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1 year ago

4.

Mathematics

1 answer:

valkas [14]1 year ago

4 0

Answer: $\boxed{y=\frac{4}{5}x-2}$

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.

Substituting into point-slope form,

$y-6=\frac{4}{5}(x-10)\\\\y-6=\frac{4}{5}x-8\\\\\boxed{y=\frac{4}{5}x-2}$

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Rearrange y =1/2x+1to make x the subject.

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$y = \frac{1}{2} x + 1 \\$

Multiply sides by 2

$2 \times y = 2 \times ( \frac{1}{2} x + 1) \\$

$2y =( 2 \times \frac{1}{2} x) + (2 \times 1) \\$

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1 year ago

A rectangle swimming pool is 8 feet deep. One side of the pool is 4.5 times longer than the other. The amount of water needed fo

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The side lengths of the pool 10 ft and 45 ft.

<u>SOLUTION: </u>

Given, a rectangle swimming pool is 8 feet deep.

One side of the pool is 4.5 times longer than the other.

Let the length of pool be n feet, the width will be 4.5n feet

The amount of water needed for the swimming pool is 3600 cubic ft

We have to find the dimensions of the pool. Now, we know that,

$\begin{array}{l}{\text {volume of pool}=\text {depth} \times \text {length } \times \text {width}} \\\\ {\rightarrow 3600 \text { cubic } f t=8 \text { feet } \times \text { n feet } \times(4.5 n) \text { feet }} \\\\ {\rightarrow 8 n \times 4.5 n=3600} \\\\ {\rightarrow 36 n^{2}=3600} \\\\ {\rightarrow n^{2}=100}\end{array}$

On taking square root on both sides we get,

$\begin{array}{l}{\rightarrow\sqrt{n^{2}}=\sqrt{100}} \\\\ {\rightarrow n=10 \mathrm{ft}}\end{array}$

So, the width will be $4.5 n=4.5 \times 10=45 \mathrm{ft}$

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Think about plotting points in the complex plane to represent the following numbers: -3+8i, 4i, 6, 5-2i. (on the horizontal axis

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For this case we represent in the complex plane numbers of the form:
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