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Maru [420]
3 years ago
8

Rewrite 2x^2+13x+26/x+4 in the form q(x)+r(x)/b(x) . Then find q(x) and r(x).

Mathematics
2 answers:
sergey [27]3 years ago
8 0

Answer:

Q(x)= 2x+5

R(x)= 6

Step-by-step explanation:

natulia [17]3 years ago
6 0
We are dividing the polynomial 2x^{2} +13x+26 by x+4

notice that 2x^{2} is x times 2x,

so if we multiply (x+4) by 2x, which gives us 2 x^{2} +8x, we can 'separate' one 2 x^{2} +8x from 2x^{2} +13x+26  to get the following simplification:

\frac{2x^{2} +13x+26}{x+4}= \frac{ 2x^{2}+8 x}{x+4} + \frac{5x+26}{x+4}=2x+ \frac{5x+26}{x+4}

similarly we notice that 5x is x times 5, so if we multiply (x+4) by 5, we get 5x+20 so we can rewrite 

\frac{5x+26}{x+4}= \frac{5x+20}{x+4}+  \frac{6}{x+4}=5+\frac{6}{x+4}

\frac{6}{x+4} can not be simplified any further since the degree of 6, is smaller than the degree of x+4

combining our work, we have:

\frac{2x^{2} +13x+26}{x+4}=2x+5+\frac{6}{x+4}

Answer:

q(x)= 2x+5
r(x)=6
b(x)=x+4


Remark: we can solve the problem by long division or the division algorithm as well.
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The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a
liubo4ka [24]

Answer:

(x,y,z)=(1477, 1464, 1437)

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

<h3>Case-1:</h3>
  • Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
  • Mr.A earns Rs6000

So, the equation would be

3x  +  5y - 4z = 6000

<h3>Case-2:</h3>
  • Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
  • Mr B neither lose nor gain meaning he has made 0₹

hence,

2x   - 3y  +  z = 0

<h3>Case-3:</h3>
  • Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
  • Mr.C earns 13000₹

therefore,

- x    + 4y  +  6z = 13000

Thus our system of equations is

\begin{cases}3x  +  5y - 4z = 6000\\2x   - 3y  +  z = 0\\ - x    + 4y  +  6z = 13000\end{cases}

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

\begin{cases}3x  +  5y - 4z = 6000\\2x   - 3y  +  z = 0\end{cases}\\\begin{cases}2x   - 3y  +  z = 0\\ - x    + 4y  +  6z = 13000\end{cases}

Now solve the equation accordingly:

\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}

Solving the equation for x and y yields:

\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

\implies z= \dfrac{217000}{151}

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

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Answer: 829 3/4 or 829 75/100

Step-by-step explanation:

6 0
3 years ago
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77julia77 [94]
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4 0
3 years ago
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There are between 50 and 60 number of eggs in a basket. When Loza counts by 3's, there are 2 eggs left over. When she counts by
Strike441 [17]

Answer:

The number of eggs in the basket is 56

Step-by-step explanation:

Given as :

Let The number of eggs in the basket = 3x + 5x

When Loza counts 3's , there are 2 eggs left over

I.e , 3 ( x - 2 )

And  When Loza counts 5's , there are 4 eggs left over

I.e 5 ( x - 4 )

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Or, 20 - 6 = 5 x - 3 x

Or,  14 = 2 x

∴     x = 7

So, the number of eggs = 3 × 7 + 5 × 7

                                        = 21 + 35 = 56

Hence The number of eggs in the basket is 56   Answer

4 0
2 years ago
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