Simplify the product. (–7) + (–7) + (–7) + (–7)

Answer:

1.  (12 - 2x)(11 - 2x)x

2. 4(11 - 2x)²(x + 1)

3. π(x³ + 15x² + 63x + 81)

Step-by-step explanation:

1. Write the polynomial function that models the given situation.

A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.

Since the length of the rectangle is 12 units and its width 11 units and squares of x by x units are cut from its corners, it implies that a length x is cut from each side. So, the length of the open box is L = 12 - 2x and its width is w = 11 - 2x.

Since the cut corners of the rectangle are folded, the side x which is cut represents the height of the open box, h. so, h = x

So, the volume of the open box V = LWh = (12 - 2x)(11 - 2x)x

2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.

Since the square has sides of 24 units and squares of x + 1 by x + 1 units are cut from its corners, it implies that a length x + 1 is cut from each corner and the length 2(x + 1) is cut from each side. So, the length of side open box is L = 24 - 2(x + 1) = 24 - 2x - 2 = 24 - 2 - 2x = 22 - 2x = 2(11  - x)

Since the cut corners of the square are folded, the side x + 1 which is cut represents the height of the open box, h. so, h = x + 1

Since the area of the base of the pen box is a square, its area is L² = [2(11 - 2x)]²

So, the volume of the open box V = L²h = [2(11 - 2x)]²(x + 1) = 4(11 - 2x)²(x + 1)

3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.

The volume of a cylinder is V = πr²h where r = radius and h = height of cylinder.

Given that r = x + 6 and h is 3 units more than r, h = r + 3 = x + 6 + 3 = x + 9

So, V = πr²h

V = π(x + 3)²(x + 9)

V = π(x² + 6x + 9)(x + 9)

V = π(x³ + 6x² + 9x + 9x² + 54x + 81)

V = π(x³ + 15x² + 63x + 81)

Answer:

8/9

Step-by-step explanation:

Let the geometric series have the first term=a and common ratio=r. ATQ, ar^3=8 and ar^6=216. r^3=27. r=3. a=8/3^3=8/27. t2=ar=8/9

Answer:

A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2

Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5

B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle

A) The length of each side of the square is (2x + 5).

B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).

Used the concept of a quadratic equation that states,

An algebraic equation with the second degree of the variable is called a Quadratic equation.

Given that,

Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.

Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.

A) Now the length of each side of the square is calculated by factoring the area expression completely,

[tex](4x^2 + 20x + 25)[/tex]

[tex]4x^2 + (10 + 10)x + 25[/tex]

[tex]4x^2 + 10x + 10x + 25[/tex]

[tex]2x (x + 5) + 5(2x + 5)[/tex]

[tex](2x + 5) (2x+5)[/tex]

Hence the length of each side of the square is (2x + 5).

B) the dimensions of the rectangle are calculated by factoring the area expression completely,

[tex](4x^2 - 9y^2)[/tex]

[tex](2x)^2 - (3y)^2[/tex]

[tex](2x - 3y) (2x + 3y)[/tex]

Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).

To learn more about the rectangle visit:

https://brainly.com/question/2607596

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Answer:

[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]

Step-by-step explanation:

factor out the 8

then you have the sum/difference of cubes..

look that up SOAP: same opposite, always a plus

[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]

[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]

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Answer:

  3/2

Step-by-step explanation:

Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.

  [tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]

Hey there! I'm happy to help!

Here is our equation.

[tex]2y-3x=10[/tex]

Let's add 3x to both sides.

[tex]2y=3x+10[/tex]

Divide both sides by 2.

[tex]y=\frac{3}{2}x+5[/tex]

Here is slope intercept form.

[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]

So, we can just find those two things in the equation, and here are our answers.

[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]

The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.

[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]

Have a wonderful day and keep on learning! :D

Answer:

5:10

6 (-2,0)

7 (-5,6)

8 (5,3)

9 No, ab=8 CD=6

Step-by-step explanation:

Answer:

hi amki nai patajjdkfkejd

Answer:

luke won

Step-by-step explanation:

he is 2 meters ahead of azam witch is in 2dn place

Answer:

The Next fiver tems are - 2, -2,-8,-12,-16

Step-by-step explanation:

Answer:

2,-6,2,-6,2

Step-by-step explanation:

a1 = 2

an = -an-1 -4

Let n =2

a2 = -a1 -4 = -2-4 = -6

Let n=3

a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2

Let n = 4

a4 = -a3 -4 = -2 -4 = -6

Let n=5

a5 = -a4 -4 = -(-6) -4 = +6-4 = 2

Answer:

270.47625

Step-by-step explanation:

249 is the original price

(249/100) · 8.625 = 21.47625 the tax total

249 + 21.47625 = 270.47625

Answer:

A. If the side lengths are the same, then a triangle is not scalene.

Step-by-step explanation:

A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

Simply stated, any polygon with three (3) lengths of sides is a triangle.

In Geometry, a triangle is considered to be the most important shape.

Generally, there are three (3) main types of triangle based on the length of their sides and these include;

I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.

II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.

III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.

Answer:

x >7

Step-by-step explanation:

There is an open circle at 7, which means it cannot equal 7.  The line goes to the right

x >7

Answer:

Y = -x + 2

Step-by-step explanation:

y = -x + 8

y = 1x + b

10 = 8 + b

b = 2

Answer:

y-y1=m(x-x1)

y-10=8(x-8)

y-10=8x-64

y-10+64-8x

y+54-8x

y-8x+54

Answer:

The root of the equation is 2 with multiplicity 3

Step-by-step explanation:

8(x-2)^3=0

(x-2)^3=0

The root of the equation is 2 with multiplicity 3

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Answer:

  A

Step-by-step explanation:

The parallelogram has rotational symmetry of degree 2. It looks the same after rotation by 180°.

_____

Additional comment

When a figure only looks like itself after a full rotation of 360°, it is said to have rotational symmetry of degree 1. All of the figures here will return to their original appearance after one 360° rotation. So, we assume the intent of the question is to identify figures with a rotational symmetry of degree greater than 1.

It looks like the integral you want to find is

[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy[/tex]

where C is the circle x ² + y ² = 4. By Green's theorem, the line integral is equivalent to a double integral over the disk x ² + y ² ≤ 4, namely

[tex]\displaystyle \iint\limits_{x^2+y^2\le4}\frac{\partial(-xy^2)}{\partial x}-\frac{\partial(x^2y)}{\partial y}\,\mathrm dx\,\mathrm dy = -\iint\limits_{x^2+y^2\le4}(x^2+y^2)\,\mathrm dx\,\mathrm dy[/tex]

To compute the remaining integral, convert to polar coordinates. We take

x = r cos(t )

y = r sin(t )

x ² + y ² = r ²

dx dy = r dr dt

Then

[tex]\displaystyle \int_C x^2y\,\mathrm dx - xy^2\,\mathrm dy = -\int_0^{2\pi}\int_0^2 r^3\,\mathrm dr\,\mathrm dt \\\\ = -2\pi\int_0^2 r^3\,\mathrm dr \\\\ = -\frac\pi2 r^4\bigg|_{r=0}^{r=2} \\\\ = \boxed{-8\pi}[/tex]

Answer:

I don't see the problem.

Step-by-step explanation:

Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]

(I assume I is the identity matrix and 0 is the zero matrix.)

Answer:

Step-by-step explanation:

if it's only true or false there are 2¹⁷=131072 outcomes

if it's true, false, or blank there are 3¹⁷=129140163 outcomes

Answer:

Hence the answer is TRUE.

Step-by-step explanation:

If event A is taking 15 or more minutes to urge to figure tomorrow and event B is taking but a quarter-hour to urge to figure tomorrow, then events A and B must be complimentary events. this is often because the occurring of 1 is going to be precisely the opposite of the occurring of the opposite event and that they cannot occur simultaneously. In other words, events A and B are mutually exclusive and exhaustive.  

Mathematically,  

P(A) + P(B) = 1.

Answer:

200

Step-by-step explanation:

Break down 25 = 5*5

Break down 8 = 2*2*2

They have no common factors

The least common multiple is

5*5*2*2*2 = 25*8 = 200

Answer:

200

Step-by-step explanation:

list the factors of 25: 5,5

factors of 8:2,2,2,

Answer:

the correct answer is, 4

Answer:

[tex]\displaystyle\frac{19,683}{200,000}\text{ or }\approx 9.84\%[/tex]

Step-by-step explanation:

For each planted seed, there is a 90% chance that it grows into a healthy plant, which means that there is a [tex]100\%-90\%=10\%[/tex] chance it does not grow into a healthy plant.

Since we are planting 6 seeds, we want to choose 2 that do not grow and 4 that do grow:

[tex]\displaystyle \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}[/tex]

However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):

[tex]\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15[/tex]

Therefore, we have:

[tex]\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%[/tex]

Answer:

[tex] {?}^{?} However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):

\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15(26)=2!6⋅5=230=15

Therefore, we have:

\begin{gathered}\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%\end{gathered}P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅(26),P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅15,P(exactly 2 don’t grow)=200,00019,683≈9.84%

[/tex]

Answer:

98

Step-by-step explanation:

2, 10, 18, 26, 34, 42, 50... 98

Hope this helps. Have a great day!

explainion:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.

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Answer:

  (x, y) = (4, -3)

Step-by-step explanation:

The solution is the point on the graph where the lines intersect:

  (x, y) = (4, -3)

Answer:

[tex]43.13 = 5.25h + 9[/tex]

Step-by-step explanation:

Let's solve this by making an equation.

$9 for the helmet, and $5.25 per hour.

h will stand for hours, C will stand for Amanda's cost.

[tex]C = 5.25h + 9[/tex]

Now, substitute in what we learned from the problem.

[tex]43.13 = 5.25h + 9[/tex]

This is an equation you can use to solve for the hours.