6. Write the following cubes in expanded form:

(iii) (3a + 4b)³

8. Evaluate the following cubes using suitable Identities:

(ii) (999)³

Answers

Answer 1

Answer:

Step-by-step explanation:

we can use this algebraic identity:

[tex](a+b)^{3} =a^{3} +b^{3} +3ab(a+b)[/tex]

So,[tex](3a+4b)^{3} =(3a)^{3} +(4b)^{3}+3(3a)(4b)(3a+4b)[/tex]

=[tex](3a+4b)^{3} =27a^{3} +64b^{3} +36ab(3a+4b)[/tex]

=[tex](3a+4b)^{3} =27a^{3} +64b^{3} +108a^{2} b+144ab^{2}[/tex]

[tex](999)^{3}[/tex]=[tex](1000-1)^{3}[/tex]

Now, we can use the following identity:

[tex](a-b)^{3} =a^{3} -b^{3} -3ab(a-b)[/tex]

=[tex](1000-1)^{3} =1000^{3} -1^{3} -3(1000)(1)(1000-1)\\[/tex]

[tex](1000-1)^{3} =1,000,000,000-1-2,997,000[/tex]

[tex](1000-1)^{3} =997,002,999[/tex]


Related Questions

A student performed the following steps to find the solution to the equation
x2 - 2x - 8 = 0. Where did the student go wrong?
Step 1. Factor the polynomial into (x-4) and (x - 2)
Step 2. X-4 = 0 and x - 2 = 0
Step 3. x = 4 and x = 2
A. The student did not make any mistakes, the solution is correct
B. in Step 2
C. in Step 1
D. in Step 3


Answers

Answer:

step 1, c

Step-by-step explanation:

he was wrong in step 1.

when factoring out (x-4) and (x-2), you have to distribute x*x, x*-2, -4*x, and -4*-2

if you do it you get x^2 - 2x -4x + 8

the correct way to factor will be (x-4)(x+2)

when you factor out you will get the original equation you started with.

Your bedroom is 20 feet long by 12 feet wide. You are make a scale drawing of you bedroom with the scale 1⁄2 inch = 4 feet, what would the dimensions be?

Answers

Divide actual feet by scaled feet then multiply by scale inches:

20 feet / 4 = 5

5 x 1/2 = 2 1/2

12 feet / 4 = 3

3 x 1/2 = 1 1/2

Dimensions are 2 1/2 inches by 1 1/2 inches

Help me please i need the equation of axis of symmetry

Answers

Answer:

x = -2

Step-by-step explanation:

It's a vertical line at x = -2

Naomi and Stefan are selling pies for a school fundraiser. Customers can buy cherry pies and pumpkin pies. Naomi sold 11 cherry pies and 4 pumpkin pies for a total of
$208. Stefan sold 13 cherry pies and 12 pumpkin pies for a total of $384. Write the
system of equations that would allow you to determine the cost each of one cherry
pie (c) and one pumpkin pie (p)?

Answers

The answer is the first option

The cost of one cherry pie (c) is $12 and one pumpkin pie (p) is $19 and the equation system will calculate the cost of one cherry 11c + 4p = 208  and 13c + 12p = 384 .

What is the Linear equation?

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let the number of cherry pies be c,

And the number of pumpkin pies be p,

As per the given information, an equation system will calculate the cost of one cherry.

11c + 4p = 208    ...(i)

13c + 12p = 384  ...(ii)

Multiplying 12 by equation (i) and 4 by equation (ii), we get

132c + 48p = 2496 …(iii)

52c + 48p = 1536 …(iv)

Equation (iii) subtracts from (iv) and we get c = 12 then substitute the value of 'c’ into equation (i) and we get

11(12) + 4p = 208

4p = 208 - 132

4p = 76

p = 19

Thus, the cost of one cherry pie (c) is $12 and one pumpkin pie (p) is $19

Learn more about the Linear equations here:

https://brainly.com/question/13738061

#SPJ2

Apply the distributive property:
-3(x+2) =

Answers

Answer:

-3x-6

Step-by-step explanation:

you multiply x by -3 getting -3x then you multiply -3 by positve 2 getting -6

Hello skm413002!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

Apply the distributive property:

-3(x+2) =

[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]

By applying the distributive property, we can solve it as....

[tex] \sf \: - 3(x + 2) \\ = \sf \: (- 3 \times x) -( 3 \times 2) \\ = \large \boxed{\boxed{ \bf - 3x - 6}}[/tex]

Method :-Distributive property.

Steps :-Multiply -3 with x & 2.Add the 2 products.You'll get the answer as -3x - 6.

__________________

Hope it'll help you!

ℓu¢αzz ッ

Use synthetic division to find the result when 4x^3+3x^2– 8x – 7 is divided by x+1.

Answers

Answers:

4x^2 - x - 7

Simplify the radical please I need sleep it's 1 am I wake up at 4

Answers

Answer:

[tex]4cba*\sqrt{5bc}[/tex]

Step-by-step explanation:

[tex]\sqrt{4^{2} *5a^{2}b^{2}bc^{2} c }[/tex]

[tex]4cba*\sqrt{5bc}[/tex]

Someone pls help me I will make you brain

Answers

Answer: -75

Step-by-step explanation:Because basically the slope is how much money is going down in the loan so 850 minus 75 is 775 so -75 is the answer

-75 is the correct answer i hope i helped you out so i hope i can get brainlist :)

true or false Typically, a plot begins with conclusions that introduce the characters and the conflict they face.

Answers

Answer:

Hello!!

The correct answer is false. The exposition begins with conclusions that introduce the characters and the conflict they face

Hope this helps!!

HELPOOPPP AND IF YOU DONT GET IT RIGHT I REPORT

Answers

Answer:

(-4,2)

Step-by-step explanation:

Answer:

(-4,2)

Step-by-step explanation:

hope this helps

what integer is equivelent to 25 3/2

Answers

Answer:

27

Step-by-step explanation:

HELP ASAP PLEASE

If the bowling fans get their way, and the group plays only 1 game of laser tag, will they have
enough money to bowl 5 games? Use your expression from question 3 to calculate the cost of 1
game of laser tag and 5 games of bowling. (3 points: 1 point for the answer, 1 point for showing
your work, and 1 point for answering the question

Answers

x+yz : is the answer to your question.

What is the value of x that makes this equation true?
(10 raised to the power of 4) = 10 raised to the power of x

Enter only a number as your answer.

Answers

Answer:

pot0tsafgxxgcgcycguchchcui

if i had 475 cannolis ans a box can only carry 15 how many boxes will i need.​

Answers

Answer:

you would need 32 boxes

Step-by-step explanation:

475/15 = 31.666

32 boxes

475/15=31.7 but you can't get 0.7 boxes so you would need 32 to carry all of the cannolis.

does anyone know how to do this​

Answers

Answer:

(2,2)

Step-by-step explanation:

To draw a graph you find the y value for a couple of x values. For a linear equation like the one given, two points are enough because the graph is always a straight line.

First graph

First, convert the equation into the y=... form:

x - y = 0 => y = x

No choose two x values at random, e.g., 0 and 5:

for x=0, you find y=0, so (0,0) is a point on  the graph

for x=5, you find y=5, so (5,5) is a point on the graph

Now plot these two points and draw a line through them.

Second graph

First, convert the equation into the y=... form:

x + y = 4 => y = 4 - x

No choose two x values at random, e.g., 0 and 5:

for x=0, you find y=4, so (0,4) is a point on  the graph

for x=5, you find y=-1, so (5,-1) is a point on the graph

Now plot these two points and draw a line through them.

Plz help will give brainliest
Simplify square root of five times the quantity six minus four square root of three.

Group of answer choices

9

thirty square root of three

six square root of five minus four square root of fifteen

square root of thirty minus twenty square root of three

Answers

Answer:

C

Step-by-step explanation:

Answer:

6√5-4√15

Step-by-step explanation:

√5(6-4√3)

6√5-4√3*√5 division property

6√5-4√3*5 combining like terms

6√5-4√15

Solve for x 3/8(2x+16)−2=13

The "/" is for a fraction btw

Answers

X= -623/96


I hope this helped

The sixth-grade classes have 28, 20, 30, and 25 students. What is the mean number of students in a class?

Answers

Answer:

25.75

Step-by-step explanation:

mean=sum of all numbers/number of numbers given

we have 4 numbers given 28,20,30 and 25

mean=28+20+30+25/4

mean=103/4

mean=25.75 :)

Which of the following functions represents an absolute value function?
y = |x - 21
O y = x-2
y = x

Answers

y = |x - 21| represents an absolute value function.

The radius of a smaller circle is half the length of the radius of a larger circle. The area of the larger circle is 20 square inches. What is the approximate area of the smaller circle?

Answers

Answer:

4

Step-by-step explanation:

The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The waiting times are shown below.
2
3
7
21
19
8
S
12
6
5
7
2
Find the mean waiting time. Round your answer to one decimal place.
8.0 min
7.2 min
7.5 min
6.8 min

Answers

The answer is 6.8 minutes


[tex]The \: value \: of \: \sqrt{6 + \sqrt{6 + \sqrt{6} + .......... \: to \: \infin } } \: is \: \underline{ \: \: \: \: \: \: \: \: \: \: \: .}[/tex]
CORRECT EXPLANATION WILL BE MARK AS BRAINLIEST.​

Answers

[tex]\large\underline{\sf{Solution-}}[/tex]

Let us assume that:

[tex] \sf \longmapsto x = \sqrt{6 + \sqrt{6 + \sqrt{6 + ... \infty } } } [/tex]

We can also write it as:

[tex] \sf \longmapsto x = \sqrt{6 + x } [/tex]

Squaring both sides, we get:

[tex] \sf \longmapsto {x}^{2} =6 + x[/tex]

[tex] \sf \longmapsto {x}^{2} - x - 6 =0[/tex]

By splitting the middle term:

[tex] \sf \longmapsto {x}^{2} - 3x + 2x - 6 =0[/tex]

[tex] \sf \longmapsto x(x - 3) + 2(x - 3 ) =0[/tex]

[tex] \sf \longmapsto (x+ 2)(x - 3 ) =0[/tex]

Therefore:

[tex] \longmapsto\begin{cases} \sf (x+ 2) =0 \\ \sf (x - 3) = 0 \end{cases}[/tex]

[tex] \sf \longmapsto x = - 2,3[/tex]

But x cannot be negative.

[tex] \sf \longmapsto x = 3[/tex]

Therefore, the value of the expression is 3.

[tex]\large\underline{\sf{Verification-}}[/tex]

Given:

[tex]\sf\longmapsto x=3[/tex]

We can also write it as:

[tex]\sf\longmapsto x = \sqrt{9}[/tex]

[tex]\sf\longmapsto x = \sqrt{6+3}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{9}}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+3}}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{9}}}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+3}}}[/tex]

This pattern will continue.

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+...\infty}}}[/tex]

60% of all bald eagles survived their first flight. If 25 randomly selected bald eagles are observed, what is the probability that at least 15 of them will survive their first flight.

a) Use the binomial distribution to approximate the probability.

Answers

Answer:

[tex]100%[/tex][tex]\%[/tex]

Problem:
−(−8y−6.6z−10)
Please help me if possible!

Answers

your answer should be -8y + 6.6z + 10

if you take 3 apples from 10 apples how many apples do you have

Answers

Answer:

still 10 even tho you took 3

Step-by-step explanation:

PLEASE ANSWER ASAPEnter the equation of the line in slope-intercept form. Slope is − 2 3 , and (−6, −5) is on the line. The equation of the line is y =

Answers

Step-by-step explanation:

there seems to be something missing.

I assume the slope of the line is -2/3.

the slope of a line is always the factor of x in the equation.

the slope is the y/x ratio indicating how many units y changes, when x changes by a certain amount of units (e.g. when going from one point on the line to another).

the equation for the line looks like this then :

y = (-2/3)×x + b

to get b we use the provided point (-6, -5) and it's x and y values.

-5 = (-2/3)×-6 + b = 4 + b

b = -9

so, the full equation of the line is

y = (-2/3)×x - 9



The black line is the graph of y = x. Which of these
equations could represent the blue line?

Answers

Answer:

A

Step-by-step explanation:

Answer:

The answer is (y=1/2x )

Please show all steps to 2- (-1)

Answers

Answer:

3

Step-by-step explanation:

2-(-1)=2+1=3

Is it possible to list all the fractions between 2 and 3? Explain.

Answers

Answer: No

Step-by-step explanation:

There are infinitely many numbers. Numbers so big that they are beyond our comprehnsion. Numbers can also be infinitly small. A fraction is something less than a whole. So the answer is no you can't list them all.

Solve for X then find the measure of

Answers

Answer:

x=11

m<a=80º

m<b=80º

Step-by-step explanation:

They are congruent so

8x-8=5x+25

8x=5x+33

3x=33

x=11

Answer:

Step-by-step explanation:

8x-8=5x+25

8x+5x=25--8

13x=33

x=2.5

x=3cm

Other Questions
Who is the strongest Dragon Ball Character? Simplify the following:[tex]\sqrt{50} x^{2} y^{3}[/tex] If you were to rotate ABCD 180 about the origin, what would the coordinate of A' be?-5 -5 -3 -5 -5 -3 -3 3 To find out what kind of credentials if physician or surgeon must have which sections should the reader study What makes chewing gum acceptable in your country and unacceptable in Singapore? Qu'est-ce que tu achtes l'picerie?' You reply: * answer If Im in daep and got 30 days started oct 22 how long will it be till I get out minus all the weekends? discuss the separation of solid of different sizes How do I find all the angles? The area of a fenced in back yard can be 144 square feet. The owners are trying to decide on the dimensions of the back yard, and have decided they want the length to be 10 feet more than its width. What will the dimensions of the back yard be? Write 1 and 1/5 and 1 and 1/3 using a common denominator :) Find the area of the parallelogram. When it comes to credit scores, why is having athin file NOT good?What reasons might an 18-year-old have forhis/her thin file? Write an article on a local Festival in your village (Descriptive essay) 2Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.The numbers 7. 11, 12, 13, 14, 18, 21, 23, 27 and 29 are written on separate cards, and the cards are placed on a table with the numbers facingdown.The probability of picking a card with an even number is? Find the missing lengths of the sides. What is one meaningful change that a local police agency can make to improve the profession? How should they practically accomplish that change (be specific)? In what way can they measure whether this change really caused improvement? Why is making this one change so important? fill in the blank (Geometry B) a debit balance in the allowance for uncollectible accounts before year-end adjustment indicates that the company wrote off more bad debts in the current year than it had estimated. true or false? What connection does the author draw between thecrimes the juvenile offender committed leading up toher sister's murder and the murder itself?