Factor the polynomial using Pascal's Triangle and the properties of binomial cubes. 8x^(3)+12x^(2)+6x+1

The [tex]4\frac{3}{8}-2\frac{1}{8}[/tex] [tex]=2\frac{1}{8}[/tex] This is the correct way to solve the equation it.

The meaning of an equations in algebra is a logical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When we say we're "solving" an equation, we truly mean we're "solving" the issue or "answering" the question since, in most circumstances, a formula reflects a problem (or query) of some type. A mathematical phrase with two equal sides and an equal sign is called an equation.

Given,

[tex]4\frac{3}{8}-2\frac{1}{8}[/tex]

[tex]=2\frac{1}{8}[/tex]

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To determine whether the given vectors in $\mathbb{R}^3$ form a basis for $\mathbb{R}^3$, we need to check if they are linearly independent and span $\mathbb{R}^3$.

To check for linear independence, we set up the augmented matrix:

[

0

5

7

0

0

2

2

0

2

9

11

0

]

⎣

⎡

​

0

0

2

​

5

2

9

​

7

2

11

​

0

0

0

⎦

⎤

We reduce this to echelon form:

[

1

0

2

0

0

1

1

0

0

0

0

0

]

⎣

⎡

​

1

0

0

​

0

1

0

2

1

0

​

0

0

0

​

⎦

⎤

​

Since there is a row of zeros, the rank of the matrix is less than 3, which means the vectors are linearly dependent.

Therefore, the given vectors do not form a basis for $\mathbb{R}^3$.

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it should be +60 not +78

when you multiply 18x by X - 3 you obtain 18x² - 54x . Subtract what you have gotten from 18x²-6x you obtain 60x

when x=24, y = y(3)/(2).

Given that y is directly proportional to the cube root of (x+3), we can write this relationship as:

y = k * cube root (x+3)

Where k is the constant of proportionality. We can use the given values of x and y to find k:

y(2)/(3 ) = k * cube root (5+3)

y(2)/(3 ) = k * cube root (8)

y(2)/(3 ) = k * 2

k = y(2)/(3 ) / 2

Now we can use this value of k to find y when x=24:

y = k * cube root (24+3)

y = (y(2)/(3 ) / 2) * cube root (27)

y = (y(2)/(3 ) / 2) * 3

y = y(2)/(3 ) * (3/2)

y = y(3)/(2)

Therefore, when x=24, y = y(3)/(2).

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Using synthetic division, we can find that h(-1) = -5.

To find h(-1) using synthetic division, we can use the following steps:

Write the coefficients of the polynomial in descending order of the exponents: 36, 36, 0, 7, 12, 39
Write the value of -1 to the left of the coefficients: -1 | 36 36 0 7 12 39
Bring down the first coefficient: -1 | 36 36 0 7 12 39
         36
Multiply the first coefficient by -1 and write the result under the second coefficient: -1 | 36 36 0 7 12 39
         36 -36
Add the second coefficient and the result: -1 | 36 36 0 7 12 39
         36   0
Repeat steps 4 and 5 for the remaining coefficients: -1 | 36 36 0 7 12 39
         36   0  0 -7 -5
The last number in the bottom row is the remainder, which is the value of h(-1): h(-1) = -5

Therefore, using synthetic division, we can find that h(-1) = -5.

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Step-by-step explanation:

The formula for the standard error of a proportion is:

SE = sqrt((p*(1-p))/n)

where p is the sample proportion and n is the sample size.

To find p, we need to first calculate the proportion of people who smoke regularly:

p = 71/635 = 0.1118

Now we can plug in the values for p and n:

SE = sqrt((0.1118*(1-0.1118))/635) = 0.0194

Therefore, the standard error for the sample proportion is 0.0194.

These two numbers are -4, 2. The smallest possible product is -8.

To find a pair of numbers that satisfy the given conditions, we can use algebra. Let x be the first number and y be the second number. According to the problem, one number is 8 less than twice a second number. This can be written as:
x = 2y - 8
We need to find the product of these two numbers, which is x*y. Substituting the value of x from the equation above, we get:
x*y = (2y - 8)*y
= 2y^2 - 8y
To find the smallest possible product, we need to minimize this expression. We can do this by finding the vertex of the parabola represented by this equation. The vertex of a parabola in the form ax^2 + bx + c is given by (-b/2a, f(-b/2a)). In this case, a = 2, b = -8, and c = 0. So, the vertex is:
(-b/2a, f(-b/2a)) = (-(-8)/(2*2), f(-(-8)/(2*2)))
= (2, f(2))
Substituting y = 2 into the equation for the product, we get:
x*y = 2(2)^2 - 8(2)
= 8 - 16
= -8
So, the smallest possible product is -8. To find the pair of numbers that give this product, we can substitute y = 2 into the equation for x:
x = 2y - 8
= 2(2) - 8
= -4
Therefore, the pair of numbers are -4 and 2.

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The dot plot allows us to know the exact data we are graphing.

In a dot plot, we have the different possible values on the horizontal axis, and dots above each of these values that count how many times that value has appeared in an experiment.

Instead, in a whisker plot or a box plot we have a representation in a kinda of "rectangle with whiskers".

This type of plot is usefull to find the quartiles of the data set, but not to know exactly how many of each data points we have, like in the dot plot.

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300  kilowatt-hours per month does one have to return to the grid to break even.

To find out how many kilowatt-hours per month one has to return to the grid to break even, we need to set up an equation and solve for x, where x is the number of kilowatt-hours returned to the grid.

The equation would be:

24 = 0.08x

To solve for x, we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by 0.08:

24/0.08 = x

x = 300

Therefore, one would have to return 300 kilowatt-hours per month to the grid to break even.

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Answer:

Step-by-step explanation:

SHORT ANSWER: perimeter = 4 * (6x+8) = 24x + 32

So, depending on which expression represents the length of the side of the square, the perimeter would be either 40x or 24x + 32.

LONG ANSWER WITH STEP-BY STEP:

If one side of the square has a length of 10x, then all sides have a length of 10x. Alternatively, if one side has a length of 6x+8, then all sides have a length of 6x+8. Therefore, we can write:

perimeter = 4 * side length

Substituting in the given expressions for the side length, we get:

perimeter = 4 * (10x) = 40x

or

perimeter = 4 * (6x+8) = 24x + 32

So, depending on which expression represents the length of the side of the square, the perimeter would be either 40x or 24x + 32.

Answer:

The height of the kite from the ground nearest to the tenth will be 443.6 feet.

Step-by-step explanation:

Answer:

(5,7)



x = 5

y = 7

The equation that shows the volume of the rectangular prism as a product of its edge lengths is (5/3)(1/3)(2/3) = 10/27 in cube. Option 2 is the correct answer.

The quantity of space within a three-dimensional object is its volume. The fundamentals of such forms are described in our page on three-dimensional shapes. Calculating volume is probably not something you will do as frequently as calculating area in the real world.

Even so, it may still be significant. Knowing how to calculate volume will help you determine things like how much room you have for packing when moving house, how much room you need for an office, or how much jam you can put into a jar. It can also be helpful for deciphering what the media means when they discuss a dam's capacity or a river's flow.

The volume of the rectangular prims is given by the formula:

V = lwh

Substituting the values we have:

V = (5/3)(1/3)(2/3) = 10/27

Hence, the equation that shows the volume of the rectangular prism as a product of its edge lengths is (5/3)(1/3)(2/3) = 10/27 in cube. Option 2 is the correct answer.

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The partial derivatives of f with respect to u and v at (u,v) = (-2, -2) are ∂f/∂u(-2,-2) = 224 and ∂f/∂v(-2,-2) = -1056.

To evaluate the partial derivatives ∂f/∂u and ∂f/∂v at (u,v) = (-2, -2) using the Chain Rule, we need to find the derivatives of f with respect to x, y, and z, and then multiply them by the derivatives of x, y, and z with respect to u and v.

First, let's find the derivatives of f with respect to x, y, and z:
∂f/∂x = 3x^2
∂f/∂y = z^2
∂f/∂z = 2yz

Next, let's find the derivatives of x, y, and z with respect to u and v:
∂x/∂u = 2u
∂x/∂v = 1
∂y/∂u = 1
∂y/∂v = 2v
∂z/∂u = 4v
∂z/∂v = 4u

Now, we can use the Chain Rule to find the partial derivatives of f with respect to u and v:
∂f/∂u = (3x^2)(2u) + (z^2)(1) + (2yz)(4v)
∂f/∂v = (3x^2)(1) + (z^2)(2v) + (2yz)(4u)

Finally, we can plug in the values of u and v to find the partial derivatives at (u,v) = (-2, -2):
∂f/∂u(-2,-2) = (3((-2)^2 + (-2))^2)(2(-2)) + ((4(-2)(-2))^2)(1) + (2((-2)+(-2)^2)(4(-2)))
= (3(0)^2)(-4) + (16^2)(1) + (2(2)(-8))
= 0 + 256 - 32
= 224

∂f/∂v(-2,-2) = (3((-2)^2 + (-2))^2)(1) + ((4(-2)(-2))^2)(2(-2)) + (2((-2)+(-2)^2)(4(-2)))
= (3(0)^2)(1) + (16^2)(-4) + (2(2)(-8))
= 0 - 1024 - 32
= -1056

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The vectors [[4],[0],[0]],[[9],[3],[-6]],[[6],[6],[-18]] are linearly independent.

To determine if the vectors are linearly independent, we can use the determinant of the matrix formed by the vectors. If the determinant is not equal to 0, then the vectors are linearly independent.

The matrix formed by the vectors is:
\begin{bmatrix}
4 & 9 & 6\\
0 & 3 & 6\\
0 & -6 & -18
\end{bmatrix}

The determinant of this matrix is:
\begin{vmatrix}
4 & 9 & 6\\
0 & 3 & 6\\
0 & -6 & -18
\end{vmatrix} = 4\begin{vmatrix}
3 & 6\\
-6 & -18
\end{vmatrix} - 9\begin{vmatrix}
0 & 6\\
0 & -18
\end{vmatrix} + 6\begin{vmatrix}
0 & 3\\
0 & -6
\end{vmatrix} = 4(-54-(-36)) - 9(0-0) + 6(0-0) = 4(-18) = -72

Since the determinant is not equal to 0, the vectors are linearly independent. Therefore, the vectors [[4],[0],[0]],[[9],[3],[-6]],[[6],[6],[-18]] are linearly independent.

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The expression is (+(13)/(18))+(-(1)/(3)). To simplify this expression, we need to combine like terms. First, we can combine the fractions with different denominators. The LCD (Least Common Denominator) for this expression is 18. Therefore, we need to convert each fraction to an equivalent fraction with a denominator of 18.

For the first fraction, (+(13)/(18)), 13/18 can be reduced to 1/2. To get this, multiply both the numerator and denominator by 2, resulting in 13/18 = 2/4 = 1/2.

For the second fraction, +(-(1)/(3)), 1/3 can be reduced to 6/18. To get this, multiply both the numerator and denominator by 6, resulting in 1/3 = 6/18.

Now that all the fractions have a common denominator, we can add the two fractions together. 1/2 + 6/18 = 8/18. Therefore, the simplified form of the expression is 8/18.

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The approximate value of x to the nearest tenth of a degree is 36.9 degrees.

To find x to the nearest tenth of a degree, we can use trigonometric ratios for right triangles. First, we need to determine which trigonometric ratio to use based on the given information.

If we are given the opposite side and the adjacent side of the right triangle, we can use the tangent ratio:

tan(x) = opposite/adjacent

If we are given the opposite side and the hypotenuse, we can use the sine ratio:

sin(x) = opposite/hypotenuse

If we are given the adjacent side and the hypotenuse, we can use the cosine ratio:

cos(x) = adjacent/hypotenuse

Once we have determined the appropriate trigonometric ratio, we can plug in the given values and solve for x. To find x to the nearest tenth of a degree, we can use a calculator to find the approximate value of x and then round to the nearest tenth.

For example, if we are given a right triangle with an opposite side of 3 and an adjacent side of 4, we can use the tangent ratio to find x:

tan(x) = 3/4

x = tan^-1(3/4)

Using a calculator, we find that x is approximately 36.87 degrees. To the nearest tenth of a degree, x is approximately 36.9 degrees.

Therefore, the approximate value of x to the nearest tenth of a degree is 36.9 degrees.

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Answer:

We can use the given information to find the ant's crawling speed and then use that to calculate how far it can crawl in a given amount of time.

The ant crawls 12 feet in 10 minutes, so its crawling speed is:

12 feet / 10 minutes = 1.2 feet/minute

To find how far the ant can crawl in 20 minutes, we can multiply its crawling speed by the time:

Distance in 20 minutes = crawling speed x time

Distance in 20 minutes = 1.2 feet/minute x 20 minutes

Distance in 20 minutes = 24 feet

Therefore, the ant can crawl 24 feet in 20 minutes.

To find how far the ant can crawl in 30 minutes, we can use the same formula:

Distance in 30 minutes = crawling speed x time

Distance in 30 minutes = 1.2 feet/minute x 30 minutes

Distance in 30 minutes = 36 feet

Therefore, the ant can crawl 36 feet in 30 minutes.

Answer:

20 mins=24 feet

30 mins=36 feet

Step-by-step explanation:

if 12 feet = 10 mins and 10 times 2 = 20 then 12 times 2 =24

same for 30 mins.

10 times 3= 30 then 12 times 3= 36

The total surface area of the cube is 3.84 m². The solution has been obtained by using the area of cube.

The total surface area of a given cube is said to be equal to the sum of all the surface areas of the cube's faces, according to the definition of surface area. Given that the cube has six faces, its total surface area will be equal to the sum of its six faces.

We are given a cube with side length 0.8 metres.

We know that total surface area of a cube is given by 6a².

Now, by substituting a = 0.8 in the formula, we get

⇒Total surface area of cube = 6 (0.8)²

⇒Total surface area of cube = 6 (0.64)

⇒Total surface area of cube = 3.84 m²

Hence, the total surface area of the cube is 3.84 m².

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Answer:

Step-by-step explanation:

1+2x)5

First you minus the 1 with the 5

Which you'll get a four then divide it by 2

Which you'll get x=2

But then times it by 5

Then you get y=10

Answer:

[tex]\dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5 = \boxed{\dfrac{5}{\sqrt{1+2x}}}[/tex]

Step-by-step explanation:

Given [tex]y = \left(\sqrt{1\:+\:2x}\right)5[/tex]

we are asked to find [tex]\dfrac{dy}{dx}[/tex]

[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5\\\\= 5\dfrac{d}{dx}\left(\sqrt{1+2x}\right)\\\\[/tex]

Find [tex]\dfrac{d}{dx}\left(\sqrt{1+2x}\right)[/tex]:
[tex]Let \;u = 1 + 2x\\\\f(u) = \sqrt(u)\\\\[/tex]

[tex]\mathrm{Apply\:the\:chain\:rule}:\quad \dfrac{df\left(u\right)}{dx}=\dfrac{df}{du}\cdot \dfrac{du}{dx}[/tex]

[tex]= \dfrac{d}{du}\left(\sqrt{u}\right)\dfrac{d}{dx}\left(1+2x\right)[/tex]

[tex]\dfrac{d}{du}\left(\sqrt{u}\right) = \dfrac{d}{du}\left(u^{\dfrac{1}{2}}\right)\\\\= \dfrac{1}{2}u^{\dfrac{1}{2}-1}\\\\= \dfrac{1}{2\sqrt{u}}\\\\\\[/tex]

Substitute back u = 1 + 2x
[tex]= \dfrac{1}{2\sqrt{1+2x}}[/tex]

[tex]\dfrac{d}{dx}(1 + 2x) =\dfrac{d}{dx}(1)} + \dfrac{d}{dx}{2x}\\\\= 0 + 2 \\\\= 2\\[/tex]

Therefore
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}\left(\sqrt{1\:+\:2x}\right)5\\\\= 5\dfrac{d}{dx}\left(\sqrt{1+2x}\right)\\\\[/tex]

[tex]= 5\cdot \dfrac{1}{2\sqrt{1+2x}}\cdot \:2\\\\= 5\cdot \dfrac{1}{\sqrt{1 + 2x}}\\\\=\dfrac{5}{\sqrt{1+2x}}[/tex]

the area of the shaded region:

[tex]= 2(the \ area \ of \ a \ quarter \ circle) - (the \ area \ of \ the \ square)\\[/tex]

[tex]= 2\Big(\dfrac{\pi 12^{2} }{4}\Big) - 12^{2} = \dfrac{144 \pi}{2} - 144 = 72 \pi - 144\\[/tex]

[tex]= 72 (\pi - 2) \ m^{2}[/tex]

Answer:

  72π-144 m²

Step-by-step explanation:

You want the area of a shaded region consisting of the overlap of two quarter circles in a 12 m square.

If we draw a diagonal from upper left to lower right through the figure, the shaded area is divided into two 90° segments of a circle of radius 12 m.

The formula for the area of a segment is ...

  A = 1/2r²(θ -sin(θ))

where θ is the measure of the central angle.

For θ = π/2 radians, this is ...

  A = 1/2r²(π/2 -1) . . . . . half the shaded area

Then the whole shaded area is ...

  2 × 1/2r²(π/2 -1) = (12 m)²(π/2 -1) = 72π -144 m²

The area of the shaded region is 72π -144 m².

__

Additional comment

If we expand the shaded area formula, we get ...

  A =1/2πr² -r²

This is recognizable as twice the area of a quarter circle, less the area of the square.

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Answer:

Step-by-step explanation:

So all that you have to do is just multiply 15 by 110kg and you'll get a answer of 1500kg total.

Answer:

Step-by-step explanation:

based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole number8957647h3ny4y4y7

1) The ratios 1/3 , 7/21 are in proportion.

2) The ratios 2/5 , 40/16 are not in proportion.

3) the ratios 48/9 , 16/3 are in proportion.

We know that two ratios are said to be in proportion when both the ratios are equivalent.

Consider 1/3 , 7/21

Here 7/21 = (7 × 1)/(7 × 3)

                = 1/3

This means 1/3 = 7/21

Thus, the ratios 1/3 , 7/21 are in proportion.

Consider 48/9, 16/3

Here 48/9 = (16 × 3)/(3 × 3)

                = 16/3

This means 48/9 = 16/3

Thus, the ratios 48/9, 16/3 are in proportion.

Now consider 2/5 , 40/16

Here 40/16 = (8 × 5)/(8 × 2)

                = 5/2

This means 2/5 ≠ 5/2

Thus, the ratios 2/5 , 40/16 are not in proportion.

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Step-by-step explanation:

Refer to pic.............

Check the picture below.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0}\implies \cfrac{18-12}{2}\implies \cfrac{6}{2}\implies \text{\LARGE 3}[/tex]

The final answer is 16 - 1 = 15 linear extensions of the poset P.

The poset P has 8 linear extensions. We can determine the number of linear extensions by counting the number of topological sorts of the poset. A topological sort of a poset is a linear ordering of its vertices that respects the partial ordering. There are two ways to obtain a topological sort of the poset P:

1. Start with vertex A, then choose either B or F, then choose either C or G, then choose either D or H, and finally choose E. This gives us a total of 2 x 2 x 2 x 1 = 8 topological sorts.

2. Start with vertex F, then choose either A or G, then choose either B or H, then choose either C or D, and finally choose E. This also gives us a total of 2 x 2 x 2 x 1 = 8 topological sorts.

Therefore, the total number of linear extensions of the poset P is 8 + 8 = 16.

However, we need to subtract the number of topological sorts that are counted twice. These are the topological sorts that start with A, then choose F, then choose G, then choose H, and finally choose E. There are 1 x 1 x 1 x 1 x 1 = 1 of these topological sorts.

So the final answer is 16 - 1 = 15 linear extensions of the poset P.

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There are 72 pupils in bertha if the ratio of 1 Bertha to form 1 Florence is 12:20 if there are 120 pupils in Florence.

The problem can be solved by using the concept of ratios and inverse ratios. It involves setting up a proportion based on the given ratio and using algebra to solve for the unknown quantity.

If the ratio of Bertha to Florence is 12:20, then the ratio of Florence to Bertha is 20:12 (inverse ratio).

Let the number of pupils in Bertha be x. Then, the number of pupils in Florence would be:

20/12 * x = 120

Simplifying:

x = 120 * 12/20

x = 72

Therefore, there are 72 pupils in Bertha.

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Answer: I could be wrong but its either going to be 13.5 or 13.

Step-by-step explanation:

Answer:

13.5 goals

Step-by-step explanation:

We can use a ratio to solve

3 goals                   x

---------------  = -------------

2 games            9 games

Using cross products

3 * 9 = 2x

27 = 2x

Divide each side by 2

27/2 = x

13.5 goals

Using the numbers 1 to 9 (one time each), the boxes can be filled in the following way to make the equation true. 2:2 = 3×3:9 = 4×4 =16.

An arithmetic contrast among two numbers is known as a percentage. Two sets of provided numbers are considered to be approximately equal with respect to one another in conformity with the rules of proportion if they increase or decrease by the same ratio.

We must create the equation to prove the equality by utilizing each of the numerals 1 through 9 once. Any of the numbers between 1 and 9 are equivalent to 1 and 2.

Let the ratio equal 1.

The comparable ratios are therefore 1:1, 2:2, and 3:3.

2:2 = 3×3:9 = 4×4 =16

Therefore, using the numbers 1 to 9 (one time each), the boxes can be filled in the following way to make the equation true. 2:2 = 3×3:9 = 4×4 =16.

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