Mathematics: Eric has only pennies in dimes in his coin collection he has five times as many pennies and dimes which is an expression for the number of coins in his collection using d for the number of dimes

Eric has only pennies in dimes in his coin collection

Ответ:

PompousCoyote

12.03.2022

Mathematics

Amount that Eric has got in dimes = d

Number of coins which is in pennies = p

It is given that amount in dimes is five times the number of coins which is in penny.

So,the expression will become

A.T.Q

⇒ Total dime = 5× Total number of coins which is in penny

⇒ d = 5 p

If you want solution of this equation , the graph will be a straight line which passes through the origin making an angle of $\tan^{-1}{5}$ with the positive direction of X-axis.

The solution of the linear expression lies in First quadrant.

For every positive integral value of p>0 , there are infinite number of solutions for number of dimes.For example take p =1,2,3,...

we get d=5,10, 15,....

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Ответ:

jorden73

16.07.2021

Mathematics

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

$1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}$

And the rewritten forms:

$(x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}$

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

$(x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}$

So, correct option is 3.

$(x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}$

So, correct option is 1.

$(x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}$

So, correct option is 2.

$(x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}$

So, correct option is 4.

The answer is also attached in the answer area.

Match the following rational expressions to their rewritten forms.

Rational Expressions:
x^2+x+4/x-

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Eric has only pennies in dimes in his coin collection he has five times as many pennies and dimes which is an expression for the number of coins in his collection using d for the number of dimes

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