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3 years ago

Please help me answer questions 48 and 48 with the working out please. This is very urgent and i’m giving out 8 points not 5!!!

Mathematics

1 answer:

mariarad [96]3 years ago

4 0

Answer: 65°

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

$E=w(t_f-t_o)\\\\E: 10\ cubic\ feet\times \dfrac{1000\ BTU}{1\ cubic\ foot}\times \ 60\%\quad \rightarrow \quad E=6000\ BTU\\\\\\w:50\ gallons\times \dfrac{8\ pounds}{1\ gallon}\quad \rightarrow \quad w=400\ pounds\\\\\\\\E=w(t_f-t_o)\\\\6000=400(t_f-50)\\\\\dfrac{6000}{400}=\dfrac{400(t_f-50)}{400}\\\\.\quad 15=t_f-50\\\\\\.\quad 15=t_f-50\\.\ \underline{+50}\quad \underline{\quad \ +50}\\.\quad 65=t_f$

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Rationalise the denominator of (12)/(\sqrt(10)+\sqrt(7)+\sqrt(3))

jasenka [17]

Answer:

$\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210} }{21 }$

Step-by-step explanation:

$\frac{12}{\sqrt{10} +\sqrt{7} +\sqrt{3} }$

$=\frac{12\left( \sqrt{10} -\left( \sqrt{7} +\sqrt{3} \right) \right) }{(\sqrt{10}+(\sqrt{7} +\sqrt{3 } ))( \sqrt{10} -( \sqrt{7} +\sqrt{3}))}$

$=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{10^2} -(\sqrt{7} +\sqrt{3})^2}$

$\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{10-(10+2\sqrt{21} )} }$

$=\frac{12\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{-2\sqrt{21} }$

$=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{21} }$

$=\frac{-6\left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{\sqrt{21} } \times\frac{\sqrt{21} }{\sqrt{21} }$

$=\frac{-6\sqrt{21} \left( \sqrt{10} -\sqrt{7} -\sqrt{3} \right) }{21 }$

$=\frac{-6\sqrt{210} +6\sqrt{147} +6\sqrt{63} }{21 }$

$=\frac{6\sqrt{147} +6\sqrt{63}-6\sqrt{210} }{21 }$

<u><em>Remark</em></u>:

You can simplify moreover if you want to.

5 0

3 years ago

Which is the completely factored form of 12x4 + 39x3 + 9x2?

Troyanec [42]

<h3><u>Explanation</u></h3>

Given expression

${12x}^{4} + {39x}^{3} + {9x}^{2}$

Factor the expression by using common factor.

We csn pull out 3x² out of the expression.

${3x}^{2} (4 {x}^{2} + 13x + 3)$

We simply pull out the x-term with lowest degree and 3 out of the expression. If another expression cannot be factored after first factoring then that's the final answer.

The expression can still be factored. Factor the expression by using two brackets.

${4x}^{2} + 13x + 3 \\ (4x + 1)(x + 3)$

New factored form

$3 {x}^{2} (4x + 1)(x + 3)$

<h3><u>Answer</u></h3>

$\large \boxed { {3x}^{2} (4x + 1)(x + 3)}$

6 0

3 years ago

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Nimfa-mama [501]

Step-by-step explanation:

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3 years ago

Hey, does anyone know the answer?

Arlecino [84]

Answer:

the bottom one my dude. hope it helps!

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3 years ago

A girl scout troop makes $1100 in two weekends of selling cookies. If they continued at this rate, how much money would they mak

baherus [9]

Answer:

$3850

Step-by-step explanation:

It is given that,

A girl scout troop makes $1100 in two weekends of selling cookies.

2 weekend = $1100

1 weekend = $550

For 7 weekend, we will multiply $550 by 7 as follows :

7 weekend = $550 × 7

= $3850

So, for 7 weekend she will need $3850.

6 0

3 years ago