simplify (a+b)^3 + (a-b)^3 + 6a(a^2-b^2)

Answer:

32x^3 + 4x^2  + 41x - 35

Step-by-step explanation:

Multiply each of the terms in bracket 1 with those in bracket 2.

4x^2 x 8x = 32x^3

4x^2 x -5 = -20x^2

3x x 8x = 24x^2

3x x -5 = - 15x

7 x 8x = 56x

7 x -5 = -35

Now, put them together and simplify:

32x^3 - 20x^2 + 24x^2 - 15x + 56x - 35

After simplifying:

32x^3 + 4x^2  + 41x - 35

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Answer: x < 2

Explanation: To solve for x in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.

Since 3 is being subtracted from x, we add 3

to both sides of the inequality to get x < 2.

Before we graph, write your answer in set notation.

We can write this as {x: x < 2}.

It's important to understand what this means.

This means that any number less than 2 is a solution to this inequality.

I have graphed the inequality for you below.

Start with an open dot on +2.

We use an open dot because +2 is not included as a solution.

Then draw an arrow going to the left.

Answer:

53

Step-by-step explanation:

Answer:

(540 - π60 cm²) or 350cm³(351.5)

Step-by-step explanation:

You'll have to subtract the volume of the rectangular prism with the cylinder.

We know that the prism's volume is V = s*s*h = 6*6*16 = 540 cm²

We also know the cylinder's volume: V = πr²h = π(4/2)²*15 = π*4*15 = π*60

Now the only step remaining is to subtract the volume of the prism with the cylinder: 540 - π*60 cm³

540 - π*60 cm³ is the full answer

350 is the approximate answer (rounded it down from 351.5 to 350cm³)

 Recursive formula of an arithmetic sequence is given by the expression,

                          [tex]T_n=a+(n-1)d[/tex]

                 Where, [tex]T_n=[/tex] nth term

                              [tex]a=[/tex] First term of the sequence

                              [tex]n=[/tex] Number of term

                              [tex]d=[/tex] Common difference

Therefore, number of sticks in the 6th pattern are 32.

                   And number of sticks in the nth pattern are [tex]T_n=5n+2[/tex]

From the picture attached,

Number of sticks in 1st pattern = 7

Number of sticks in 2nd pattern = 12

Number of sticks in 3rd pattern = 17

Sequence formed is 7, 12, 17..... nth term

This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.

Therefore, nth term of the sequence will be,

       [tex]T_n=a+(n-1)d[/tex]

       [tex]T_n=7+(n-1)5[/tex]

       [tex]T_n=5n+2[/tex]

If [tex]n=6,[/tex]

       [tex]T_n=7+(6-1)5[/tex]

       [tex]T_n=7+25[/tex]

       [tex]T_n=32[/tex]

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Answer:

Measure of angle DBF = 106°.

Step-by-step explanation:

Given in the question,

m∠DGE = 53°

and line segment GE is the angle bisector of ∠DGF.

Since segment GE is the angle bisector of ∠DGF that means it divides the angle DGF into two equal parts.

Therefore, m∠DGE ≅ m∠FGE

m∠DBF = m∠DGE + m∠FGE

m∠DBF = 2(m∠DGE)

             = 2(53)°

             = 106°

Therefore, measure of angle DBF = 106°.

Ay is any one down to work together on this? Not just this question but the whole unit of geometry

Answer:

exponential growth

Step-by-step explanation:

f(x)  = 2  * 2^x

This is in the form

y = a * b^x  where a is the initial value and b is the growth rate or decay rate

b > 1 so it is growth

This is  the exponential form

y = mx+b is the linear form

Answer:

Step-by-step explanation:

6--6 = 12

4-1 = 3

12/3 = 4

y=4x

-6-4 = -10

y=4x-10

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through (1, -6) and (4, 6).

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

Now,

(1, -6) = (a, b) and (4, 6) = (c, d)

Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4

m = 4

The equation of a line is given as y = mx + c.

(1, -6) = (x, y)

-6 = 4 x 1 + c

-6 = 4 + c

-6 - 4 = c

c = -10

Now,

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

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Answer:

" Expected Payoff " ⇒ $ 1.80 ; Type in 1.80

Step-by-step explanation:

Take the probability of winning into consideration;

[tex]Total Number of Tickets - 500,\\Tickets 1 Person Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 500,\\Money Won - 900 Dollars,\\\\Proportionality - 1 / 500 = x / 900 - where, x = " Expected Payoff "\\1 / 500 = x / 900 - CrossMultiplication,\\\\500 * x = 900,\\x = 900 / 500,\\x = 1.80 Dollars Won!\\\\Conclusion ; x = 1.80 Dollars[/tex]

Solution ; " Expected Payoff " ⇒ $ 1.80

Answer: 39

Step-by-step explanation:

Its easy! The triangles CEF and CDE are equals because they have three sides respectively equal. So the angles FCE and angle m1 (DCE) are equal.

Then:

m1 = 39

Step-by-step explanation:

Before we find the ninth term, we need to find the common ratio. The common ratio in a geometric sequence is the number that every number after the first one is multiplied by. For example, in the sequence {2, 4, 8, 16, 32, ...}, the common ratio is 2.

Now, for our example, the numbers in the sequence alternate between negative and positive numbers. What does that tell us about the common ratio? Well, the common ratio has to be negative because the negative sign keeps alternating.

So we know the common ratio is negative. But what about the rest of the number? Well, we can see that the ratio has a 1 in the numerator because the numerator is the same throughout the sequence (aside from the alternating negative sign).

Now that we've narrowed down the possibilities to -1/x, let's figure out the denominator of the common ratio. The denominator changes from 3 to 9 to 27 to 81. Do you see a pattern there? Each denominator is 3 times the value of the previous denominator. The denominator of the common ratio, then, must be 3.

Ok. We have our common ratio, -1/3, but the question we still need to find the 9th term in the sequence. Well, we can write out the pattern until we get to the term we want. But what if you were trying to find the one hundredth or the one thousandth term? That would take a very long time to write out. Instead, we can take the first number in the sequence (1/3) and multiply it by the our common factor to the power of the remaining terms. As a formula, this looks like: [tex]a_{1} *f^{n-1} = a_{n}[/tex], where a is your first term, f is your common factor and n is the number of the term you are trying to find.

So, finally, we can solve the problem.

1/3 * (-1/3)⁸ = a₉

1/3 * 1/6561 = 1/19683

So the value of the ninth term of the given geometric sequence is 1/19683.

I hope you learned something and it wasn't too difficult to understand.

Answer:

^^ what he said xD

Step-by-step explanation:

It was snowing again and I smiled as I stared at the white flakes fluttering by my window. It was (capitalized the C)Christmas, and my day had been one of the best all year. First I (had removed) awakened in the morning to the sound of my brother (added the n to runing)running madly around the house, yelling that it was Christmas. Jumping out of bed, (capitalized the i that was there)I skipped happily down the stairs, with my brother at my heels, and made my way to the Christmas tree in the living room. My parents(apostrophe removed from between the t and s) groggily walked down the stairs to watch us open (up removed) our presents. My Mom sat down on the couch and dad plopped himself on the floor, grumbling something about coffee. I started opening my presents because, after all, its ladies first. Ripping open the wrapping paper, I stared down at my brand(removed dash)new pink boom box. It was beautiful!(question mark changed to exclamation) (capitalized e)Even more, it came with little, stick-on jewels to decorate the boom box. Mom and Dad finally got their coffee and we all took turns watching each other open presents. I got(get turned to got) many more presents that were absolutely amazing. (changed every one into one word)Everyone spends the rest of the day admiring their gifts and playing with their new toys. "I will remember this Christmas forever,"(added endnote) I thought. (capitalized s)Sighing contentedly, I finally turned away from the snow (removed the e from what was danceing)dancing outside the window and rejoined my family.

Answer:

1

Step-by-step explanation:

Answer:

1,1.5,2.5

Step-by-step explanation:

f(x) = 3 - .5x

The domain is 1,3,4 so theses are the only inputs

f(1) = 3 - .5 = 2.5

f(3) = 3 - .5(3) = 3- 1.5 = 1.5

f(4) = 3 - .5(4) = 3-2 =1

The only outputs are 1,1.5,2.5

Answer:

-5+(-6 )= -11 so you would pinpoint -11 on the number line

Step-by-step explanation:

Answer:

1 : 80

Step-by-step explanation:

So you want to check Length of model : Length of real boat

50 cm : 40 m

But since the units don't match, make 40 m into 4000 cm

50 cm : 4000 cm

Divide both sides by 50 and you get

1 : 80

Answer:

WE need the numbers

Step-by-step explanation:

a

Answer:

a)3

b)3

c)?

Step-by-step explanation:

Answer:

[tex]=24a^2[/tex]

Step-by-step explanation:

[tex]4a\cdot \:6a=24a^2\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:6=24\\=24aa\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\aa=\:a^{1+1}\\=24a^{1+1}\\=24a^2[/tex]

Answer:

Simply multiply across.

since they both have the same base(a),add the powers ie.(1+1)=2.

Hence 4a×6a=24a²

Answer:

5 ( r+8) (r-6)

Step-by-step explanation:

5r^2+10r-240

First factor out the greatest common factor

5( r^2 +2r - 48)

Now factor what is inside the parentheses

What multiplies to -48 and adds to 2

8*-6 = -48

8-6 = 2

5 ( r+8) (r-6)

Answer:

x=±8

Step-by-step explanation:

You add 11 on both sides

x^2=53+11

x^2 = 64 so

x=8 or x=-8

Answer:

8

Step-by-step explanation:

8 times 8 = 64

Answer:

Candle B: 36 minutes

Candle C: 12 minutes

Step-by-step explanation:

Since Candle A burns for 72, and Candle B burns twice as fast, we can divide the 72 by 2 in order to get the time it burns. We will then see that Candle B burns for 36 minutes.

Candle C burns 3 times as fast as candle B so we can divide the 36 minutes it takes for candle B to burn by 3 to get how long it takes Candle C to burn. We then see that it takes 12 minutes for candle C to burn.

Hope this helps!

Answer:

No it's not a function. (-2, 0) and (-2, 6) don't pass the vertical line test.

Step-by-step explanation:

The right answer is of option C.

hope it helps..

good luck on your assignment

Answer:

c

Step-by-step explanation:

Answer:

[tex]78.54:314.16[/tex]

Step-by-step explanation:

First circle area with diameter 10 inches =

[tex]\pi r^2[/tex]

[tex]\pi \times 5^2[/tex]

[tex]=78.53981[/tex]

Second circle area with diameter 20 inches =

[tex]\pi r^2[/tex]

[tex]\pi \times 10^2[/tex]

[tex]=314.159265[/tex]

[tex]78.53981:314.159265[/tex]

Answer:

78.5 : 314.2

Step-by-step explanation:

Diameter of the first Circle = 10 inches

Diameter of the second Circle = 2(10) [TWICE] = 20 inches

So,

Area of the first circle:

Radius = 5 inches

Area = πr²

A = (3.14)(5)²

A = 78.5 inches²

Area of the second circle:

Radius = 10 inches

Area = πr²

Area = (3.14)(10)²

Area = 314. 2 inches

Now the ratio of the area of smaller circle to the larger circle is

78.5 : 314.2

Answer:

See explanation

Step-by-step explanation:

Line A

gradient = 4

x-intercept = -1

y-intercept = 4

Line B

gradient = -3

x-intercept = -1

y-intercept = -3

y + 8x = - 72

x-intercept = -9

y-intercept = -72

Answer:

[tex] \boxed{112} [/tex]

Step-by-step explanation:

[tex]Evaluate - 4v {c}^{2} \: where \: v= - 7 \: and \: c= - 2 : \\ = > - 4v {c}^{2} \\ = > - 4( - 7) {( - 2)}^{2} \\ \\ {( - 2)}^{2} = 4: \\ = > - 4( - 7)4 \\ \\ - 4( - 7) = 28: \\ = > 28 \times 4 = 112[/tex]

Answer:

A. 2x+6   is the correct answer

Answer:

8 weeks

Step-by-step explanation:

Answer:

-1/2

Because, for every one square, the line goes down by 1/2.

Answer:

- 0.5

Step-by-step explanation:

To find the gradient of a line,

divide the value of decrease by the value across.

So, count across from the extreme left toll the extreme right = 13

Where you completed in the extreme right, you have to count down till you reach the other end of the line = 6.5

Now, you divide: 6.5 divided by 13 = 0.5

Since we counted down, it is negative = -0.5

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