The length of a rectangle is three times longer than its width. The perimeter of the rectangle is 16 feet. If x represents the width of the rectangle, which equation can be used to find its value?

Answers

Answer 1
Answer: l = 3x
perimeter = 2(l + w) = 2(3x + x) = 2(4x) = 8x = 16
x = 16/8 = 2 feet
l = 3x = 3 * 2 = 6 feet



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Laura fills a bucket with water at a rate of 6 L/min. At the same time, Sarah empties a bucket holding 30 L of water at a rate of 9 L/min. Let l represent the number of liters of water and let t represent time in minutes. The system models this situation.How many minutes will it take for the buckets to hold equal amounts of water, and how much water will that be?

l = 6t

l = 30 – 9t


It will take ____ minutes for both buckets to hold equal amounts of water. They will each hold ____ liters.

Answers

0+6 L per min
30-9 L per min
so let x represent the time
0+6 times x and
30-9 times x
we want to know what time they will be equal so set them equatl to each other
0+6x=30-9x
6x=30-9x
add 9x to both sides
15x=30
divide both sides by 15
x=2
at 2 mins, they will be equal
find out what that is
subsitute in 0+6x
0+6(2)=0+12=12L

the answers are 2 minutes and 12 liters respectively

Write an algebraic expression for the following word phrase: the quotient of r and 12?

Answers

quotient= division so 12/r would be your answer 

Final answer:

The algebraic expression for the word phrase 'the quotient of r and 12' is r/12. This represents a division operation where r is divided by 12.

Explanation:

The phrase 'the quotient of r and 12' can be translated into an algebraic expression as r/12. In this expression, 'quotient' refers to the mathematical operation of division. Hence, the expression means that the variable 'r' is divided by '12'.

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6. Write two rational numbers which are their own reciprocals ?

Answers

1 and -1 are the only rational numbers which are their own reciprocal.\:

How can you solve -2y+5y=14

Answers

you add the terms that are the same and then simplify.

-2y+5y=3y
3y=14
y=4.666 or 4 2/3

What is the value of x, given that the two prisms are similar?

Answers

x = 10
The size of the larger prism is twice the size of the smaller one.
For example, as you can see from the base length of the triangular side: Larger is 3 units and the smaller is 1.5 units. 3÷2=1.5
So I did the same with the length of the base: 20÷2=10

Answer:

x=10

Step-by-step explanation:

right answer

Which expression is equivalent to 15 + 6x?

Answers

Answer:

Step-by-step explanation:

The expression 15 + 6x can be simplified further. The term 15 is a constant because it does not contain a variable. On the other hand, 6x is a variable term because it contains the variable x.

To simplify the expression, you can combine like terms by adding or subtracting the coefficients of the variable terms. In this case, you can't combine 15 and 6x because they are not like terms.

Therefore, the expression 15 + 6x is already simplified and does not have an equivalent expression. It represents the sum of 15 and 6 times x.