MATHEMATICS HIGH SCHOOL

Which expression is a difference of cubes?
X^6-6
X^6-8
x^8-6
X^8-8

Answers

Answer 1

Answer:

Answer: The correct expression is, $x^6-8$

Step-by-step explanation:

$x^6$ is represented in cube form as, $(x^2)^3$

'8' is represented in cube form as, $2^3$

$x^8$ and '6' will not show cube form of integer power.

The expanded form of the given expression, $x^6-8$ is represented as,

$x^6-8=(x^2)^3-2^3$

This expression will showing the difference of cubes.

And the other options, $x^6-6,x^8-6,x^8-8$ will not show the difference of cubes.

Therefore, the correct answer is, $x^6-8$

Answer 2

Answer:

The expression $\boxed{{x^6} - 8}$ is a difference of cubes. Option (b) is correct.

Further Explanation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

Given:

The options are as follows,

(a). ${x^6} - 6$

(b). ${x^6} - 8$

(c). ${x^8} - 6$

(d). ${x^8} - 8$

Calculation:

8 is a cube of 2 and can be written as follows,

$8 = {2^3}$

${x^6}$ can be written as a cube of ${x^2}.$

${x^6} = {\left( {{x^2}} \right)^3}$

Use the identity ${a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)$ in above expression.

$\begin{aligned}{x^6} - 8&= {\left( {{x^2}} \right)^3}- {\left( 2 \right)^3} \n&= \left( {{x^2} - 2} \right)\left( {{x^4} + 2{x^2} + 4} \right)\n\end{aligned}$

The expression $\boxed{{x^6} - 8}$ is a difference of cubes. Option (b) is correct.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, $x^12y^18+1$ , exponents, power, equation, power rule, exponent rule.

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During the year, FastDry Corporation has $ 340,000 in revenues, $ 155,000 in expenses, and $ 12,000 in dividend declarations and payments. Net income for the year was:

Answers

Answer:

$185,000

Step-by-step explanation:

We have been been given that during the year, Fast Dry Corporation has $ 340,000 in revenues, $ 155,000 in expenses, and $ 12,000 in dividend declarations and payments.

We will use following formula to solve our given problem.

$\text{Net income}=\text{Revenues}-\text{Expenses}$

$\text{Net income}=\$340,000-\$155,000$

$\text{Net income}=\$185,000$

Therefore, the net income for the year was $185,000.

permutations 2.4 statistics answers A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra large. If it has 2 small, 3 medium, 6 large, and 2 extra large in stock, in how many orders can it sell all the shirts?

Answers

Answer: 360,360

Step-by-step explanation:

The number of permutations of n things of which a are identical, b are identical and so on... :-

$(n!)/(a!\ b!....)$

Given : A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra large.

If it has 2 small, 3 medium, 6 large, and 2 extra large in stock, then total shirts : $2+3+6+2=13$

Then, the number of orders in which the store can sell all the t-shirts will be :_

$(13!)/(2!3!6!2!)\n\n=(13*12*11*10*9*8*7*6!)/(2*3*2*6!*2)\n\n=360360$

Hence, the number of orders in which the store can sell all the t-shirts = 360,360

Emily wants to make a regtangular model with a height of one connecting cube. she wants to make the model in exactly 2 different ways. how many connecting cubes could Emily use to make the model in only 2 ways. A6, B12, C16, D18

Answers

A 6, because it can be 6x1x1 or 3x2x1

How to graph y=-4|x+2|-5

Answers

$y= -4|x+2| -5 \n \nx= -6 \Rightarrow y=-4|-6+2|- 5= -4|-4|- 5= -4*4 -5 =\n \n=-16-5=-21\n \n \nx= -4\Rightarrow y=-4|-4+2|- 5= -4|-2|- 5= -4*2 -5 =\n \n =-8-5=-13\n \n \nx= -2 \Rightarrow y=-4|-2+2|- 5= -4|0|- 5= -4*0 -5 =-5\n \n \nx= 0 \Rightarrow y=-4|0+2|- 5= -4|2|- 5= -4*2 -5 =-8-5=-13\n \n \nx= 2 \Rightarrow y=-4|2+2|- 5= -4| 4|- 5= -4*4 -5 =-16-5=-21$