The equation below describes a proportional relationship between x and y. What is the constant of proportionality?

Prism A and Prism B have the same volume. Which could be the dimensions of prism B. Please help!

pentagon [3]

Question : Prism A and Prism B have the same volume. Which could be the dimensions of prism B?

Prism A :

Length = 8 feet

Width = 4 feet

Height = 5 feet

Prism B:

Length = ? feet

Width = ? feet

Height = ? feet

Option 1:

Length = 6 feet

Width = 10 feet

Height = 2 feet

Option 2:

Length = 4 feet

Width = 4 feet

Height = 10 feet

Option 3:

Length = 5 feet

Width = 4 feet

Height = 7 feet

Option 4:

Length = 8 feet

Width = 4 feet

Height = 6 feet

Here, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet.

We know that if the a and b be the length and width of the base respectively and c be the height of a prism, then the volume of the prism is abc.

Given that

length of 1st prism = 8 feet

width of 1st prism = 4 feet

height of 1st prism = 5 feet

So volume of 1st prism = 8 * 4 * 5 = 160 feet³

Now the volume of 1st and 2nd prisms are the same.

So, we have to check the options for length, width, and height of the 2nd prism.

1st option:

Height = 6 feet

Width = 10 feet

Length = 2 feet

So, volume = 6 * 10 * 2 = 120 feet³

Then the 1st option is incorrect.

2nd option:

Height = 4 feet

Width = 4 feet

Length = 10 feet

So, volume = 4 * 4 * 10 = 160 feet³

Then the 2nd option is correct.

Therefore, the dimensions of the prism B will be length = 4 feet, width = 4 feet, and height = 10 feet. The 2nd option is correct.

Learn more about the volume of a prism here -

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4 0

3 years ago

Jesse is a pizza delivery driver. Each day his employer gives him $20 plus $0.50 for every pizza that he delivers.

zzz [600]

Answer:

+÷×i think it i one of these correct me if i am wrong

Step-by-step explanation:

cuz i think so

8 0

3 years ago

*Please help* (20 POINTS) Hint: Both of the slopes are 2/3

agasfer [191]

Slope of blue using their 2 points is 4/6 or 2/3

slope of green using their points is 2/3 which is the same as the other triangle.

4/6 = 2/3. and this is true, the slopes are equal

7 0

4 years ago

Read 2 more answers

A law firm is going to designate associates and partners to a hug new case. The daily rate of charged to the client for each ass

goldenfox [79]

Answer:

There are 3 associates and 5 partners assigned to the case.

Step-by-step explanation:

We know that the combined cost of the unknown number of associates and partners equals $6500 per day, and that the amount of associates and partners assigned to the case equals 8, so we can derive these two equations (where a is associates and p is partners):

500a + 1000p = 6500

a + p = 8

Let's use the second one first to isolate the a..

a + p = 8

If we subtract p from both sides of the equation we get:

a = 8 - p

Now we may use this in our original equation to solve for p

500(8-p) + 1000p = 6500

If we simplify by distribution, we get:

4000 - 500p + 1000p = 6500

Now let's add those two p's together...

4000 + 500p = 6500

And subtract 4000 from both sides to get:

500p = 2500

Now finally, divide both sides of the equation by 500 to get p:

p = 5

We now have the number of partners involved (5), and we know that the amount of associates plus the amount of partners assigned to the case equals 8, so we can plug the amount of partners assigned into the second formula to get a:

a + 5 = 8

And by subtracting 5 from both sides we get...

a = 3

3 0

3 years ago

If you are examining a function over an interval ( a , b ) , for a and b finite, is it possible not to have an absolute maximum

uysha [10]

Yes, it is not possible to have an absolute maximum or absolute minimum.

Here,

We are examining a function over an interval ( a , b ) , for a and b finite,

We have to find, is it possible not to have an absolute maximum or absolute minimum.

What theorem indicates the existence of absolute maxima or absolute minima of a function?

If f is continuous on a closed interval [a, b] (that is: on a closed and bounded interval), then, the Extreme Value Theorem indicates the existence of an absolute maximum or minimum value of f on the interval [a, b].

Now,

The function is define over an interval (a, b).

Hence, the function is define on open interval.

So, it is not possible to have an absolute maximum or absolute minimum.

Learn more about the existence of maxima and minima visit:

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3 0

2 years ago

The equation below describes a proportional relationship between x and y. What is the constant of​ proportionality?

The equation below describes a proportional relationship between x and y. What is the constant of proportionality?