If there are 4 prizes of every 9 boxes how many prizes are in 54 boxes

Find the distance between the points. (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.

5 0

1 year ago

The sequence below shows the

serious [3.7K]

Answer:

Step-by-step explanation:

Option B 2. Now is the correct answer because when we multiply 6 by 2 we get 12 then we multiply 12 by 2 we get 24

8 0

2 years ago

Is 42/7 a rational or natural number

Brilliant_brown [7]

Answer: rational

Step-by-step explanation:

-6 can be written as such an infinite number of ways (just as any rational can be). For example, -6/1, 6/-1, 12/-2, -666/111 and so indeed -6 is rational.

5 0

2 years ago

Read 2 more answers

A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 5 hours, while the outlet pipe can empty it

Rashid [163]

Answer:

$time=40/3hours\approx 13.3hours$

Step-by-step explanation:

The rates are additive: you can calculate the inlet rate and the outlet rate and add them algebraically, i.e. the inlet rate will be positive and the outlet rate will be negative.

1. Inlet rate:

$1vat/5hours$

2. Outlet rate:

$1vat/8hours$

3. Net rate:

$\text{Inlet rate - outlet rate}=1vat/5hours-1vat/8hours\\\\ \text{Net rate}=(8-5)vat/40hour=3vat/40hour=(3/40)vat/hour$

4. Time to fill the vat

$rate=amount/time\implies time=amount/rate\\ \\ time=1vat/(3vat/40hour)$

$time=40/3hours\approx 13.3hours$

7 0

2 years ago

PLEASE HELP ASAP 25 POINTS

Lisa [10]

We're going to go ahead and eliminate one answer out of the four. It cannot be B (the second answer) because the graph is made of dotted lines.

Dotted Lines = > or <

Solid Lines = ≤ or ≥

Next, let's focus on the straight line on the graph.

The equation for the line is

y = x - 4

Since the shaded region is below the line,

the equation will be y < x - 4

We can now eliminate answer A

Since the second equation is y < - l x - 2 l

It will be shaded below the graph since it uses the ( < ) (less than symbol)

This means the answer is C

Hope I helped, message me if you have any questions : )

8 0

3 years ago