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3 years ago

15

A rectangular prism has a length of 3 1/2 in., a width of 3 1/2 in., and a height of 7 in. Danny has a storage container for the

prism that has a volume of 90 in³. What is the difference in volume between the prism and the storage container?

1 answer:

marta [7]3 years ago

6 0

The difference is 4.25in^3

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The diameter of a circle measures 17 mm. What is the measure of its radius ?

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The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integ

Nutka1998 [239]

Answer:

equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
values: -21, -19, -17, -15

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

(x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

-18-3 = -21
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A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

(x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

4x +12 = -72 . . . . . collect terms

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4 years ago

7. Veronica is choosing between two health clubs.

vesna_86 [32]

Answer:

The total cost for each health club will be the same after 4 months.

Step-by-step explanation:

Let A = membership fee for studio A

B = membership fee for studio B

x= membership month

$A = 22 + 24.5x$

$B = 47.00 + 18.25x$

We want to when the total cost at each health studio is the same.

In other words, when A = B.

Therefore, the expression becomes

$A = B$

$22\:+\:24.5x=47.00\:+\:18.25x$

Step 1: Simplify both sides of the equation.

$24.5x+22=18.25x+47$

Step 2: Subtract 18.25x from both sides.

$24.5x+22-18.25x=18.25x+47-18.25x$

$6.25x+22=47$

Step 3: Subtract 22 from both sides.

$6.25x+22-22=47-22$

$6.25x=25$

Step 4: Divide both sides by 6.25

$\frac{6.25x}{6.25}=\frac{25}{6.25}$

$x=4$

Therefore, the total cost for each health club will be the same after 4 months.

8 0

3 years ago