Solve for x!

2 answers:

7 0

First multiply by 9x. 7 = 378x. Divide each side by 378 to isolate x. 1/54 = x. Check your answer: 7/(1/6) does indeed equal 42.

attashe74 [19]3 years ago

6 0

I'm assuming you meant (7/9)x = 42.

If that's correct, then we can quickly and easily solve for x by multiplying both sides of this equation by 9/7:

(9/7)(7/9)x = (9/7)(42) = 54. x = 54

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Find the distance between the points.<br> (r, s) and (0, 0)

zhenek [66]

Answer: $\sqrt{r^2+s^2$

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Reason:

Plot the points (0,0) and (r,s). You can place (r,s) anywhere you want.

Connect the two points mentioned and form a right triangle such that the segment from (0,0) to (r,s) is the hypotenuse of said right triangle.

The horizontal leg has a length of r-0 = r units, while the vertical leg will be 's' units.

Check out the diagram below.

We then apply the pythagorean theorem to say $r^2+s^2 = h^2$ where h is the hypotenuse. Solving for h gets us $h = \sqrt{r^2+s^2}$ . We only focus on the positive square root since a negative hypotenuse makes no sense.

Since we made the hypotenuse the segment with endpoints (r,s) and (0,0), this means the hypotenuse length and the distance are the same thing.

Therefore, the distance from (r,s) to (0,0) is $\sqrt{r^2+s^2}$

As an alternative, you can use the distance formula to get the same answer. The distance formula is effectively the pythagorean theorem phrased a different way.