Find the distance between the points (-3, -6) and (5,9). Hint: Use the Pythagorean theorem.

Mathematics

1 answer:

Zinaida [17]3 years ago

4 0

Answer:

The distance between the points (-3, -6) and (5, 9) is 15 units.

Step-by-step explanation:

Given the points

(-3, -6)

(5, 9)

First, we need to find the distance between the two x-coordinates. For this, we need to count the distance from 0 to another point. Then we just add them together.

i.e.

-3 to get to 0 takes 3 units

0 to 5 takes 5 units

3+5=8 units

Just do the same for y-coordinate

From -6 to 0 takes 6 units

0 to 9 takes 9 units

6+9 = 15 units

Therefore, we get the base and height.

Now using the Pythagoras' Theorem to find the distance:

c² = 8² + 15²

c² = 289

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$c=\sqrt{289},\:c=-\sqrt{289}$

$c=17,\:c=-17$

As the distance can not be negative.

c = 15 units

Thus, the distance between the points (-3, -6) and (5, 9) is 15 units.

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Which graph correctly represents (5/2)x - y < 3?

Setler79 [48]

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Note that

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is the equation of the line drawn in the pictures. This means that, for every point on the line, the y coordinate is exactly image of the x coordinate, i.e. $f(x)$

The inequality is satisfied by all points whose y coordinate exceeds the image of the x coordinate. Since the y axis is positively oriented upwards, a greater value for the y coordinate means that the point has to be higher than the line.

Also, since the equality inlves a $>$ and not a $\geq$ sign, the line itself is excluded.