The surface area of a rectangular prism is 792 units2. The length of the prism is 2 times the width, and the width is 4 times the height. What is the volume of the prism?

Answers

Answer 1

Answer:

The real answer is 846 ^-^ I got it right

Answer 2

The volume of the rectangular prism is 105.57

What is the volume of a rectangular prism?

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

Where l, h and w represent the length, height and width respectively.

Given that;

Length of the prism is 2 times the width L = 2w

the width is 4 times the height w = 4h

Now let’s plug these values;

the surface area equation, it becomes;

A = 2(2w(w) + w(w/4) + w/4(2w))

A = 2(2w^2 + w^2/4 + w^2/2)

A = 1/2(7w^2)

792 x2 = 7w^2

w = 15.04

The volume of a rectangular prism=Length X Width X Height

V = 2w x w x w/4

V x 2 = w³

V = 15.04³/2

V = 105.57

Thus, the volume is 105.57.

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Related Questions

emily is converting 9 feet per hour into inches per minute. which conversion factor should she use

Answers

[tex] 9 \dfrac{ft}{hr} \times \dfrac{12~in}{ft} \times \dfrac{hr}{60~min} = [/tex]

[tex] = 9 \dfrac{ft}{hr} \times \dfrac{12~in \times hr}{60~ft \times min} [/tex]

[tex] = 9 \dfrac{ft}{hr} \times \dfrac{1~in \times hr}{5~ft \times min} [/tex]

The conversion factor is 1/5.

I’m not sure how to use integration to solve this question (4)

Answers

Hello,
[tex]Area= \frac{16}{3}=2*( k*\sqrt{k}- \int\limits^{\sqrt{k}}_{0} {x^2} \, dx )\\\\ \dfrac{8}{3}=k ^\frac{3}{2}- \frac{1}{3}* [x^3]^{\sqrt{^k}}_0\\\\ 2* k ^\frac{3}{2}=8\\\\ k = \sqrt[3]{16}\\ [/tex]

(40 POINTS!)
What is the center of the circle that has a diameter whose endpoints are (-3, -5) and (-11, -7)

A. (-8, -1)
B. (-7, -6)
C. (-4, -6)

Answers

Hello there!

The center of any circle is the midpoint of the diameter.
Let's use the midpoint formula to find the midpoint of the diameter.

The midpoint of a line segments with endpoints [tex](x_1, y_2)[/tex] and [tex](x_2, y_2)[/tex] will have a midpoint of [tex]( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

Midpoint of the diameter:

[tex]( \dfrac{-3-11}{2}, \dfrac{-5-7}{2})[/tex]

[tex]=(-7, -6)[/tex]

Your answer is B. Hope this helps!

Expand the logarithmic expression.

log5(7)a^5

A. log57 • 5log5a
B. log57 + 5log5a
C. 7log5a^5
D. log57 – 5log5a

Answers

The answer for the exercise shown above is the option B, which is:
B. log5(7)+5log5(a)
The explanation of the problem is shown below:
1. You have the following expression given in the problem above:
log5(7)(a^5)
2. To expand it, you must use the logaritms properties, as following:
log5(7)(a^5)
log5(7)+log5(a^5)
log5(7)+5log5(a)
3. Therefore, as you can see, the answer is the option B.

Answer: is b. log57 + 5log5a

Water is flowing into a 50-gallon bathtub at a rate of 2.3 gallons per minute (gpm). To the nearest minute, how long will it take to completely fill the bathtub?

A. 48 minutes
B. 22 minutes
C. 26 minutes
D. 115 minutes

Answers

It would be b. If you divide the 2

What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box.

Answers

Answer: The length of side X is 4.

In triangle KLJ, the hypotenuse is 8 square roots of 2. The side opposite the 30 degree angle is half of that amount. Therefore, it is only 4 square roots of 2.

That side is also the hypotenuse in the 45 45 90 triangle. To find the leg, we simply divide by the square root of 2. We will end of with legs that are 4.

This is a word problem where you have to create an equation and a solution to.

"Michaela and Aleah play on the same basketball team. In one game Michaela scored one fifth of the team's points and Aleah scored one tenth's of the teams points. Together they scored a total of 42 points. How many points did the team score?"

(I might find an equation for it, but I doubt it so if anyone is good with creating equations for word problems please help me!!)

-matty

Answers

You are asked to find the team score, so it is convenient to let a variable represent that value. Let's call it "s", for "score". The problem statement tells you
.. Michaela scored s/5 . . . . . one fifth of the team's points
.. Aleah scored s/10 . . . . . . . one tenth o the team's points
These scores together are (s/5 +s/10) and that amount is 42 points.
.. s/5 +s/10 = 42
.. s(2/10 +1/10) = 42 . . . . . factor out s
.. s(3/10) = 42 . . . . . . . . . . form the sum of the numbers in parentheses
.. s = 42*10/3 = 140 . . . . . multiply by the inverse of the coefficient of s

The team scored 140 points.

______
Michaela scored 140/5 = 28 points; Aleah scored 140/10 = 14 points.

Final answer:

To solve this word problem, set up the equation (1/5) x + (1/10) x = 42 and solve for x. The team scored 140 points.

Explanation:

To solve this word problem, we can start by letting the total number of points scored by the team be represented by 'x'. Since Michaela scored one-fifth of the team's points, her score can be represented as (1/5)x. Similarly, Aleah's score can be represented as (1/10)x. Together, their scores add up to 42 points, so we can set up the equation:

(1/5)x + (1/10)x = 42

To simplify the equation, we can find a common denominator of 10:

(2/10) x + (1/10) x = 42

Combining like terms, we get:

(3/10) x = 42

To isolate x, we can multiply both sides of the equation by 10/3:

x = 42 * (10/3)

Simplifying further, we get:

x = 140

Therefore, the team scored 140 points.

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What is the value of n? Enter you answer in the box.

Please help! Even just explaining how to do it will help a lot.

Answers

check the picture below.

Answer:

The value of n is [tex]n=4[/tex]

Step-by-step explanation:

we know that

The intersecting chords theorem states that the products of the lengths of the line segments on each chord in a circle are equal

In this problem

[tex](n+2)16=(n+8)8[/tex]

solve for n

[tex]16n+32=8n+64[/tex]

[tex]16n-8n=64-32[/tex]

[tex]8n=32[/tex]

[tex]n=4[/tex]

HURRY!!! PLEASE
Which equation represents a direct variation?

y = 2x
y = x + 4
y =1/2x
y = 3/x

Answers

The answer is y = x + 4 because both x and y are being multiplied by the same thing. They both have a coefficient of 1. When ever the same number is being multiplied or divided by both x and y, it is considered a direct variation. This means the coefficients would be the same.

Answer:

A. [tex]y=2x[/tex]

Step-by-step explanation:

We are asked to find the equation that represents a direct variation.

We know that a direct variation is in form [tex]y=kx[/tex], where y is directly proportional to x and k is constant of variation.

Upon looking at our given choices, we can see that equation [tex]y=2x[/tex] represents direct variation, where [tex]k=2[/tex].

Therefore, option A is the correct choice.

Simplify each expression. Use positive exponents.
m^3 n^-6 p^0

Answers

m^3 is the first one
1/n^6 is the second one
1 is the third answer

The following sequence is an arithmetic sequence what comes next ? 7,___,17

Answers

Since this is an arithmetic sequence, you can conclude that the addition to the number is constant.

Let x = the number asked

k = constant number added to the sequence

7 + k = x

x + k = 17

Solve the system of equation:

7 + k + k = 17

7 + 2k = 17

2k = 10

k = 5

Therefore, the missing number is 12 (7 + 5).

what is: 2/3 X 5/6 X 14 =

this is so that i can help a 5th grader. and i am horrible at fractions. please show work and or explain how to do it. so that i can show her how to do it as well.,

Answers

sure. (2/3)=.667 and 5/6=.833. when you multiply them it should look like (.667) x (.833) x 14 which equals 7.778. i hope this helps.

Solve the system by substitution.

x - 2y = 4
2x - 6y = 8

Answers

1.) x - 2y = 4 , add 2y to both sides. ---> answer is, X = 2y + 4
2.) 2x - 6y = 8, Add 6y to both sides, then divide both sides by 2. --> answer is, X = 3y + 4

Hi there!

To solve this system with substitution, we need to set x equal to [its value] and plug it into the second equation.

x = 2y + 4

2(2y + 4) - 6y = 8
4y + 8 - 6y = 8
-2y + 8 = 8
-2y = 0
y = 0

Now, we plug y into the equation and solve for x.

x = 4

Hope this helps!

The formula v =sqrt 64h can be used to find the velocity, v, in feet per second, of an object that has fallen h feet. Find the velocity of an object that has fallen 75 feet. Round to the nearest tenth.,

Answers

I think first that the 64 h should be in parantheses so v=sqrt(v*h) where sqrt means square root. If it falls 75 feet, then here h is 75 ft. Then v=sqrt(64*75)=sqrt (4800)=69.282. Rounded to the nearest tenth our answer would be 69.3 ft/sec.

Calculate the difference 12.0875 – 7.50 using significant digits.

A. 4.5
B. 4.587
C. 4.59
D. 4.6

Answers

Answer:

C. 4.59

Step-by-step explanation:

Significant digits are digits expressing precision of a measurement. Non-zero digits are always significant but zeroes can be either included or ignored. For instance, zeroes that comes before other digits aren't significant. For example 0.058 has two significant digits. In this exercise, we have two numbers:

12.0875

7.50

The number 12.0875 has five significant digits while 7.50 has three significant digits. If we add or subtract two numbers, the least number of decimal places (that isn't the same as significant digits) in any of the two numbers must be the same as the number of decimal places in the result. Hence, for 12.0875 we have four decimal places and for 7.50 we have two decimal places. Therefore, the result must have two decimal places:

12.0875 - 7.50 = 4.59

The Answer is C. 4.59

Which is the graph of f(x)= square root of x

Answers

The bottom graph is the graph for the sqrt(x)!

f (x) = root (x)
For this case what you must do is build a table with the values that the function takes when inserting a value of x.
We have then:
x f (x)
1 1
4 2
16 4
25 5
36 6
When you get a sufficient number of points, graph each orderly and see the behavior of the graph.
Answer:
The graph looks like in the attached image.

A person invested $7,200 in an account growing rate allowing money to double every 8 years. How much money would be in the account after 19 years, to the nearest dollar?

Answers

273600 in his bank account

After 19 years, the final amount is $29,936.93, to the nearest dollar.

What is the formula for exponential growth?

The formula for exponential growth:

[tex]final amount = initial amount * (rate)^(number of time periods)[/tex]

In this case, the initial amount is $7,200, the rate is 2 (since the money doubles every 8 years), and the number of time periods is 19/8=2.375 (since 19 years is 2.375 times the 8-year doubling period). Plugging these values into the formula, we get:

final amount = $7,200 * 2^2.375

The final amount is $29,936.93, to the nearest dollar.

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Mark raises guppies in an aquarium. He finds out that guppies reproduce very rapidly, and the number quadruples every month. He starts out with only 2 guppies, and the function y equals 2 times 4 to the x models the number of guppies he will have after x months. Which graph represents this function?

Answers

For this case what we should know is that the function that best adapts to this problem is given by:
y = 2 * (4) ^ x
The graph of the function is shown for two different intervals:
A small interval of -1.5 to 0.5
A larger interval of -6.5 to 6.5.
In both intervals the exponential growth of the function is demonstrated.
Answer:
See attached image.

Choose the correct product of (7x − 3)(7x + 3). 49x2 + 9 49x2 − 42x + 9 49x2 − 9 49x2 + 42x + 9

Answers

Using FOIL (First Outside; Inside, Last), we find our product.

(7x - 3)(7x + 3) // Given
7x * (7x + 3) // First Outside
49x^2 + 21x // Distribute (remember this)
-3 * (7x + 3) // Inside Last
-21x - 9 // Distribute (remember this)
49x^2 + 21x - 21x - 9 // Add both answers (the one from Outside and the one from Inside)
49x^2 - 9 // Simplify. This is your answer

You can do this, or you can remember that this is a factor for a difference of squares, where

a^2 - b^2 = (a + b)(a - b)

Plug in “7x” for a, “3” for b

Final answer:

The product of the binomials (7x - 3)(7x + 3) is calculated using the difference of squares formula, resulting in 49x² - 9.

Explanation:

To find the correct product of the binomials (7x − 3)(7x + 3), we use the difference of squares formula, a² - b² = (a - b)(a + b). In this case, a is 7x and b is 3. Thus, the product is:

(7x − 3)(7x + 3) = (7x)² - (3)²
= 49x² - 9

Therefore, the correct product is 49x² - 9.

Think it’s b not sure though

Answers

yes, b is correct, imm pretty sure.

For this case what you should know is that you have the area of a quarter of a circle which is:
A1 = 30.25pi cm ^ 2
We now look for the area of the triangle, which by definition is:
A2 = (1/2) * (b) * (h)
Where,
b: base
h: height
Substituting the values:
A2 = (1/2) * (11) * (11)
A2 = 60.5 cm ^ 2
The area of the shaded region will be given by the subtraction of both areas:
A1-A2 = (30.25pi - 60.5) cm ^ 2
Answer:
A1-A2 = (30.25pi - 60.5) cm ^ 2
option 3

Your friend wants to borrow $1,137.45 from you to pay off a credit card that charges a 14.7% APR. You agree to the loan but require your friend to pay you interest of 3.6% APR on the loan and your friend agrees.
Your friend pays you $200.00 at the end of the first month. How much goes toward the principal?

Answers

$196.59
Let's start by calculating the interest on the first month. 1137.45 * (0.036/12) = 1137.45 * 0.003 = 3.41235
So at the end of the 1st month, the amount owed will be 1137.45 + 3.41 = 1140.86
And after the 200 payment is done, the new balance will be:
1140.86 - 200 = 940.86
Meaning that the principle reduced is: 1137.45 - 940.86 = 196.59
We could have also gotten the amount going towards the principle by subtracting the interest from the paying like: 200 - 3.41 = 196.59

The amount that goes into the principal when friend pays you $200.00 at the end of the first month is $296.56.

How to calculate the amount?

The first interest will be:

= 1137.45 × (0.036/12)

= 3.41

The amount owed at the month end will be:

= 1137.45 + 3.41

= 1140.86

The new balance after 200 payment will be:

= 1140.86 - 200

= 940.86

Therefore, the reduction in principal will be:

= 1137.45 - 940.86

= 196.59

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pls help me with this one question

Answers

No soulution
This should m=be the answer, but i am 51.1111%sure

2. Solve 10^6x = 93. Round to the nearest ten-thousandth. (1 point)

11.8109
1.0986
13.3801
0.3281

3. Use a graphing calculator. Solve 5.5^3x = 805 by graphing. Round to the nearest hundredth. (1 point)

2.91
3.92
1.31
0.97,

Answers

2. 0.3281
3. 1.31

2. 10^(6x) = 93
For this problem, using a calculator makes it quite simple. What you want is the power that you can raise 10 to that gives you 93. That value is the logarithm of 93 to base 10. So
10^(6x) = 93
log(10^(6x)) = log(93)
6x = 1.968482949
x = 0.328080491
x = 0.3281

3. This problem is both trickier and easier than the previous. All you need to do is plot the function on your calculator and look for the answer that's nearest which is 1.31, you could also get a more precise answer by calculating the logarithm to base 5.5 of 805. You won't find such a logarithm function on your calculator, but that isn't a major problem since you can easily convert a logarithm from any base to any other base by simply dividing by the logarithm of the desired base. So:
5.5^(3x) = 805
log(5.5^(3x)) = log(805)
log(5.5^(3x))/log(5.5) = log(805)/log(5.5)
log to base 5.5 of 5.5^(3x) = log(805)/log(5.5)
3x = 2.90579588/0.740362689
3x = 3.92482755
x = 1.30827585
x = 1.31

1. B

2. D

3. C

4. A

5. B

ESKETIT

The population of wild horses on a wildlife refuge decreased from 110 to 99 in a year. If this trend were to continue, what exponential equation could be used to predict the horse population in the future?
y = 110(1.1)^x
y = 99(0.9)^x
y = 99(1.1)^x
y = 110(0.9)^x,

Answers

The exponential equation for this situation is y = 110(0.9) ^x. This is because 110 is the principal or the initial number of horses and y is the resultant population after a certain number of years X with a rate of 0.9. Note that the rate is less than 1 which means that the population is decreasing as time goes by.

Answer:

The person is right.

Step-by-step explanation:

Look at his profile.

Which of the following is true for the angular momentum of a rotating bicycle wheel?
(Points : 1)
It is a vector that points in the direction the bike would travel.

It is a vector that points along the axis of rotation perpendicular to the wheel.

It is a vector pointing radially outward from the center to the edge of the wheel.

It is a scalar.,

Answers

What is true is that it’s a vector that points along the axis of the rotation of the wheel. With each spin of the bike’a wheel, the vector is continuolously being pressed where the momentum goes

A circle of radius 1 centered at (4, 0) is rotated about the y-axus. Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis. In two or more complete sentences, describe the three-dimensional shape. Upload both parts A and B as your final answer.

Answers

Answer: The three-dimensional shape that would result would be in the shape of a donut.

Imagine taking a knife and cutting a slice in a donut. The cross-section of where you cut would be a circle. This is what would happen if you rotated the circle around the y-axis. It would be like that cross-section of the donut going around the entire circle.

Final answer:

When a circle rotates around the y-axis, it forms a three-dimensional object known as a cylinder. The cylinder will have a radius of 1 and height equal to the diameter of the circle, which is 2.

Explanation:

When a circle of radius 1 centered at (4,0) is rotated about the y-axis, the three-dimensional shape that is produced is known as a cylinder.

This cylinder would have a radius of 1, and its height would be equal to the length of the diameter of the original circle, which is 2 units (from -1 to 1 along the x-axis).

In terms of the visual representation, imagine a circle on a piece of paper, now pick up the paper and rotate it about the line that is the y-axis. The paper, on which the circle is drawn, forms a cylindrical shape when rotated. The edges of the paper represent the bases of the cylinder and the surface of the paper forms the curved surface of the cylinder.

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Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. (2 points)
Question 1 options:

1) 203

2) 197

3) 168

4) 163,

Answers

Arithmetic sequences have the same value added repeatedly. There are 17 increments between a1 and a18 and the value changes a total of 102 (95 - -7). 102 divided by 17 shows that the value of 6 is being added each time. The 35th term is then given by a1+(35-1)*6 = -7 + 34*6 = -7 + 204 = 197.

Answer: 197

Step-by-step explanation: I took the test :)))

Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.

Answers

Answer:

Step-by-step explanation:

We will make a substitution to make our work easier (when we get there). We also need to know that

[tex]i^2=-1[/tex]

We will use that as another substitution. First, let's make the job of factoring a bit easier. Here's the first substitution. We will let

[tex]x^4=u^2[/tex]

Therefore,

[tex]x^2=u[/tex]

Now we will write the polynomial in terms of u instead of x:

[tex]f(x)=u^2+21u-100[/tex]

Solve for the values of u by setting the polynomial equal to 0 and factoring. When you factor, you will get:

[tex](u+25)(u-4)[/tex]

But don't forget that

[tex]x^2=u[/tex]

so we have to put those back in now:

[tex](x^2+25)(x^2-4)=0[/tex]

By the Zero Product Property, either

[tex]x^2+25=0[/tex] or

[tex]x^2-4=0[/tex]

We will factor the first term. Solving for x-squared gives us:

[tex]x^2=-25[/tex] and

x = ±√-25

which simplifies down to

x = ±√-1 × 25

we can sub in an i-squared for the -1:

x = ±√[tex]i^2*25[/tex]

The square root of i-squared is "i" and the square root of 25 is 5, so

x = ±5i

The next one is a bit easier. If

[tex]x^2=4[/tex], then

x = ±2

You can see you have 4 solutions. But you knew that already, since this is a 4th degree polynomial. The types of solutions are: 2 real, 2 imaginary

a factory worker can make 14 products in 45 minutes. what is the worker's unit rate?

Answers

Divide the number of products by the time.

unit rate = (14 products)/(45 minutes) = 0.311 products/minute

Since there are 60 minutes in an hour, if you want the unit rate in products per hour, just multiply what we got above by 60.

unit rate = 18.667 products/hour

3.2 minutes per products

divide 14 by 45.0 = 3.2 r 30

hope this helps

What are the coordinates for this graph!

Answers

the correct answer is (2,4)

(2,4)? It has to be because 2 is on the x-axis and 4 is on the y-axis

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