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Gekata [30.6K]
3 years ago
12

The local zoo is filling two water tanks for the elephant exhibit. One water tank contains 30 gal of water and is filled at a co

nstant rate of 7 gal/h. The second water tank contains 18 gal of water and is filled at a constant rate of 4 gal/h. Let x = the number of hours the tanks are filling and let y = the number of gallons in the tank. Write and solve a system of equation to determine when the two tanks will have the same amount of water. Explain
This question was at my math test. Can someone explain to me how to do this kind of question step by step?

FYI, the answer is They will never have the same amount of water because the solution to the system is (–4,2). It is not possible to have time be –4 hours.
Mathematics
1 answer:
kakasveta [241]3 years ago
3 0
You first have to set up the two equations. Y is equal to the total number of gallons in a tank and x is equal to the number of hours the tanks are filling.

Since the two equations both equal y I can make them equal each other. I then solved for x as you see and got -4.

Once I found my x value I now needed to find my y. You only needed to chose one equation to solve for y, so I decided to do the first one. I plugged in -4 where my x value currently was and solved for y. I got 2.


If you have any questions please comment!! Hope this helps!!
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Which statement is supported by the histograms? The two data sets have the same distribution and same range. The two data sets h
Ad libitum [116K]

Answer:

The two data sets have different distributions and different ranges.

Step-by-step explanation:

When you subtract for both of the ranges they are different numbers. So that's the second part. The numbers along the bottom are different too so that is the different distributions.

5 0
3 years ago
An employee puts 10000 in a retirement account that offers 4% interest. How much will he have in 12 years
steposvetlana [31]

Answer:

14800

Step-by-step explanation:

The formula for simple interest (I) in terms of principal (P), rate (R) and time (T) is given as follows;

I = P x R x T / 100         ------------- (i)

Given:

Principal (P) = Initial amount being put into the account = 10000

Rate (R) = The interest rate being offered by the account manager = 4%

Time (T) = Time taken = 12 years

Substitute these values into equation (i) as follows:

I = 10000 x 4 x 12 / 100

I = 4800

Therefore, the initial amount will yield an interest of 4800 for those 12 years.

The total amount the employee will thus have in 12 years will be the sum of the initial amount and the interest. i.e

Amount = P + I

Amount = 10000 + 4800

Amount = 14800

4 0
3 years ago
Help Fast! Answer in The Picture Below!
o-na [289]

Answer:

D. 912 square inches.

hope that helps!

7 0
3 years ago
If a simple harmonic motion is described by x = 3 cos(πt), starting from t = 0 s, what is the first occurrence of a value of t f
poizon [28]

Answer:

The first occurence of t for which x = 0 is t = 0.5.

Step-by-step explanation:

The harmonic motion is described by the following equation.

x(t) = 3\cos{\pi t}

What is the first occurrence of a value of t for which x = 0?

This is t when x(t) = 0. So

x(t) = 3\cos{\pi t}

3\cos{\pi t} = 0

\cos{\pi t} = \frac{0}{3}

\cos{\pi t} = 0

The inverse of the cosine is the arcosine. So we apply the arcosine function to both sides of the equality.

\arccos{\cos{\pi t}} = \arccos{0}

\pi t = \frac{\pi}{2}

t = \frac{\pi}{2 \pi}

t = \frac{1}{2}

t = 0.5

The first occurence of t for which x = 0 is t = 0.5.

3 0
3 years ago
John and Karen plan on building a garden in their new home. They plan on designing a rectangular garden with a perimeter of 70 f
valentinak56 [21]

Answer:

Length of the garden= 7 feet while the width =28 feet

Step-by-step explanation:

Let the length of the garden be L while the width represented as W

From the question, we deduce the following:

W = 4L

Perimeter = 2(L + W) = 70 feet .... substituting W = 4L into this equation gives

70 = 2(L + 4L)

70 = 2(5L)

70 = 10L ... dividing both sides by 10 gives

L = 7

Recall from the first equation that W = 4L

W = 4 * 7 =28

7 0
3 years ago
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