Use the binomial theorem to expand the binomial (x + -2y)8.
x8 + 8x6y + 28x7y2 + 56x5y4 + 70x5y4 + 56x3y7 + 28x2y +
8xy + y 8
x8 + 8x7y + 28x6y2 + 56xy3 + 70x4y4 + 56x3y5 + 28x2y6 +
8xy7 + y8
x8 + 16x7y + 112x6y2 + 448x5y3 + 1,120x4y4 +
1,792x3y5 + 1,792x2y6 + 1,024xy7+ 256y8
256x8 + 1,024x7y + 1,792x6y2 + 1,792x5y3 + 1,120x4y4 +
448x3y5 + 112x2y6 + 16xy7 + y8

Answer/Step-by-step explanation:

The scale factor = the ratio of the corresponding sides of the image and the preimage.

That is, A'B'/AB = B'C'/BC

The preimage is the smaller figure, given as ABCD.

AB = 3 - 1 = 2 units

BC = 4 - 1 = 3 units

The image is the larger figure, given as A'B'C'D'.

A'B' = 9 - 5 = 4 units

B'C' = 7 - 1 = 6 units

Scale factor = [tex] \frac{4}{2} = \frac{6}{3} = 2 [/tex]

Answer:

AC =5

BC =  12

AB = 13

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

(n-1)^2 + (2n)^2 = (n+7)^2

FOILing

n^2-2n+1  + 4n^2 = n^2+14n+49

Combine like terms

5n^2-2n+1   = n^2+14n+49

Bring everything to the left

5n^2-2n+1 -n^2-14n-49  = n^2+14n+49-n^2-14n-49

4n^2 -16n -48 = 0

Divide by 4

n^2 -4n -12 = 0

Factor

( n-6)(n+2) =0

Using the zero product property

n-6 =0  n+2 =0

n=6    n=-2

Since the length cannot be negative

n=6

AC = n-1 = 6-1 =5

BC = 2n = 2*6 = 12

AB = n+7 = 6+7 = 13

Given :

Hypotenuse of right angle triangle = n + 7

Base = n - 1

Altitude = 2n

Using Pythagoras theorem :

→ ( n + 7 )² = (n - 1)² + (2n)²

→ n² + 14n + 49 = n² - 2n + 1 + 4n²

→ n² + 14n + 49 = 5n² - 2n + 1 = 0

→ n² + 14n + 49 - 5n² + 2n - 1 = 0

→ -4n² + 16n + 48 = 0

→ -4(n² - 4n - 12) = 0

→ n² - 6n + 2n - 12 = 0

→ n(n - 6) + 2(n - 6) = 0

→ (n - 6)(n + 2) = 0

As n ≠ Negative

So, n ≠ -2

So, n = 6

Hypotenuse = n + 7 = 6 + 7 = 13

Base = n - 1 = 6 - 1 = 5

Altitude = 2n = 2 × 6 = 12

So,

AB = 13

AC = 5

BC = 12

Answer:

20x - 16

Step-by-step explanation:

We can first do 1/2 (36x - 14), getting 18x - 7.

Then our expression becomes 18x - 7 + 2x - 9.

We can combine like terms, getting 20x - 16.

Answer:

5-x=1+3x  the number is 1

Step-by-step explanation:

Answer:

v = 13w

Step-by-step explanation:

[tex]7w = \frac{1}{2} (w+v)\\\\7w =\frac{(w+v)}{2} \\\\Cross\:Multiply\\7w\times 2 =w+v\\\\14w = w+v\\\\Collect\:like\:terms\\14w-w =v\\\\v = 13w[/tex]

Answer:

Real numbers are mainly classified into rational and irrational numbers. Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.

There are 4 types of real numbers.

Rational Numbers

Irrational Number

Natural Numbers

Whole Numbers

Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers.

The set of real numbers, which is denoted by R, is the union of the set of rational numbers (Q) and the set of irrational numbers.

Rational Numbers; Any number specified in the form of a p/q or ratio fraction is called a rational number. The numerator is defined as p, and the denominator is represented as q, where q is not equal to zero. A rational number may be an integer, whole, and natural number.

For example: 0.67, 17, 214, etc.

Irrational Number; Irrational numbers are defined as the real number that cannot be represented as a simple fraction. In other words, it cannot be represented as a ratio, such as p/q, where p and q are integers, q≠0. It is the opposite of rational numbers.

For example; √5, √11, √21, etc.

Natural Numbers; An integer greater than 0 is a natural number. Natural numbers start at 1 and move to infinity.

For example; 1, 2, 3, 4, 5.

Whole Numbers; The whole number is the number system that contains all positive integers from 0 to infinity. The whole number is an integer of 0 or greater numbers.

For example: 1, 2, 3, 4, 5…..

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Answer:

26 hours + 6 minutes can also be said as 1560 min + 6 minutes

1560+6/6 = 1566/6 = 261

That is = 4 hours and 21 minutes

Answer:

2/3 can be classified as..

Step-by-step explanation:

It can be classified as a rational number because it can be in the form of p/q as of fraction and is made up of two integers making p the numerator and for q a denominator not involving a zero.

Answer:

real

rational

Step-by-step explanation:

Answers & Step-by-step explanation:

A square root is a number that when multiplied by itself, equals the number you were asked to square root. For example, 2 is the square root of 4, because 2 x 2 = 4.

There is a method in algebra to simplify square roots into smaller square roots, where one can be solved. To do this, we need to find a perfect square that can be multiplied with the other square root to equal the number you were asked to square root.

Now, let's solve your problems!

___________________________________________________________

[tex]\sqrt{56}[/tex] = [tex]\sqrt{2^{2} * 14[/tex]

Now, we pull out the [tex]2^{2}[/tex] from under the radical, since we can square root this. [tex]\sqrt{2^{2} }[/tex] is simply 2.

[tex]2\sqrt{14}[/tex]

Since we can't solve [tex]\sqrt{14}[/tex], this is the final answer that your assignment is wanting.

___________________________________________________________

[tex]\sqrt{84}[/tex] = [tex]\sqrt{2^{2} * 21[/tex]

Now, we pull out the [tex]2^{2}[/tex] from under the radical, since we can square root this. [tex]\sqrt{2^{2} }[/tex] is simply 2.

[tex]2\sqrt{21}[/tex]

Since we can't solve [tex]\sqrt{21}[/tex], this is the final answer.

___________________________________________________________

[tex]\sqrt{-9}[/tex] = [tex]\sqrt{-1 * 9}[/tex]

Now, since this the number is negative, we must separate the negative out. so [tex]\sqrt{-9}[/tex] becomes [tex]\sqrt{-1 * 9}[/tex]. Since the square root of 9 is 3, we can rewrite this as:

[tex]3\sqrt{-1}[/tex]

However, since [tex]\sqrt{-1}[/tex] is imaginary, we must replace it with i. This also allows us to get rid of the square roots.

The answer becomes:

3i

___________________________________________________________

[tex]3\sqrt{18}[/tex]

This one is already partly simplified. Notice how the 3 is not under the radical. The only thing we have to work with is the [tex]\sqrt{18}[/tex].

[tex]\sqrt{18}[/tex] = [tex]\sqrt{9 * 2}[/tex]

We can square root 9 to get 3.

[tex]3\sqrt{2}[/tex]

Now, we multiply back the 3 from earlier to get:

[tex]9\sqrt{2}[/tex]

___________________________________________________________

[tex]\sqrt{28a^{2}b^{3} }[/tex]

This one may look daunting because we have the variables, but we can break it down and solve it just as easily as the rest. The first step is to square root the a² term, the answer is a. We can rewrite this as:

[tex]a\sqrt{28b^{3} }[/tex]

Next, we need to simplify [tex]\sqrt{28}[/tex], just like we did with all the other problems.

[tex]\sqrt{28}[/tex] = [tex]\sqrt{4 * 7}[/tex]

Since [tex]\sqrt{4}[/tex] is 2, we can move it out of the radical.

[tex]\sqrt{28} = 2\sqrt{7}[/tex]

Since we can do anything with the [tex]b^{3}[/tex] term, that stays under the radical.

The answer is:

[tex]2a\sqrt{7b^{3} }[/tex]

___________________________________________________________

Answer:

and independent variable It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable. and a Just like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.

Answer:

13

Step-by-step explanation:

|3(5)-2|

|15-2|

|13|

13

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

In a square ABCD, if AB = (3x-8) and BC = (x+12), find the value of x. Also, find the length of each side of the square.

Note that all sides of a square are equal. Hence AB = BC for the square ABCD.

Given AB = (3x-8) and BC = (x+12), then AB = BC

3x-8 = x+12

collect like terms;

3x-x = 12+8

2x = 20

x = 20/2

x = 10

Substitute x = 10 into any of the side. Using side AB

AB = 3x-8

AB = 3(10)-8

AB = 30-8

AB = 22

BC = x+12

BC = 10+12

BC = 22

Hence x = 10 and the length of each side is 22

Answer:

I'm not sure but I believe it is "Three plus one-half times x."

Answer:

x + 6

Step-by-step explanation:

From the question given above, the following data were obtained:

Length of rectangle = 3x + 6

Width of rectangle = 4x – 1

Width of door =..?

A careful observation of the diagram shows that the door is located along the length of rectangular room.

In a rectangle, two sides are equal. Therefore,

x + door + x = 3x + 6

Making door subject of the above formula, we have:

x + door + x = 3x + 6

door + x + x = 3x + 6

door + 2x = 3x + 6

Subtract 2x from both side

door + 2x – 2x = 3x + 6 – 2x

door = 3x – 2x + 6

door = x + 6

Therefore, the width of the door is x + 6

Answer:

9abc(ac² - 3)

Step-by-step explanation:

Given polynomial:

Factors of the terms:

Common factors of the above:

So the answer:

Answer:

-6x-5y+2

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \frac{1}{9}}[/tex]

Step-by-step explanation:

[tex]\sf y=a(x-h)^2+k[/tex]

[tex]\sf Vertex = (h,k)[/tex]

y-value is 0 and the x value is 5

h = 2

k = -1

[tex]\sf 0=a(5-2)^2+-1[/tex]

Solve for [tex]\sf a[/tex] (the coefficient of the squared term).

[tex]\sf 0=a(3)^2+-1[/tex]

[tex]\sf 0=9a-1[/tex]

[tex]\sf 9a=1[/tex]

[tex]\displaystyle \sf a=\frac{1}{9}[/tex]

The coefficient of the squared term in the parabola equation is 1/9.

Answer:

Fot this parabola the coefficient for squared term is 7

Step-by-step explanation:

The formula for vertex equation is:

x = a*(y-h)^{2}+kx=a∗(y−h)

2

+k

if vertex is at (-3,-1) and in the formula the vertex is (k,h), we replace this values

x = a*(y +1)^{2} -3x=a∗(y+1)

2

−3

The other point of this parabola is (4,0), so we replace it in the formula below:

4 = a*(0 + 1)^{2} -34=a∗(0+1)

2

−3

4 = a*(1)-34=a∗(1)−3

4 +3= a*(1)4+3=a∗(1)

a=7a=7

Answer: -6/7

Step-by-step explanation:

3(5f+2)-f=2(-3)

  15f+6-f=-6 ⇔ distributive property

    14f+6=-6 ⇔ subtract f from 15f

        14f=-12 ⇔ subtraction property of equality (subtract 6 on both sides)

            f=-12/14 ⇔ division

            f=-6/7

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

14f =-12

Step-by-step explanation:

3×5f+ 3×2-f = 2×-3

15f - f + 6 = -6

14f= -6

Answer:

The answer is c

Step-by-step explanation:

You have to do everything backwards,

-9 divide it by 3 to get -3, then add seven to that answer

Answer:

C

Step-by-step explanation:

You can work backward to find out the answer!

Start with -9. Instead of multiplying by 3, you can divide.

-9/3 = -3

Now, instead of decreasing -3 by 7, increase by 7.

-3+7 = 4

You get 4, which is C!

Hope this helps!

Answer:

[See Below]

Step-by-step explanation:

C.

The solution to this is x ≤ 4.

So then we look at the graphs and choose the correct one.

When the sign is ≤ it's like an arrow whatever way it's pointing it goes that way. In this case it'd go the other way even though the sign is ≤, because the solution is stating 4 is greater then or equal to so it can't be less than 4. And the only option of +4 and higher is C.

Answer:

4  1/4

Step-by-step explanation:

10 1/3 = 33/3      33/3  divided by 4 = 33/12      so one quarter of your tank can hold 33/12

now just do 33/12 times 3 which is 33/4 or simplified 4  1/4

Say it is two o'clock, draw an imaginary line between the hour hand and twelve o'clock to create the north-south line. You know the sun rises in the east and sets in the west so this will tell you which way is north and which way south. If you are in the Southern Hemisphere then it will be the other way round.

Answer:

a translation is the movement of the shape from units left to right or up and down so its basically scooching over to the left for example but the size or shape doesn't change, hope this helped

Step-by-step explanation:

Answer:

choice b d and e

Step-by-step explanation:

Answer:

obviously they will produce same output because the elevation of object and image will be same

Answer:

b

Step-by-step explanation:

2m is term because it is what you are looking for

In the expression 4(2m-n), (2m-n). is a term and  In expression 4(2m-n), 2m is also a term. The correct options are B and B for both.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (positive or negative), or the number of variables multiplied but never added or subtracted.

Variables in certain words have a number in front of them. A term is defined as a single number or single variable or number and variable multiplying with each other in a mathematics expression.

The first expression is 4(2m-n), then in the expression 2m - n will be the term of the expression.

The second expression is 4(2m-n), then in the expression 2m is the term of the expression.

Therefore, the expression 4(2m-n), (2m-n). is a term and  In expression 4(2m-n), 2m is also a term.

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"G plus Ten equals Three-G".

or

"The Variable G plus Ten equals Three-G".

The verbal expression is you putting it in the way that you would say the expression.

~

Answer:

The sum of a number and 10 is equal to three times that number.

Step-by-step explanation:

Break the parts down and put them together.

The sum of a number and 10: 'g + 10'

Is equal to: '='

Three times that number: '3g'

So:

The sum of a number and 10 is equal to three times that number: 'g + 10 = 3g'

Hope this helps.

===============================================

Let a,b,c,d be scalars.

In general if v and w are two vectors such that

v = <a, b>

w = <c,d>

then the difference of the two vectors is

v - w = <a-c, b-d>

so we subtract the coordinates

-----------------

Using that idea for the given vectors leads to

v = <9, -1>

w = <-1, -6>

v - w = <9 - (-1), -1-(-6)>

v - w = <9+1, -1+6>

v - w = < 10, 5 >

Answer: Phelan now have 44.69 US dollars. of the original 250 US dollars.

Step-by-step explanation:

Given, Phelan spent 150 euros on his trip.

1 European euro = 1.3687 US dollars

So, 150 euros = 150 × 1.3687 US dollars

= 205.305 US dollars

≈ 205.31 US dollars [ Rounded to the nearest cent. ]

Initially he had 250 US dollars, now he has left (250-205.31)US dollars that is

44.69 US dollars.

Hence, Phelan now have 44.69 US dollars. of the original 250 US dollars.

Phelan now have 44.69 US dollars. of the original 250 US dollars.

Answer:

-7

Step-by-step explanation:

Answer: -7

explanation: simplify the expression

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