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3 years ago

What is the following simplified product? Assume

Mathematics

2 answers:

Assoli18 [71]3 years ago

8 0

<h2>Answer:</h2>

The simplified product is:

$10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$

<h2>Step-by-step explanation:</h2>

The expression is given by:

$(\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})$

Now we know that:

$\sqrt{x^2}=x\\\\and\\\\\sqrt{x^4}=\sqrt{(x^2)^2}=x^2$

Hence, we get the expression as follows:

$(\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})=(x^2\sqrt{10}-x\cdot x\sqrt{5})(2x^2\sqrt{15}+x\sqrt{3x})$

Now, we will use the property that:

$(a+b)(c+d)=a(c+d)+b(c+d)$

Hence, we have the expression as:

$=x^2\sqrt{10}(2x^2\sqrt{15}+x\sqrt{3x})-x^2\sqrt{5}(2x^2\sqrt{15}+x\sqrt{3x})$

$=2x^4\sqrt{10}\sqrt{15}+x^3\sqrt{10}\sqrt{3x}-2x^4\sqrt{5}\sqrt{15}-x^3\sqrt{5}\sqrt{3x}$

Now we know that:

$\sqrt{a}\sqrt{b}=\sqrt{ab}$

i.e. we have:

$=2x^4\sqrt{150}+x^3\sqrt{30x}-2x^4\sqrt{75}-x^3\sqrt{15x}\\\\=2x^4\sqrt{5^2\cdot 6}+x^3\sqrt{30x}-2x^4\sqrt{5^2\cdot 3}-x^3\sqrt{15x}\\\\=10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$

Yanka [14]3 years ago

4 0

<u>Answer:</u>

The correct answer option is D. $10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$ .

<u>Step-by-step explanation:</u>

We are given the following expression:

$\left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right )$

Assuming that $x\geq 0$ , we are to find its simplified product.

$\left ( \sqrt { 10 x ^ 4 } -x \sqrt { 5 x ^ 2 } \right ) \left ( 2 \sqrt { 15 x ^ 4 } + \sqrt { 3 x ^ 3 } \right )$

$\\\\ = 2 \sqrt { 150 x ^ 8 } + \sqrt { 3 0 x ^ 7 }-2x\sqrt{75x^6}-x\sqrt{15x^5} \\\\ =2\sqrt{25\times6x^8}+x^3\sqrt{30x}-2x\sqrt{25\times3x^6}-x^3\sqrt{15x} \\\\ =10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$

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Chan receives a bonus from his job. He pays 30% in taxes, gives 30% to charity, and uses another 15% to pay off an old debt. He

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Answer:

Chan's Bonus amount was $2400.

Step-by-step explanation:

Let the Total amount receive from bonus be 'x'.

Given:

Chan pays 30% in taxes;

So we can say;

Amount paid in taxes will be equal to 30% of total amount receive

framing in equation form we get;

Amount paid in taxes = $\frac{30}{100}x=0.3x = 0.3x$

Now Given:

Chan pays 30% in Charity;

So we can say;

Amount paid in charity will be equal to 30% of total amount receive.

framing in equation form we get;

Amount paid in Charity = $\frac{30}{100}x=0.3x$

Also Given:

Chan pays 30% in old debts;

So we can say;

Amount paid in Old debts will be equal 30% of total amount receive

framing in equation form we get;

Amount paid in Old debts = $\frac{15}{100}x=0.15x$

Money left with him = $600

Now we can say that Total Amount Receive in bonus will be equal to Amount paid in taxes plus Amount paid in charity plus Amount paid in old debts plus amount left.

framing in equation form we get;

$x=0.3x+0.3x+0.15x+600\\\\x= 0.75x +600\\\\x-0.75x=600\\\\0.25x=600\\\\x=\frac{600}{0.25} = \$2400$