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antiseptic1488 [7]
3 years ago
7

Any help? Much appreciated ​

Mathematics
1 answer:
natulia [17]3 years ago
5 0

Answer:

\frac{6+\sqrt{27} }{4-\sqrt{3} } = \frac{r+s\sqrt{3} }{13} \\We\ may\ multiply\ the\ numerator\ and\ denominator\ with\ (4+\sqrt{3} ).\\Hence,\\\frac{(6+\sqrt{27})(4+\sqrt{3})  }{13} =  \frac{r+s\sqrt{3} }{13} \\Hence,\\24+6\sqrt{3} +4\sqrt{27} +9= r+s\sqrt{3}\\24+6\sqrt{3} +4*3\sqrt{3} } +9= r+s\sqrt{3}\\24+6\sqrt{3} +12\sqrt{3}+9 = r+s\sqrt{3}\\33+18\sqrt{3} = r+s\sqrt{3}\\Hence,\\r=33, s=18

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What is the answer to this solution. -7r−4≥ 4r+2
tia_tia [17]

Answer:

The solution is:

-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}

Please check the attached line graph below.

Step-by-step explanation:

Given the expression

-7r-4\ge \:4r+2

Add 4 to both sides

-7r-4+4\ge \:4r+2+4

Simplify

-7r\ge \:4r+6

Subtract 4r from both sides

-7r-4r\ge \:4r+6-4r

Simplify

-11r\ge \:6

Multiply both sides by -1 (reverses the inequality)

\left(-11r\right)\left(-1\right)\le \:6\left(-1\right)

Simplify

11r\le \:-6

Divide both sides by 11

\frac{11r}{11}\le \frac{-6}{11}

Simplify

r\le \:-\frac{6}{11}

Therefore, the solution is:

-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}

Please check the attached line graph below.

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2 years ago
The shape below is a composite figure made up of two rectangular prisms, what is the volume of the figure?
gregori [183]

Answer:

<u>11098 cm³</u>

Step-by-step explanation:

<u>Volume of top prism</u>

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<u>Volume of bottom prism</u>

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⇒ Total volume = 1116 + 9982

⇒ Total volume = <u>11098 cm³</u>

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