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The completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

According to the given question.

We have a polynomial

x^3 + 4x^2 - 9x -36

Since for finding the roots of the above polynomial, first we randomly substitute any value of x and find for which value of x the above polynomial gives 0.

So, for x = 3

The above polymonial gets 0.

So, the one factor of the given polynomial is (x -3).

To find the other factors or completely factored form of the given polynomial we will divide x^3 + 4x^2 - 9x -36 by x - 3, which is called long division.

From the attatched solution or log division we can see that

The factored form of x^3 + 4x^2 - 9x -36 is (x -3)(x^2 + 7x + 12).

Now, the foctorization of x^2 + 7x + 12 is given by

x^2 + 7x + 12

= x^2 + 4x + 3x + 12

= x(x + 4) + 3(x + 4)

= (x + 3)(x + 4)

Therefore, the completely factored form of x^3 + 4x^2 - 9x -36 is

(x -3)(x + 3)(x + 4).

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Answer:

C) (x + 3)(x – 3)(x + 4)

Included the whole page!
☆
EDGE2022; Good Luck :D!!!

The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16.


To find the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen, you need to subtract the sample mean of underclassmen from the sample mean of upperclassmen.

Sample mean of upperclassmen = 0.76
Sample mean of underclassmen = 0.60

Point estimate = Sample mean of upperclassmen - Sample mean of underclassmen
Point estimate = 0.76 - 0.60
Point estimate = 0.16


The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16, which indicates that on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours.

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Answer:

The slope is 1

Step-by-step explanation:

m=4+8/3+9

m=12/12

m=1

Hope it helps :)

Brainliest maybe  . . :o

Answer:

32

Step-by-step explanation:

x^2 + 4y = 16 + 20 = 32

Just do substitution.

Hope this helps.

Good Luck

Answer:

12516

Step-by-step explanation:

Given

x² + 4\(y^{5}\)

Substitute x = 4 and y = 5 into the expression

= 4² + 4\((5)^{5}\)

= 16 + 4(3125)

= 16 + 12500

= 12516

Answer:

t = 10.70375

Step-by-step explanation:

8563=800t

Divide by 800 on both sides

t = 10.70375

Step-by-step explanation:

1/5=1/5×1000=200

1/2 of 200

1/2×200=100

The expression ,((1 - csc (-θ ))/csc (-θ)) + (1 /csc(-θ) tan(-θ) in terms of sine and cosine, and then simplify so that no quotients in final expression is cosθ - sinθ.

We use the following reciprocal identity for cosine and secant that cos θ = 1/secθ , 1/sin θ = csc θ , tan θ = 1/cotθ. We have , the expression is F =((1 - csc (-θ))/csc(-θ)) + (1 +1/ (csc(-θ)tan(-θ)))

We have to represent the final expression of it in form of cosine and sine. Using reciprocal identity, and the complimentary angle property, csc(-θ)

= -csc θ, tan(-θ) = - tanθ ,

=> T = (1 -(-cscθ))/(- cscθ) + 1 + 1/((-cscθ)(-tanθ))

=> T = - ( 1 + csc θ)/cscθ + 1 +1/(cscθtanθ)

=> T = -( 1 + 1/sin θ )/1/sinθ + 1 +1/((1/sinθ)(sinθ/cosθ)) ( since, tanθ= sinθ/cosθ)

=> T = - sinθ( 1 + 1/sin θ ) + (1 + 1 /1/cosθ)

=> T = - sinθ - 1 + 1 + cosθ

=> T = - sinθ + cosθ

Hence, the final expression is cosθ-sinθ.

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Complete question:

Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression and all functions are of 0 only. ((1 - csc (-θ ))/csc (-θ)) + (1 + 1 /csc(-θ) tan(-θ))

Answer:

D) (such a situation is not possible as with 2 points, there will be 4 tangents to the circle)

The angle that the vector makes with the positive x-axis is approximately 61.30 degrees i.e., the correct option is A.

To determine the angle, we can use the trigonometric function tangent (tan).

The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Given that the vector has a magnitude of 25 units and an x-component of magnitude 12 units, we can find the y-component of the vector using the Pythagorean theorem.

The y-component can be found as follows:

y-component = \(\sqrt{(magnitude \, of \,the \,vector)^2 - (x\,component)^2}\)

y-component = \(\sqrt{25^2 - 12^2}\)

y-component =\(\sqrt{625 - 144}\)

y-component = \(\sqrt{481}\)

y-component ≈ 21.92

Now, we can calculate the tangent of the angle using the y-component and the x-component:

tan(angle) = y-component / x-component

tan(angle) = 21.92 / 12

angle ≈ \(tan^{-1}(21.92 / 12)\)

angle ≈ 61.30 degrees

Therefore, the angle that the vector makes with the positive x-axis is approximately 61.30 degrees, which corresponds to option (a).

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The possible number of books that could be on sale is option 1: (5, 15).

Let's evaluate each option using the given system of inequalities:

a. (5, 15)

x = 5 and y = 15

The first inequality, x + y < 20, becomes 5 + 15 < 20, which is true.

The second inequality, x < y, becomes 5 < 15, which is true.

Therefore, (5, 15) satisfies both inequalities.

b. (15, 5)

x = 15 and y = 5

The first inequality, x + y < 20, becomes 15 + 5 < 20, which is true.

The second inequality, x < y, becomes 15 < 5, which is false.

Therefore, (15, 5) does not satisfy the second inequality.

c. (10, 10)

x = 10 and y = 10

The first inequality, x + y < 20, becomes 10 + 10 < 20, which is true.

The second inequality, x < y, becomes 10 < 10, which is false.

Therefore, (10, 10) does not satisfy the second inequality.

Hence based on the analysis, the possible number of books that could be on sale is option 1: (5, 15).

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The equation \(4x^2u^n + (1-x^2)u = 0\) has two solutions. One solution is given by \(u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\). The other solution is not provided in the given question.

To find the solutions, we can rewrite the equation as \(u^n = -\frac{1-x^2}{4x^2}u\). Taking the square root of both sides gives us \(u = \pm\left(-\frac{1-x^2}{4x^2}\right)^{1/n}\). Now, let's focus on finding the positive solution.

Expanding the expression inside the square root using the binomial series, we have:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{(1-x^2)}{4x^2}\right)^{1/n}\]

Since \(|x| < 1\) (as \(x\) is a fraction), we can use the binomial series expansion for \((1+y)^{1/n}\), where \(|y| < 1\):

\[(1+y)^{1/n} = 1 + \frac{1}{n}y + \frac{1-n}{2n^2}y^2 + \dots\]

Substituting \(y = \frac{1-x^2}{4x^2}\), we get:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{1}{n}\cdot\frac{1-x^2}{4x^2} + \frac{1-n}{2n^2}\cdot\left(\frac{1-x^2}{4x^2}\right)^2 + \dots\right)\]

Simplifying and rearranging terms, we find the positive solution as:

\[u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\]

The second solution is not provided in the given question, but it can be obtained by considering the negative sign in front of the square root.

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Answer:

yes

Step-by-step explanation:

It is proprtional because there is a pattern in the X and Y axis.

Answer:

no is not proportional because is not (0, 0) and that table has a y-intercept of 3

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Therefore, the rates do not form a proportion.

To determine whether the rates form a proportion or not, we must first define the meaning of proportion.

Proportion is the equality of two ratios. The ratios are considered equal if the fraction values are equal. If the given ratios are equal, then it forms a proportion. Now, let's determine whether the given rates form a proportion or not. The given rates are: 385 calories in 3.5 servings;

300 calories in 3 servings

We can write the ratios of calories to servings for each rate, as follows:

385 calories ÷ 3.5 servings = 110 calories/serving

300 calories ÷ 3 servings = 100 calories/serving

Then, we can compare the ratios:

110 calories/serving ≠ 100 calories/serving

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Answer is in the file below

tinyurl.com/wtjfavyw

Answer:

50, 90, 65, 25

Step-by-step explanation:

I dont know how to get to it that is why I searched it up :/

Answer:

2.65 feet per minute or 0.0441667 feet per second

Step-by-step explanation:

Since the right side is 0, so equate each factor by 0 and find the values of x

Put 3x - 14 = 0 and 8x + 13 = 0

3x - 14 = 0

Add 14 to both sides

3x - 14 + 14 = 0 + 14

3x = 14

Divide both sides by 3

This is the first value of x

Let us do the same with other factor

8x + 13 = 0

Subtract 13 from both sides

8x + 13 - 13 = 0 - 13

8x = - 13

Divide both sides by 8

This is the second value of x

So the two values of x are

Answer:

x= -1.5

Rounded: x= -2

Step-by-step explanation:

3(-6x)+5=32

-18x+5=32

      -5. -5

-18x=27

/-18.  /-18

x=-1.5

And I guess I round to a whole number

x=-2

Hopes this helps please mark brainliest

3(-6x) + 5 = 32

multiply out left side:

-18x + 5 = 32

subtract 5 from both sides:

-18x = 27

divide both sides by-18:

x = -3/2

or

x = -1.5

Answer:8% started saving at or before 21

30% believe their children or grandchildren should start saving at or before 21

Step-by-step explanation: on the graph, the ones in lighter color start saving for requirements

That is 3%+5%=8%

The second solution goes thus

13%+17%= 30%

the ones in dark colors believe their children or grandchildren should start saving before 21

Answer:

x=2

Step-by-step explanation:

First we can find out what \((\frac{1}{81} )^{2} \) in terms of 9 is...

\(\frac{1}{81} ^{2}=\frac{1^{2}}{81^{2}} =\frac{1}{81^{2}} =\frac{1}{9^{4}} \)

This means we need 3x-10 to be equivalent to -4 as \(9^{-4}\) is equivalent to \(\frac{1}{9^{4}} \).

3x-10=-4

Add 10 to both sides

3x=6

Divide both sides by 3

x=2

The probability of obtaining a good split when randomly picking three elements and partitioning about their median is 3/8, given that the elements are not necessarily distinct.

When randomly selecting three elements from the array, there are a total of 3! = 6 possible permutations. Out of these permutations, there are three cases where the middle element is the true median, which would result in a good split.

These cases are: (1) the elements are in ascending order, (2) the elements are in descending order, and (3) the elements are in any other order where the middle element is the median.

The other three cases, where the middle element is not the true median, would result in a bad split. These cases occur when the true median is either the smallest or largest element among the three chosen.

Therefore, the probability of obtaining a good split is 3 out of the total 6 possible permutations, which simplifies to 3/6 or 1/2. However, since the problem states that the elements are not necessarily distinct, there are additional duplicate cases. In those cases, the probability of obtaining a good split becomes 3/8.

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Answer:

(2,3)

Step-by-step explanation:

it is the point in which they intersect

i am in algebra two so you can trust my answer. if you need more help, lmk in the comments. happy holidays and stay safe!

The line passing through the points (-1, -11) and (4, 4) can be represented by the equation y = 3x - 8 in slope-intercept form.

To find the equation, we first calculate the slope using the formula:

slope = (y2 - y1) / (x2 - x1)

Plugging in the coordinates (-1, -11) and (4, 4), we get:

slope = (4 - (-11)) / (4 - (-1))

= 15 / 5

= 3

Next, we choose one of the given points, (-1, -11), and substitute it into the slope-intercept form (y = mx + b), along with the slope value:

-11 = 3(-1) + b

Simplifying the equation:

-11 = -3 + b

b = -11 + 3

b = -8

Finally, substituting the value of the y-intercept (b) into the slope-intercept form, we obtain the equation of the line passing through the given points as y = 3x - 8.

The line passing through the points (-2, 12) and (1, -3) can be represented by the equation y = -5x + 2 in slope-intercept form.

Explanation: Similarly, we calculate the slope using the given points:

slope = (y2 - y1) / (x2 - x1)

Substituting the coordinates (-2, 12) and (1, -3):

slope = (-3 - 12) / (1 - (-2))

= -15 / 3

= -5

Choosing one of the points, let's say (-2, 12), we substitute it into the slope-intercept form (y = mx + b):

12 = -5(-2) + b

Simplifying:

12 = 10 + b

b = 12 - 10

b = 2

Finally, substituting the y-intercept (b) into the slope-intercept form, we obtain the equation of the line passing through the given points as y = -5x + 2.

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The height of this hill is given as :  51.88 feet.

How to solve for the height of the hill

We can use trigonometry to find the height of the hill. Let's call the height of the hill "h".

From the information given, we know that:

tan(27°) = h / (103/2)

h = (103/2) * tan(27°)

Using a calculator, we would have to go ahead to get the value of the variable h or height.

So  that h ≈ 51.88 feet.

So, the height of the hill is approximately 51.88 feet.

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Any function of the form z=f(x+at)+(x-at) is a solution of the wave equation

The wave equation in 3-dimensional space is given by:

curl²z/curlt² = a² curl²z/curlx²

Let's differentiate the given function f(x + at) + (x - at) with respect to x and t.

∂z/∂x = ∂f/∂x + (1 - a²) ∂f/∂t

∂z/∂t = a∂f/∂x + ∂f/∂t

Now we compute the second-order partial derivatives:

∂²z/∂x² = ∂²f/∂x² + (1 - a²) ∂²f/∂x∂t

∂²z/∂t² = a² ∂²f/∂x² + 2a ∂²f/∂x∂t + ∂²f/∂t²

∂²z/∂x∂t = ∂²f/∂x∂t + a(1 - a²) ∂²f/∂t²

Taking the curl of the wave equation:

curl²z/curlt² = a² curl²z/curlx²

∇²z = a² (∂²z/∂t² - ∂²z/∂x²) = a² [a² (∂²f/∂x² + 2a ∂²f/∂x∂t + ∂²f/∂t²) - ∂²f/∂x² - (1 - a²) ∂²f/∂x∂t]

Simplifying the above expression, we get:

∇²z = a² (1 - a²) (∂²f/∂x² - a² ∂²f/∂t²)

Substituting the above equation in the wave equation, we get:

(1 - a²) (∂²f/∂x² - a² ∂²f/∂t²) = 0

Since we assume that all the given functions have continuous second-order partial derivatives, we know that the mixed partial derivatives are equal, i.e.

∂²f/∂x∂t = ∂²f/∂t∂x

Therefore, we have:

∂²f/∂x² - a² ∂²f/∂t² = 0

which is the wave equation. Hence, we have shown that any function of the form z=f(x+at)+(x-at) is a solution of the wave equation.

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Answer:

96

Step-by-step explanation:

960 ÷ 10 = 96

please mark as brainliest answer