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maks197457 [2]
3 years ago
12

Jeannie's scores on her first four tests were 80, 65, 87, and 75. What will

Mathematics
1 answer:
Ivan3 years ago
6 0
She will have to score 93.
(80+65+87+75+x)/5 = 80
307+x = 400
x =400-307=93
Another way, easier to do in your head:
Notice that 65 is 15 below 80, 87 is 7 above 80, and 75 is 5 below 80. The overall situation is 13 below 80 (because -15+7-5=-13). For a number to push the average back to 80, it must be 13 higher than 80. 80+13=93
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Answer:  3+\sqrt{2}

Step-by-step explanation:

Given the following expression shown in the picture:

\frac{7}{3-\sqrt{2} }

You need to use a process called "Ratinalization".

By definition, using Rationalization you can rewrite the expression in its simplest form so there is not Radicals in its denominator.

Then, in order to simplify the expression, you can follow the following steps:

<em>Step 1</em>. You need to multiply the numerator and the denominator of the fraction by  3+\sqrt{2}, which is the conjugate of the denominator  3-\sqrt{2}.

<em>Step 2</em>. Then you must apply the Distributive property in the numerator.

<em>Step 3</em>. You must apply the following property in the denominator:  (a+b)(a-b) = a^2 - b^2

Therefore, applying the procedure shown above, you get:

=\frac{(7)(3+\sqrt{2})}{(3-\sqrt{2})(3+\sqrt{2})}=\frac{21+7\sqrt{2}}{3^2-(\sqrt{2})^2}=\frac{21+7\sqrt{2}}{9-2}=\frac{21+7\sqrt{2}}{7}

<em>Step 4</em>.  You can observe that the expression can be simplified even more. Since:

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You get:

\frac{21+7\sqrt{2}}{7}=\frac{21}{7}+\frac{7\sqrt{2}}{7}=3+\sqrt{2}

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Step-by-step explanation:

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