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Ksenya-84 [330]
3 years ago
12

Kyle has a aquarium in the shape of a rectangular prism.The aquarium is 24 inches long and 10 inches wide. The volume of the aqu

arium is 2,880 cubic inches. How high is the aquarium?
Mathematics
2 answers:
monitta3 years ago
8 0
The aquarium is 12 inches high. The formula for finding the volume of a rectangular prism is width x height x length. So I multiplied 24 by 10 and came up with 240. Next, I divide the volume 2,880 by 240 and came up with the answer 12. Lastly, I check my answer to ensure that it is right. 24 x 10 x 12 x 2,880. 
jasenka [17]3 years ago
4 0
To calculate to volume of a rectangular prism you use the formula l × w × h = V

l, w, and h are the sides, and V is the volume

So... 24 × 10 × h = 2,880

h = 2,880 / 240

h = 12


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For the following right triangles:
CaHeK987 [17]

Let us first define Hypotenuse Leg (HL) congruence theorem:

<em>If the hypotenuse and one leg of a right angle are congruent to the hypotenuse and one leg of the another triangle, then the triangles are congruent.</em>

Given ACB and DFE are right triangles.

To prove ΔACB ≅ ΔDFE:

In ΔACB and ΔDFE,

AC ≅ DF (one side)

∠ACB ≅ ∠DFE (right angles)

AB ≅ DE (hypotenuse)

∴ ΔACB ≅ ΔDFE by HL theorem.

6 0
3 years ago
Suppose x=c1e−t+c2e3tx=c1e−t+c2e3t. Verify that x=c1e−t+c2e3tx=c1e−t+c2e3t is a solution to x′′−2x′−3x=0x′′−2x′−3x=0 by substitu
Harrizon [31]

The correct question is:

Suppose x = c1e^(-t) + c2e^(3t) a solution to x''- 2x - 3x = 0 by substituting it into the differential equation. (Enter the terms in the order given. Enter c1 as c1 and c2 as c2.)

Answer:

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

Step-by-step explanation:

We need to verify that

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

We differentiate

x = c1e^(-t) + c2e^(3t)

twice in succession, and substitute the values of x, x', and x'' into the differential equation

x''- 2x' - 3x = 0

and see if it is satisfied.

Let us do that.

x = c1e^(-t) + c2e^(3t)

x' = -c1e^(-t) + 3c2e^(3t)

x'' = c1e^(-t) + 9c2e^(3t)

Now,

x''- 2x' - 3x = [c1e^(-t) + 9c2e^(3t)] - 2[-c1e^(-t) + 3c2e^(3t)] - 3[c1e^(-t) + c2e^(3t)]

= (1 + 2 - 3)c1e^(-t) + (9 - 6 - 3)c2e^(3t)

= 0

Therefore, the differential equation is satisfied, and hence, x is a solution.

4 0
3 years ago
What is the equation of the line that passes through the point (-6,-8) and has a slope of 1/3​
Arturiano [62]

y + 8 = 1/3 (x+6)

With the given information, we can use the point-slope formula, , to write the equation of the line. Substitute values for the  , , and  in the formula to do so.

The  represents the slope, so substitute  in its place. The  and  represent the x and y values of one point the line intersects, so substitute -6 for  and -8 for . This gives the following answer and equation (just make sure to convert the double negatives into positives:  

8 0
2 years ago
The graph below represents a population
Nataliya [291]

Answer:

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Option A is correct.

Step-by-step explanation:

We need to find the average rate of  change for the function for the interval

(6, 12]

The formula used to calculate Average rate of change is:

Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}

We are given a=6 and b=12

Looking at the graph we can see that when x=6 y= 3000 so, f(a)=3000

and when x=12, y=6000 so, f(b)=6000

Putting values in formula and finding Average rate of change:

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So, average rate of  change for the function for the interval (6, 12] is 500 people per year.

Option A is correct.

6 0
3 years ago
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s2008m [1.1K]

Answer:

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C(-2,3) =C'(-2+1, 3-3) = C'(-1,0)

B(-4,3)= B'(-4+1 , 3-3) = B'(-3,0)

7 0
3 years ago
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