Mathematics High School

Find the volume of a rectangular prism if the length is 4x, the width is 2x, and the height is x3 + 3x + 6. Use the formula
V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.

6x5 + 18x3 + 36x2
6x6 + 18x3 + 36x2
8x5 + 24x3 + 48x2
8x6 + 24x3 + 48x2

Answers

Answer 1
8x2(x3 + 3x + 6)

8x5 + 25x3 + 48x2
Answer 2

Answer:

option C is correct

[tex]8x^5+24x^3+48x^2[/tex]

Step-by-step explanation:

As per the statement:

The length(l), width(w) and height(h) of the rectangular prism are:

l = 4x

w = 2x

[tex]h = x^3+3x+6[/tex]

We have to find volume.

Use the formula:

[tex]V = lwh[/tex]

Substitute the given values we have;

[tex]V = 4x \cdot 2x \cdot (x^2+3x+6)[/tex]

⇒[tex]V = 8x^2 \cdot (x^3+3x+6)[/tex]

Using distributive property, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

then;

[tex]V = 8x^5+24x^3+48x^2[/tex]

Therefore, the volume of the rectangular prism is, [tex]8x^5+24x^3+48x^2[/tex]

Related Questions

Can someone help me please ? Thanks!

Answers

Use pythagorean theorem for all of them
a. 3, 4, 5
3^2+4^2?5^2
9+16?25
25=25
right 

b. 5, 6, 7
5^2+6^2=7^2
25+36=49
61>49
acute

c. 64+81=144
145>144
acute

hope this helps!
I will give you the general approach and you can do the calculations by yourself.

Assume 3 vertices are a,b,c

if a^2 + b^2 < c^2 ->it's obtuse

a^2 + b^2 = c^2 ->it's right

a^2 + b^2 > c^2 ->it's acute

First one is right apparently, similar combination of right triangle include 6,8,10

Simplify.

6m+7n+5m−3n

15mn

11m + 10n

m + 10n

11m + 4n

Answers

to simplify combine all like terms

6m +5m = 11m

7n-3n = 4n

 so it would be 11m+4n



A sequence has its first term equal to 8, and each term of the sequence is obtained by adding 6 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?

Answers

A recursive formula for an arithmetic sequence is:

a(n)=a(n-1)+d, where n=term number and d=common difference.

Since we are told that d=6:

a(n)=a(n-1)+6, a1=8  

They may want:

f(n)=f(n-1)+6, a1=8

I never understood why they teach this instead of explicit formulas because the above is pretty useless if you simply want say the 1031st term, you would need to do a lot of calculations to find it. :P.  The explicit function is:

a(n)=a+d(n-1), here a=8 and d=6 so

a(n)=8+6(n-1)

a(1031)=8+6(1031-1)=6188

Try finding the 1031st term with the recursive formula :D

Answer:

f(1) = 8 and f(n) = f(n − 1) + 6; n > 1


Read the following statement: x + 6 = 6 + x. This statement demonstrates:

the substitution property.
the reflexive property.
the symmetric property.
the transitive property.

Answers

The reflexive property because the reflexive property states that anything is equal to itself, and x+6 is the same as 6+x
the reflexive property

Find all the real zeros of the function.

Answers

For the expression as a whole to equal zero, any of the three terms could equal zero ie:

[tex]-2x=0[/tex] or [tex]x-2=0[/tex] or [tex]x^{2}-25=0[/tex]

We can find one zero by solving each in turn:

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

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

[tex]x^{2}-25=0[/tex]
[tex]x^{2}=25[/tex]
[tex]x=\sqrt{25}=5[/tex]

The zeros are 0,2 and 5.

To check, plug back into the original equation and verify that f(x)=0. 

Analyze the diagram below and complete the instructions that follow.

2004-04-02-05-00_files/i0370000.jpg

Find the area of triangle QRS. Round the answer to the nearest tenth.

A.
19.4 square units
B.
91.2 square units
C.
1,040.5 square units
D.
1,052.4 square unts

Answers

The extended version of the link given shows a triangle with sides of measurements equal to 13, 16, and 15 units. 

Since we are given with the measurements of all sides, we use the Heron's formula.

                         A = sqrt ((s)(s - a)(s - b)(s - c))

where s is the semiperimeter and a, b, and c are the measures of the sides.
    
                        s = (a + b + c) /2
                        s = (13 + 15 + 16) / 2 = 22

Substituting this to the equation for the area,
                      A = sqrt ((22)(22 - 13)(22 - 15)(22 - 16))
                            A = 91.19 square units

Thus, the area is approximately equal to 91.2 square units. The answer is letter B. 

Jorani flips two standard american quarters. how many ways can she get at least one head?

Answers

at least means 1 or more head

she can get

1 head 1 tail
1 tail 1 head
2 tails
2 heads

3 of the ways has at least 1 head


3 ways

Two friends left school at the same time and drove in opposite directions. One friend averages 40 miles per hour and the other friend averages 35 miles per hour. when will they be 150 miles apart?

Answers

Therefore, the two friends will be 150 miles apart in 2 hours.

Answer:

The two friends will be 150 miles apart in 2 hours

Step-by-step explanation:

The two friends left the school at the same time and drove in opposite directions. One of them have a speed of 40 miles per hour while the other have a speed of 35 miles per hour .

The both of them are moving apart at the rate  = 40 + 35 = 75 miles per hour

let

t = time at which they are 150 miles apart

speed = distance/time

time  = distance/speed

time = 150/75

time = 2 hours

The two friends will be 150 miles apart in 2 hours

A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base, as shown below. Find an equation for the parabola if the vertex is put at the origin of the coordinate system

Answers

To determine the equation of the parabola of the arch, we need to know the general equation for a parabola and its elements. The arch is facing down so the general equation written in its vertex form would be as follows:

y - k =  - a(x - h)^2

where (h,k) represents the vertex of the parabola and a represents the focus and tells you where the graph opens. If a is positive then it opens upward and if its is negative, it opens downward. 

For this given situation, the vertex is at point (0,0) or at the origin so that h and k are zero.

y=  - a(x)^2

To determine the value of a, we use the measurements given above. We make use of the maximum height and the span of the parabola. The point we will be using would be  (18/2 , 96 ).
 
y=  - a(x)^2
96=  - a(9)^2
a = -32/27

So, the equation of the parabola would be 
y=  - (32/27)(x)^2

The equation of the parabola if the vertex is put at the origin of the coordinate system is y =-32/27x^2

The height of the arch is given s:

height = 96 ft

The width of the base is given as:

width = 18 ft

A point on the building would be

(x,y) = (width/2, height)

So, we have:

(x,y) = (18/2, 96)

Simplify

(x,y) = (9, 96)

A parabola is represented as:

y = -a(x - h)^2 + k

The vertex of the parabola is at the origin.

So, we have:

y = -ax^2

Substitute (x,y) = (9, 96)

96 = -a * 9^2

This gives

96 = -81a

Divide both sides by 81

a= -96/81

So, the equation of the parabola is

y =-96/81x^2

Simplify

y =-32/27x^2

Read more about parabolas at:

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A cyclist rides her bike at a speed of 10 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.

Answers

Final answer:

The speed of the cyclist is 16 km/h and she will travel a distance of 32 kilometers in 2 hours.

Explanation:

To convert the speed from miles per hour (mph) to kilometers per hour (km/h), we can use the conversion factor of 1 mile = 1.6 kilometers. So, if a cyclist rides her bike at a speed of 10 mph, we can multiply 10 by 1.6 to find the speed in km/h. Therefore, the speed of the cyclist is 16 km/h.

To calculate the distance traveled in 2 hours, we can use the formula: distance = speed × time. Since the speed of the cyclist is 16 km/h and the time traveled is 2 hours, we can multiply 16 by 2 to find the total distance. Therefore, the cyclist will travel 32 kilometers in 2 hours

Final answer:

To convert the speed from miles per hour (mph) to kilometers per hour (km/h), multiply the speed by the conversion factor. The cyclist will travel 32 kilometers in 2 hours.

Explanation:

To convert the speed from miles per hour (mph) to kilometers per hour (km/h), we can use the conversion factor of 1 mile = 1.6 kilometers. Thus, if the cyclist rides at a speed of 10 mph, we can find the speed in km/h by multiplying it by the conversion factor:

Speed (km/h) = Speed (mph) x Conversion factor

Speed (km/h) = 10 mph x 1.6 km/mi = 16 km/h

Next, to calculate the distance the cyclist will travel in 2 hours, we can use the formula:

Distance = Speed x Time

Distance = 16 km/h x 2 hours = 32 kilometers

Perform the following food service calculation. Size of juice can = 54 oz. Portions of juice served = 6 oz. Number of cases used = 2 Number of cans per case = 12 How many guests can be served? 54 216 1,944 7,776

Answers

2 cases x 12 cans = 24 cans

24 cans x 54 oz per can = 1296 oz

1296 oz / 6 oz per serving = 216 guests served

Answer: 216 guests.


Step-by-step explanation: We are given total number of cases = 2 Number of cans.

Number of cans per case = 12 cans.

Total number of cans in 2 cases = 2 cases × 12 cans = 24 cans

Each can contain = 54 oz of juice.

24 cans would contain total = 24 cans × 54 oz per can = 1296 oz juice.

Number of oz per serving = 6 oz.

Total number of guests can be served = 1296 oz / 6 oz per serving = 216 guests.


How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.

Answers

Answer:

40,320.

Step-by-step explanation:

We are asked to find the number of ways in which 8 books could be arranged on a shelf.

The 1st could be arranged in 8 ways. Since one place is filled, so 2nd book could be arranged in 7 ways.

Similarly, the 3rd book could be arranged in 6 ways as first two places are already taken. This process will go on.

So the 8 books can be arranged in [tex]8\times 7 \times 6\times5\times4\times3\times2\times1=8![/tex]

[tex]8!=40,320[/tex]

Therefore, 8 books could be arranged in 40,320 ways.

The number of ways to arrange 8 books on a shelf is 40,320.

We have to determine

How many ways can 8 books be arranged on a shelf?

According to the question

There is total number of books is 8.

Then,

The arranging the way of 8 books also be 8.

If one of the 8 books is placed in the first place, only 7 of them can be placed in 2nd place. In 3rd place, only 6 of them can be placed.

This continues all the way to 1.

A permutation is an arrangement of objects in a particular way.

Then,

The number of ways to arrange 8 books on a shelf is,

[tex]= 8!\\ \\ = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\\ \\ =40,320 [/tex]

Hence, The number of ways to arrange 8 books on a shelf is 40,320.

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given that (-2,7) is on the graph of f(x), find the corresponding point for the function f(x+4)

Answers

it would be considered-5,7 6,8

Answer:

CORRECT ANSWER ON PLATO: -6,7

Step-by-step explanation:

12.252525... is an example of a ___ decimal?

Answers

Repeating decimal, these should be expressed as rational numbers...

If x=12.25...

100x-x=1225.25...-12.25...

99x=1213

x=1213/99  

x=12 25/99

The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282

Answers

In order to determine the value of the rent after x years, we need to generate a function which would relate the value of the rent and the time in years. The rate by which the rent increases is said to be 3.5% per year. So, if we do it manually, we would have:

value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) + ........

However, this is a tedious and long process since we need to continue until year 8. We need to simplify it to an expression. We do as follows:

value of the rent = 225000 + 225000 (.035) + 225000 (.035)(.035) + ........

We factor out the initial rent, 

value of the rent = 225000 (1 + (.035) + (.035)(.035) + ........)

Then, we simplify the terms inside the first parentheses,


value of the rent = 225000 (1 + (.035))^x

where x is the number of years. We then substitute 8 to x to determine the value of the rent.

value of the rent = 225000 (1 + (.035))^8 = 296282.03

the system of equations graphed below has how many solutions?

Answers

parallel lines never intersect, therefore, they have no solutions.
The solution would be where the lines intersect

Answer:

answer is C. 0


Step-by-step explanation:


Write x2 - 12x + 8 = 0 in vertex form.

Answers

(x-4)^2-19=y
you first add the three to the other side, then add 16 on both sides, make the left side x-4 squared, and lastly you subtract 19 from both sides.
I have not learned this stuff yet, but by using online calculators, I can determine that the vertex form of your equation is:

n/a. It cannot be written in vertex form because it is not a conic section.

But if you are referring to x^2 - 12x + 8, the answer is: Y = (x - 6)² - 28 (i think)

How do you write 12 hundreds

Answers

12 hundreds is 12 • 100
which equals to
1200
hope this helped!! xx
100 *12
Because it is 12 100s

If you have a $1 bill a 5 bill a 10 bill and a 20 bill how many different sums of money

Answers

You need to find every combinaison of bills.

ex : $1 + 10$   or   5$+10$

I takes for ever to list all the possibilities so you need to think about probabilities to chose a bill.

For each bill, you can add it to your sum or not; so it gives you 2 possibilities; you do that for each bill and you multipliate each what gives you :

2 * 2 * 2 * 2 = 16 different sums


Solve for h: a = 1/2bh

h = A over 2b
h = A/b (1 /2)
h = 2Ab
h = 2A/b

Answers

The answer is: [tex]A=(1/2)bh 2A=2(1/2)bh 2A=bh (2A)/b=(bh)/b h=2A/b [/tex]

Assume that all chickens have 4725 feathers. if it takes you 5.6 seconds to pluck 24.8 feathers, how many hours would it take you to defeather 7728 chickens? answer in units of hours.

Answers

This question needs to be solved in steps rather than all at once. That being said, will start by find "feathers per second" or f/s.

So it takes 5.6 seconds to plucks 24.8 feathers. To find f/s we needs to find 24.8 divided by 5.6 which is 4.429f/s.

Now we need to find how long it will take to pluck one entire chicken. Since it takes us one second to pluck 4.429 feathers, we need to divide 4,725 by 4.429 to find how many seconds it will take us to pluck an entire chicken. This value is 1,066.832 seconds.

Since it takes us 1,066.832 seconds to pluck one chicken, it will take us
7,728 • 1,066.832 seconds to pluck 7,728 chickens. This value is 8,244,477.696 seconds.

To convert seconds to hours, we need to divide by 60 to get minutes and then divide by 60 again to reach our desired unit of measurement: hours

8,244,477.696 / 60 / 60 = 2,290.133 hours
Final answer:

It would take approximately 2284.722 hours to defeather 7728 chickens.

Explanation:

To find out how many hours it would take to defeather 7728 chickens, we need to consider the time it takes to pluck a certain number of feathers. We are given that it takes 5.6 seconds to pluck 24.8 feathers. First, we find the time it takes to pluck one feather by dividing the time by the number of feathers: 5.6 seconds ÷ 24.8 feathers = 0.2258 seconds per feather.

Next, we find the total number of feathers on 7728 chickens by multiplying the feather count per chicken by the total number of chickens: 4725 feathers/chicken × 7728 chickens = 36,396,000 feathers.

Finally, we find the total time it would take to defeather all the chickens by multiplying the time per feather by the total number of feathers: 0.2258 seconds/feather × 36,396,000 feathers = 8,224,996.8 seconds. Converting this to hours, we divide by the number of seconds in an hour: 8,224,996.8 seconds ÷ 3600 seconds/hour ≈ 2284.722 hours.

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Suppose your walking rate is 4 feet per second. write that in miles per hour

Answers

4 ft/sec X 3600 sec/hour = 14400 ft/hour

14400 ft/hour / 5280 ft/mile = 2.727 miles/hour

Choose the linear inequality that describes the graph. The gray area represents the shaded region

Answers

(0,3)(1,-2)
slope = (-2-3) / (1 - 0) = -5

y int is (0,3)

line is dashed, means no equal sign....shading above the line, means greater then

ur inequality is : y > -5x + 3


Answer:

y > -5x + 3

Step-by-step explanation:

Two exterior angles of a triangle equal 100° and 150°. Find all the interior angles

Answers

180°-100°= 80° (angle 1)
180°-150°= 30° (angle 2)

180°-80°-30°= angle 3
angle 3 = 70°

∴ the interior angles are 80°, 30° and 70°

The angles of the triangle will be 70°, 30°, and 80°.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

We know that the sum of the interior and the exterior angles is 180 degrees.

Two exterior angles of a triangle equal 100° and 150°.

The interior angle corresponding to the exterior angle of 100° will be

⇒ 180° - 100°

⇒ 80°

The interior angle corresponding to the exterior angle of 100° will be 80°.

The interior angle corresponding to the exterior angle of 150° will be

⇒ 180° - 150°

⇒ 30°

The interior angle corresponding to the exterior angle of 150° will be 30°.

Then the third angle of the triangle will be

⇒ 180° - 80° - 30°

⇒ 70°

The angles of the triangle will be 70°, 30°, and 80°.

More about the triangle link is given below.

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What is the area of triangle PQR?

Answers

area = 1/2 bh = 1/2(86)(52) = 2236
answer
2236 square inches

Answer:

B. 2236square inches

Step-by-step explanation:

Formula for calculating the area of a triangle = 1/2 × base × height.

According to the triangle,

Base = QR = 86inches

Height = 52inches

Area of ∆PQR = 1/2 × 86 × 52

Area of ∆PQR = 43 × 52

Area of ∆PQR = 2236square inches

A barge that is used to transport bulk items is the shape of a rectangular prism and is 90 feet long, 35 feet wide, and 12 feet deep. If the barge can only be filled to a height of 75% of its depth, what volume of bulk items can the barge hold? ft3

Answers

Barge volume = 90 * 35 * 12 = 37 800 ft³

75% = 75/100 = 0.75

37 800 * 0.75 = 28 350 ft³ (barge can hold).

Final answer:

The barge can hold 28,350 cubic feet of bulk items when filled to 75% of its depth, calculated by using the volume formula for a rectangular prism.

Explanation:

To calculate the volume of bulk items the barge can hold, we first determine the maximum height to which it can be filled. This is 75% of the barge's depth. Therefore, the fill height is 75% of 12 feet, which equals:

0.75 × 12 ft = 9 ft.

The volume V that the barge can hold is given by the formula for the volume of a rectangular prism:

V = length × width × height

Substituting the given dimensions and the fill height into the formula, we get:

V = 90 ft × 35 ft × 9 ft = 28,350 ft³.

So, the barge can hold 28,350 cubic feet of bulk items when filled to 75% of its depth.

Find the degree of the polynomial and indicate whether the polynomial is a monomial binomial trinomial or none of these 10x4-3w3+7w+5y5-4

Answers

Degree: Highest exponent in your polynomial expression.
Therefore; degree =5
The polynomial has five "terms", therefore, is none of the above
Final answer:

The given polynomial 10x^4-3w^3+7w+5y^5-4 has a degree of 5 as the highest power of variable is 5. Also, it has five terms, hence it is neither a monomial, binomial nor trinomial.

Explanation:

The polynomial in question is 10x4-3w3+7w+5y5-4. The degree of a polynomial is determined by the highest power of the variable in the polynomial. Here, the highest powers are 4 (from 10x4) and 5 (from 5y5). Since 5 is larger than 4, the degree of the polynomial is 5.

Furthermore, the given polynomial has five terms, so it is not a monomial, binomial or trinomial. These terms refer to polynomials with one, two, or three terms respectively. Therefore, the given polynomial does not fall under any of these categories.

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What is the perimeter of the nonagon below?

Answers

The correct answer is D. 94 units. You can find this answer by simply adding all of the values around the nonagon because the perimeter is the total distance around something.

Answer:

Step-by-step explanation:

Alright, lets get started.

The sides of nonagon are given as below :

13

8

5

11

10

9

10

7

21

So, the perimeter will be addition of these sides.

Hence he perimeter is = [tex]13+8+5+11+10+9+10+7+21 = 94[/tex]

Hence the perimeter is 94 units (D)   :  Answer

Hope it will help :)

Which number produces irrational number when added to 0.5

Answers

square root of 3 and Pi

Answer with explanation:

The  number in which we have to add  a number to give irrational = 0.5

    [tex]0.5=\frac{5}{10}\\\\=\frac{1}{2}[/tex]

is a Rational Number as the decimal expansion terminates or denominator contains the number in the form of [tex]2^n \text{or} 5^m \text{or} 2^n \times 5^m[/tex].

→Sum of two Rationals Can't be a Irrational Number.

→Sum of Rational And Irrational is Irrational.

So, if you add any Irrational number like √2,π,∛2 to , 0.5  , it will give an Irrational Number.

⇒0.5 +Irrational Number=Irrational Number

Algebraic expression for 5 times a number

Answers

it could be 5x, 5 being the digit, x being "a number"

Final answer:

The algebraic expression for 5 times a number is 5x.

Explanation:

The algebraic expression for 5 times a number is 5x.

The variable x represents the unknown number.

When you multiply 5 by any number, you can represent it as 5 times that number.

So, if the number is 10, the expression would be 5 times 10, which is equal to 50.

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