Ask question

Ask question

All categories

1 year 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?

1 answer:

Tatiana [17]1 year 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

#SPJ1

You might be interested in

Factorise 2x^2 - 3x -2 < 0

Galina-37 [17]

Step 1: Factor $2 x^{2} - 3x -2$
1. <span> Multiply 2 by -2, which is -4.</span>
2. <span>Ask: Which two numbers add up to -3 and multiply to -4?
</span>3. <span>Answer: 1 and -4
</span>4. Rewrite $-3x$ as the sum of $x$ and $-4x$

$2 x^{2} +x-4x-2\ \textless \ 0$

Step 2: <span>Factor out common terms in the first two terms, then in the last two terms.

</span> $x(2x+1)-2(2x+1)\ \textless \ 0$
<span>
Step 3: </span>Factor out the common term $2x+1$

$(2x+1)(x-2)\ \textless \ 0$

Step 4: Solve for $x$

1. Ask: When will $(2x+1)(x-2)$ equal zero?
2. Answer: When $2x + 1 = 0$ or $x-2=0$
3. <span>Solve each of the 2 equations above:

</span> $x=- \frac{1}{2} ,2$
<span>
Step 5: </span>From the values of $x$ <span>above, we have these 3 intervals to test.
x = < -1/2
-1/2 < x < 2
x > 2

Step 6: P</span><span>ick a test point for each interval

</span>For the interval $x\ \textless \ - \frac{1}{2} 
$
Lets pick $x=-1.$ Then, $2(-1) ^{2} -3 * -1 -2 \ \textless \ 0$
After simplifying, we get $3\ \textless \ 0$ , Which is false.
Drop this interval.
<span>
For this interval $- \frac{1}{2} \ \textless \ x\ \textless \ 2$
Lets pick $x=0$ . Then, $2* 0^{2} - 3 * 0-2\ \textless \ 0$ . After simplifying, we get $-2\ \textless \ 0,$ which is true. Keep this <span>interval.

For the interval </span> $x\ \textgreater \ 2$

Lets pick $x = 3.$ Then, $2 * 3 ^{2} -3*3-2\ \textless \ 0.$ After simplifying, we get $7\ \textless \ 0$ , Which is false. Drop this interval.

.Step 7: Therefore,
$- \frac{1}{2} \ \textless \ x\ \textless \ 2$

Done! :)</span>

4 0

3 years ago

How do you get 1.8 from<img src="https://tex.z-dn.net/?f=f%282%29%3D%5Cfrac%7B2%7D%7B1%2Be%5E%7B-%282%29%7D%20%7D" id="TexFormul

Nataliya [291]

Answer:

see explanation

Step-by-step explanation:

$\frac{2}{1+e^{-2} }$ ← evaluate $e^{-2}$ using calculator

= $\frac{2}{1+0.135}$

= $\frac{2}{1.135}$

= 1.762.....

≈ 1.8 ( to 1 dec. place )

4 0

1 year ago

During an April rainstorm, it rained for six straight days. The amount of rainfall for each day was 0.8 inch, 2.15 inches, 2 inc

Andrei [34K]

Answer:

6.12 inches

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the gi

scoundrel [369]

The given equation is y + 2 = 4(x - 1)

The equation of the parallel line in the slope-intercept form is y = 4x - 7

Step-by-step explanation:

Parallel lines have

Same slopes
Different y-intercepts

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y + 2 = 4(x - 1)

- Change its form to slope-intercept form to find its slope

∵ y + 2 = 4(x) - 4(1)

∴ y + 2 = 4x - 4

- Subtract 2 from both sides

∴ y = 4x - 6

- Compare it with the slope-intercept form to find m

∵ the slope-intercept form is y = mx + b

∴ m = 4

∵ The parallel lines have same slopes

∴ The slope of the parallel line is 4

- Substitute it in the form of the equation

∴ The equation of the parallel line is y = 4x + b

- To find b substitute x and y in the equation by the

coordinates of a point on the line

∵ The parallel line passes through point (1 , -3)

∴ x = 1 and y = -3

∵ -3 = 4(1) + b

∴ -3 = 4 + b

- Subtract 4 from both sides

∴ -7 = b

∴ The equation of the parallel line is y = 4x + (-7)

∴ The equation of the parallel line is y = 4x - 7

The equation of the parallel line in the slope-intercept form is y = 4x - 7

Learn more:

You can learn more about the linear equations in brainly.com/question/4152194

#LearnwithBrainly

4 0

2 years ago

If the shop has 350 fish available for sale, how many of them are goldfish?

Lina20 [59]

Answer:

105

Step-by-step explanation:

multiply 350 by .30(30%) and that will tell you how many goldfish there are

3 0

2 years ago

Read 2 more answers