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3 years ago

PLEASE HELP 25 POINTS What is −4√12+√75 in simplest radical form? Enter your answer in the box.

Mathematics

1 answer:

Ber [7]3 years ago

6 0

Answer: $-3\sqrt{3}$

This the expression -3*sqrt(3) or "-3 times the square root of 3"

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Work Shown:

Factor each term inside the square root so that a perfect square is one of the pieces. Then break up the roots and simplify as shown below.

$-4\sqrt{12} + \sqrt{75}$

$-4\sqrt{4*3} + \sqrt{25*3}$

$-4\sqrt{4}*\sqrt{3} + \sqrt{25}*\sqrt{3}$

$-4*2*\sqrt{3} + 5*\sqrt{3}$

$-8\sqrt{3} + 5\sqrt{3}$

$(-8+5)\sqrt{3}$

$-3\sqrt{3}$

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Find the flaw with the following "proof" that every postage of 3 cents or more can be formed using just 3-cent and 4-cent stamps

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The main flaw of this proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp and a 3 cent postage must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

Step-by-step explanation:

From the question we are told that

The proof is

Every postage stamp of three cents or more can be formed using just 3 cent and 4 cent stamps.

Basic Step : We can form postage of 3 cents with a single 3 cent stamp and we can form postage of 4 cents using a single four cents tamp

Inductive Step: Assume that we can form postage of j cents for all non negative integers j with j <= k using just 3 cent and 4-cent stamps. We can then form postage of k+1 cents by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps

FLAW IDENTIFICATION

Looking the inductive step, the statement ''by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps '' means that it is possible to use a 3-cent stamp for postage that requires a 4 -cent stamp and this is not correct according the statement in the basic step

Generally the main flaw of this proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp and a 3 cent postage must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

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Step-by-step explanation:

Picture is missing: find it in attachment.

The area of a triangle is given by

$A=\frac{1}{2}bh$