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Murrr4er [49]
2 years ago
12

What is the smallest positive integer $n$ such that $3n$ is a perfect square and $2n$ is a perfect cube?

Mathematics
1 answer:
Agata [3.3K]2 years ago
6 0

Answer:

108

Step-by-step explanation:

Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.

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A rectangular solid object is 3 in. high, 6 in. long and 2 in. wide. What is its volume?
inn [45]

Answer:

The volume is 36 inches cubed.

Step-by-step explanation:

The volume of a rectangular prism is W*L*H.

You are given the H=3i, W=2 in, and L=6 in.

So now we plug into our formula for the volume of a rectangular prism which will result in 2*6*3=12*3=36.

The volume is 36 inches cubed.

5 0
3 years ago
Read 2 more answers
At the school talent show, 1/3 of the people were boys, 3/6 were girls, and the rest were adults. If there were 50 more girls th
strojnjashka [21]

Answer:

150 people

Step-by-step explanation:

Lets call the total amount of people at the talent show x. Since 3/6=1/2, we know that half the people are girls, 1/3 are boys. If we added 1/2 and 1/3 we get 5/6, 1-5/6=1/6, so now we know that 1/6 of the people are adults. Because it says "If there were 50 more girls than adults" so from that we can see that 1/2x =1/6x+50. If we were to simplify the equation, we 1/3x=50, so x=150

3 0
3 years ago
Write an equation for the line shown on the graph.
Irina18 [472]

Answer:

\large\boxed{y=\dfrac{2}{3}x+1}

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept → (0, </em><em>b</em><em>)</em>

<em />

The fromual of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

<em>(x₁, y₁), (x₂, y₂)</em><em> - points on a line</em>

<em />

We have the points from the graph:

(0, 1) → <em>b = 1</em> and (3, 3).

Calculate the slope:

m=\dfrac{3-1}{3-0}=\dfrac{2}{3}

Finally we have the equation of a line:

y=\dfrac{2}{3}x+1

3 0
4 years ago
What is true about rational numbers
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3 years ago
Does anyone know f(-3)=
AURORKA [14]

Answer:

Positive 1

Step-by-step explanation:

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