{71}{8}=\frac{7}{2}+\frac{11}{4}+x\\\\x=\frac{71}{8}-\frac{7}{2}-\frac{11}{4}$

Now we will make the denominator common using LCM we get.

$x=\frac{71\times 1}{8\times 1}-\frac{7\times4}{2\times4}-\frac{11\times2}{4\times2}\\\\x=\frac{71}{8}-\frac{28}{8}-\frac{22}{8}$

Now denominators are same so we will solve the numerator.

$x=\frac{71-28-22}{8}\\\\x=\frac{21}{8}\ pounds$

Now $\frac{21}{8}\ pounds$ can be Rewritten as $2\frac{5}{8}\ pounds$

Hence Regina has bought $2\frac{5}{8}\ pounds$ of apples.

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3 years ago

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RSB [31]

Answer: 8.76%

Step-by-step explanation:

The formula to find the simple interest is given by :-

$I=Prt$ , where P is the principal amount, r is rate of interest () in decimal and t is the time ( in years). (1)

Given : Justin deposited $2,000 into an account 5 years ago.

i.e. P = $2,000 , t= 5 years

He has just withdrawn $2,876. i.e. Future value = $2,876

Interest (I)=$2,876-$2,000=$876 [Subtract Principal value from Future value]

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3 years ago

Solve for k. k/8 = 64 (explain please)

Veronika [31]

The answer is k=64×8
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3 years ago

Read 2 more answers