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NikAS [45]
3 years ago
13

Everyday my cousin and I played a game of chess. To make it interesting, whoever lost the game owes a chocolate to the other. We

played many games of chess over many days. After the last game we played, we counted the number of games each of us had won and lost. Since I won more than her, she handed me 29 chocolates, even though she did win 5 games. How many total games did we play?
Mathematics
1 answer:
Sindrei [870]3 years ago
4 0

Answer:

34, I think.

Step-by-step explanation:

if you have 29 chocolates, and she won 5, 29+5 equals 34

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Simplify $\frac{1+\sqrt{2}}{2+\sqrt{3}}$. Your solution can be converted to the form $A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})$, where
Zina [86]

Answer:

A+B+C+D = 13

Step-by-step explanation:

The given expression is:

\dfrac{1+\sqrt{2}}{2+\sqrt{3}}

We have to simply it and express it in the form of:

A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})

Multiply and divide the given expression with 2-\sqrt 3:

\dfrac{1+\sqrt{2}}{2+\sqrt{3}} \times \dfrac{2-\sqrt 3}{2-\sqrt 3}\\\Rightarrow \dfrac{(1+\sqrt{2}) \times (2-\sqrt 3)}{(2+\sqrt{3})\times (2-\sqrt 3)}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{2^2-(\sqrt{3})^2}\\\Rightarrow \dfrac{2+2\sqrt2-\sqrt3-\sqrt6}{4-3}\\\Rightarrow \dfrac{2(1+\sqrt2)-(\sqrt3+\sqrt6)}{1}\\\Rightarrow 2(1+\sqrt2)-(\sqrt3+\sqrt6)

It is the simplified form of given expression.

<u>Formula used: </u>

<u></u>(a+b)(a-b) = a^{2} -b^{2}<u></u>

<u></u>

<u>Comparing the simplified expression with </u>A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})<u></u>

2(1+\sqrt2)-(\sqrt3+\sqrt6)=A(1+\sqrt{B})-(\sqrt{C}+\sqrt{D})\\\Rightarrow A =2, B=2, C=3\ and\ D=6

So, value of

A+B+C+D = 2+2+3+6 = 13

8 0
4 years ago
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Paul [167]

Answer:

Step-by-step explanation:

Hey there!

The range is the possible y values, so the range of this graph would be all real numbers less than or equal to -5.

Let me know if this helps :)

7 0
3 years ago
Which of the following equations matches the graph above?
shtirl [24]
It’s 4x -4 because at at x=0 the y = -4 so it has -4 and then it goes up by 4 each x
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3 years ago
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