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dlinn [17]
2 years ago
6

A cereal box in the shape of a rectangular prism has a volume of 18x^3 - 3x^2 - 6x. What are three possible linear expressions f

or the dimensions of the cereal box?
Mathematics
1 answer:
Tatiana [17]2 years ago
3 0

From factoring, the volume of a rectangular prism can be written as:

3x * (2x+1) * (3x-2).

<h3>Factoring</h3>

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

The question gives: 18x³-3x²-6x. You can see that, initially, 3x is a common term. Therefore, you can write: 3x * (6x²-x-6) . Nonetheless, the question also asks 3 linear expressions, here only you have one (3x).

Thus, you should factor the expression (6x²-x-6) into two linear expressions: (2x+1)* ( 3x-2).

Thus, the volume of a rectangular prism can be written as:

3x * (2x+1) * (3x-2)

Learn more about the factoring here:

brainly.com/question/11579257

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BRAINLIEST!!PLEASE HELP ME
fredd [130]

Answer:

2. The y-intercept is 33 ft. The ball is 33 feet away from the wall.  

3. It will take the ball 11 seconds to touch the wall.  

4. The slope is -3 ft. The ball is rolling toward the wall at 3 ft per second

Step-by-step explanation:

Let x be the number of seconds.

We are told that a ball is rolling at a rate of 3 ft per second toward a wall that is 33 feet away.  

Since the ball is rolling towards wall at a rate of 3 ft per second. This means that remaining distance between wall and ball is decreasing 3 ft with each passing second. Hence, the slope of our line will be negative 3 ft.

As initially ball was 33 feet away from wall, so our y-intercept will be 33.

Upon substituting our values in slope-intercept form of equation we will get equation of our line representing remaining distance between ball and wall after x seconds as:  

y=-3x+33

Let us find the number of seconds that ball will take to touch the wall by finding the x-intercept of our line. Since x-intercept is the point when line crosses x-axis and at this point y equals 0. The x-Intercept of a line is obtained by putting the value of y as zero in the equation of a line.

0=-3x+33

0-33=-3x+33-33

-33=-3x

\frac{-33}{-3}=\frac{-3x}{-3}

11=x

Therefore, after 11 seconds ball will touch the wall.

Upon looking at our choices we can see that 2nd, 3rd and 4th options are correct choices.


8 0
3 years ago
I have a list of five numbers, where the first number is 1 and the fifth number is 5. Each of the other numbers is equal to one
prohojiy [21]

The sum of all five numbers in the list is 25.

According to the question,

The first number on my list of five numbers is 1, and the fifth is 5. The other figures are all one more than their two nearest neighbors' averages.

Let the list of numbers be 1,x,y,z,5.

As each of the other numbers is equal to one more than the average of its two neighbors.

x=(1+y)/2+1

2x=3+y   -(1)

Similarly,

y=(x+z)/2+1

2y=x+z+2   -(2)

z=(y+5)/2+1

2z=y+7    -(3)

Multiply equation (2) by 2 and then substitute equations (1) and (3),

4y=3+y+y+7+4

4y=2y+14

2y=14

y=14/2

y=7

From equation (1),

2x=3+7

2x=10

x=5

From equation (3),

2z=7+7

2z=14

z=14/2

z=7

The list is: 1,5,7,7,5

Sum of the numbers of list = 1+5+7+7+5 = 25

Learn more about sum here:

brainly.com/question/17695139

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4 0
2 years ago
Very very very URGENTTT!!!
MArishka [77]

Answer:

its d

Step-by-step explanation:

the arc length is equal to (radius x 2 x angles (60)) divided by 360 which comes to equal 8/3 then you multiply by pi

5 0
3 years ago
Chemists measure the acidity of an aqueous solution using pH. The pH is pH=-log-10[H^+] where pH is a measure of hydrogen ion co
jarptica [38.1K]

Answer:

11.26

Step-by-step explanation:

pH = - log(H+ concentration)

[H^+] = 5.5 * 10^(-12)

pH = - log(5.5*10^-12)

pH = - (-11.26)

pH = 11.26

7 0
3 years ago
Find the amount of sales tax and the total cost. Complete the table below.
Lana71 [14]

Answer:

Cost of item : $6

Tax rate : 5%

Amount of tax =  $0.3

Total cost = $6.30

Step-by-step explanation:

Cost of item : $6

Tax rate : 5%

Amount of tax = 5% * $6 = 0.05*6 = $0.3

Total cost = $6 + $0.30 = $6.30

5 0
3 years ago
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