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slava [35]
3 years ago
13

A tank contains 550 gallons of water. When the valve is opened, the tank drains at a rate of 12 gallons per minute. Which functi

on shows the relationship between the time t the valve is opened and the amount of water in the tank?
Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
7 0

Answer:

y= 550-12x

Step-by-step explanation:

Given data

Content of tank= 550 gallons

Rate of drain= 12gallon per minute

let the time it will take to drain all 550 gallons be x minutes

Hence the expression for amount of water in the tank after x minutes will be

y= 550-12x

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Justin is pouring a concrete walkway around his grandmother's rectangular garden. He wants the walkway to be 3 feet wide all the
sattari [20]

Answer: The area of the top of the walkway is 1,050 square feet

Step-by-step explanation:

Hi, to answer this question we simply have to apply the next formula:

Area of a rectangle: width x length  (of the base)

Replacing with the values given and solving for A:

A = 25 feet x 42 feet = 1,050 square feet

In conclusion, the area of the top of the walkway is 1,050 square feet

Feel free to ask for more if needed or if you did not understand something.

8 0
3 years ago
Please help!!!!<br><br>what is the least common denominator of 1/6, 10/11, 5/12?<br>​
Vesna [10]
<h3>Answer: LCM = 132</h3>

===================================================

Work Shown:

LCM = least common denominator

List out the prime factorization of each denominator

  • 6 = 2*3
  • 11 = 1*11
  • 12 = 2*2*3

So we have the list of primes 2,3, and 11 that help form the denominators when we multiply some of them together.

The prime 2 shows up at most twice, so 2*2 = 4 is a factor of the LCM

The prime 3 shows up at most one time, meaning 3 is also a factor

The prime 11 shows up at most one time, so 11 is another factor

Multiply these factors to get 4*3*11 = 12*11 = 132

The LCM is 132

---------------------

Another Approach:

Focus on 1/6 and 10/11 for now. The LCM is 66 because 6*11 = 66. We simply multiply the denominators together. Then we divide over the GCF 1 to get 66/1 = 66.

The LCM of 1/6 and 10/11 is 66

The fractions 1/6 and 10/11 are equivalent to 11/66 and 60/66 respectively

The original list of fractions updates to 11/66, 60/66, 5/12

We've gone from 3 different denominators to now 2 different denominators.

Repeat the steps of multiplying the denominators and dividing by the GCF

66*12 = 792

792/(gcf of 66 and 12) = 792/6 = 132

So the LCM of all the fractions is 132.

3 0
3 years ago
Find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20​
Vsevolod [243]

Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

\displaystyle S=\frac{k}{2}(a+x_k)

Where <em>k</em> is the number of terms, <em>a</em> is the initial term, and <em>x</em>_<em>k</em> is the last term.

Since we want to find the sum of the first 20 terms, <em>k</em> = 20.

Our initial term <em>a</em> is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

x_n=a+d(n-1)

Where <em>a</em> is the initial term, <em>d</em> is the common difference, and <em>n</em> is the <em>n</em>th term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

x_n=4-8(n-1)

Then the last or 20th term is:

x_{20}=4-8(20-1)=4-8(19)=-148

Therefore, the sum of the first 20 terms are:

\displaystyle\begin{aligned} S_{20}&=\frac{(20)}{2}\left((4)+(-148))\\&=10(-144) \\&= -1440\end{aligned}

5 0
2 years ago
Read 2 more answers
If one cup is equal to 8 fluid ounces, how many fluid ounces are in 4 cups? Input only whole numbers.
Levart [38]
4 cups = 32 oz. (:

I hope this helps. (:
4 0
3 years ago
Read 2 more answers
Please help me finish these for summer school :)
ValentinkaMS [17]
13.45 will be the answer

since we are finding the hypotenuse, the formula is a^2 + b^2 = c^2

this will then be 10^2 + 9^2 = c^2

181=c^2

c=13.45 :)
5 0
2 years ago
Read 2 more answers
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