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3 years ago

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Two lines intersect in more than one point always sometimes never

1 answer:

GuDViN [60]3 years ago

5 0

The answer is never, that is, on a 2 dimensional plane. You can perform an experiment to see why it is the case. On curved surfaces though, two lines can intersect one another more than once. For instance, on the surface of planet Earth, two lines can intersect one another, both at the Earth's North Pole and South Pole.

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Find the distance between the point (-2, -3) and the line with the equation y=4-2/3x

otez555 [7]

Answer:

$D = \frac{25\sqrt{13}}{13}$

Step-by-step explanation:

Given

$y = 4 - \frac{2}{3}x$

$(x_1,y_1) = (-2,-3)$

Required

Determine the distance

$y = 4 - \frac{2}{3}x$

Write the above equation in standard form:

$Ax + By + C = 0$

So, we have:

$\frac{2}{3}x+y - 4 = 0$

By comparison:

$A = \frac{2}{3}$ $B = 1$ and $C = -4$

The distance is calculated using:

$D = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$

Where:

$(x_1,y_1) = (-2,-3)$

$A = \frac{2}{3}$ $B = 1$ and $C = -4$

This gives:

$D = \frac{|\frac{2}{3} * (-2) + 1 * (-3) - 4|}{\sqrt{(\frac{2}{3})^2 + 1^2}}$

$D = \frac{|-\frac{4}{3} -3 - 4|}{\sqrt{\frac{4}{9} + 1}}$

Take LCM

$D = \frac{|\frac{-4-9-12}{3}|}{\sqrt{\frac{4+9}{9}}}$

$D = \frac{|\frac{-25}{3}|}{\sqrt{\frac{13}{9}}}$

$D = |\frac{-25}{3}|/\sqrt{\frac{13}{9}}$

$D = \frac{25}{3}/\sqrt{\frac{13}{9}}$

Split the square root

$D = \frac{25}{3}/\frac{\sqrt{13}}{\sqrt{9}}$

Change / to *

$D = \frac{25}{3}*\frac{\sqrt{9}}{\sqrt{13}}$

$D = \frac{25}{3}*\frac{3}{\sqrt{13}}$

$D = \frac{25}{\sqrt{13}}$

Rationalize

$D = \frac{25}{\sqrt{13}} * \frac{\sqrt{13}}{\sqrt{13}}$

$D = \frac{25\sqrt{13}}{13}$

Hence, the distance is:

$D = \frac{25\sqrt{13}}{13}$

4 0

3 years ago

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harina [27]

Check the picture below.

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1 year ago

A basketball player attempts 18 baskets in a game. He makes 8 of the attempted baskets. Which ratio describes the number of bask

EleoNora [17]

Answer:

4:9

Step-by-step explanation:

8:18 in simplest form is 4:9

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2 years ago

What are prime factors of 1000?

Ede4ka [16]

Answer:

1,2,4,5,8,10,20,25,40,50,10,125,200,250,500,1000

Step-by-step explanation:

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2 years ago

Please use statemnet reasoning!

dlinn [17]

Answer:

lineHO parallel lineEN - Given

lineHW = lineNW - Given

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angle OHW <u>congruent</u> angle ENW Alternate interior angles

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[wouldn't let me use symbols sorry]

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2 years ago

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