Find the degree, leading coefficient, and end behavior of the polynomial (x-5)(x-3)^6(x+5)^8.

The average time a molecule spends in its reservoir is known as the residence time.

Residence time is an important concept in environmental science, particularly in the study of water quality and pollution. It refers to the average amount of time that a substance, such as a molecule or a pollutant, spends in a particular environment before it is either removed or transformed. For example, in a river, the residence time of a pollutant would be the amount of time it takes for that pollutant to be either broken down by natural processes or transported downstream to another location. By understanding residence time, scientists can better predict how pollutants will move through the environment and where they are likely to accumulate.

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Answer:

6

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

0.75 * ( x+4) = 9

0.75x + 3 = 9

0.75x = 9 - 3

0.75x = 6

x = 6 / 0.75

x = 8

Answer:

245°

Step-by-step explanation:

the bearing is 180° + 65° = 245°

HOPE THIS HELPS

The dot products of A = (1, 1, -1) and B = (3, 5, 8) are zero, so the cross product axb is orthogonal to both vectors A and B.

Step 1: Write down the components of the vectors A and B.
A = (A1, A2, A3) = (1, 1, -1)
B = (B1, B2, B3) = (3, 5, 8)

Step 2: Compute the cross product axb using the formula:
axb = (A2*B3 - A3*B2, A3*B1 - A1*B3, A1*B2 - A2*B1)

Step 3: Substitute the components of A and B into the formula.
axb = (1*8 - (-1)*5, (-1)*3 - 1*8, 1*5 - 1*3)

Step 4: Simplify the expression.
axb = (8 + 5, -3 - 8, 5 - 3)

Step 5: Calculate the final components of the cross product axb.
axb = (13, -11, 2)

Now, to verify if the cross product is orthogonal to both A and B, we will check if the dot product of axb with A and B is zero.

Step 6: Calculate the dot product of axb with A and B.
(axb·A) = (13*1 + (-11)*1 + 2*(-1))
(axb·B) = (13*3 + (-11)*5 + 2*8)

Step 7: Simplify the expressions.
(axb·A) = (13 - 11 - 2)
(axb·B) = (39 - 55 + 16)

Step 8: Calculate the final dot product values.
(axb·A) = 0
(axb·B) = 0

Since both the dot products are zero, the cross product axb is orthogonal to both vectors A and B.

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Answer:

```30.

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<`36ok this is your answer....

Considering the equation f(x, y) = y⁴/x, the directional derivative of f in the direction of u at the point p(1,3) is -183/39.

At the point p(1,3), the equation is calculated to determine the directional derivative in the direction of the vector u = 1 3 2i + 5j. Therefore, the directional derivative is given by:`Duf(p) = ∇f(p) · u`

We first need to calculate the gradient of the function:`∇f(x, y) = <∂f/∂x, ∂f/∂y>`Differentiating f(x, y) partially with respect to x and y gives:```
∂f/∂x = -y⁴/x²
∂f/∂y = 4y³/x
```Therefore, the gradient of f is:`∇f(x, y) = <-y⁴/x², 4y³/x>`At the point p(1,3), the gradient of f is:`∇f(1,3) = <-81, 12>`

We need to normalize the vector u to get the unit vector in the direction of u.`||u|| = √(1² + 3² + 2² + 5²) = √39`

Therefore, the unit vector in the direction of u is:`u/||u|| = (1/√39) 3/√39 2i/√39 + 5/√39j`

Therefore, the directional derivative is:`Duf(p) = ∇f(p) · u = <-81, 12> · (1/√39) 3/√39 2i/√39 + 5/√39j`

Evaluating this expression gives:`Duf(p) = (-243 + 60)/39 = -183/39`

Therefore, the directional derivative of f in the direction of u at the point p(1,3) is -183/39.

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Angle A is congruent to angle c because they are both right angles. By the angle sum theorem, angle ADB is congruent to angle CBD.

A triangle is a closed polygon with three-line segments that intersect at each of its three angles. When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.

Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.

Side DB is congruent to side BD because they are the same segment.

Angle A is congruent to angle c because they are both right angles.

By the angle sum theorem, angle ADB is congruent to angle CBD.

By angle- side triangle congruence theorem, triangle BCD is congruent to triangle DAB.

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The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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Answer:

To convert the measurements of metric system into another units of metric system we have to either multiply it by 10, 100, 1000, 10000, 100000, etc or divide by 10, 100, 1000, 10000, 100000, etc.

If we have to convert bigger unit into smaller unit then we have to multiply the unit by the multiples of 10, then the decimal point is shifted to right by 1 or 2 or 3 or 4 , etc. places.

For example, 1.2 kg is converted into g so we have to multiply it by 1000, so decimal point is shifted to right by 3 places, i.e.,

1.2 x 1000 = 1200 g

If we have to convert smaller unit into bigger unit then we have to divide the unit by the multiples of 10, then the decimal point is shifted to left by 1 or 2 or 3 or 4 , etc. places.

For example, 12 cm is converted into m so we have to divide it by 100, so decimal point is shifted to left by 2 places, i.e.,

12 / 100 = 0.12 m  

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total number of students,

→ 100 students

No. of students were absent & failed,

→ 7 + 10

→ 17 students

No. of students totally passed,

→ 100 - 17

→ 83 students

No. of students passed in Science,

→ 80 students

No. of students passed in Mathematics,

→ 71 students

Then add both science and math,

→ 80 + 71

→ 151 students

No. of students passed in both subjects,

→ 151 - 83

→ 68 students

Therefore, the number of students who passed in both subjects are 68 students.

(s - t)(-1) evaluates to 0.

To find the expressions for (s + t)(x) and (s * t)(x), we can simply add and multiply the given functions s(x) and t(x) accordingly.

(s + t)(x) = s(x) + t(x)

           = (2x - 4) + (6x)

           = 2x - 4 + 6x

           = 8x - 4

(s * t)(x) = s(x) * t(x)

           = (2x - 4) * (6x)

           = 12x^2 - 24x

To evaluate (s - t)(-1), we substitute x = -1 into the expression (s - t)(x) and simplify:

(s - t)(x) = s(x) - t(x)

           = (2x - 4) - (6x)

           = 2x - 4 - 6x

           = -4x - 4

Now, substitute x = -1:

(s - t)(-1) = -4(-1) - 4

           = 4 - 4

           = 0

Therefore, (s - t)(-1) evaluates to 0.

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Suppose that the functions s and t are defined for all real numbers x as follows. s(x) = 2x - 4 t(x) = 6x Write the expressions for (s + t)(x) and (s t)(x)and evaluate(s - t)(-1)

Answer:

2 because negatives arent greater than whole numbers

57+3x+6=90degree

60+3x=90

3x=90-60

3x=30

x=30/3

x=10

Answer:

\( \boxed{x \degree = 9 \degree} \)

Step-by-step explanation:

\( = > 90\degree + 57\degree + (3x + 6)\degree = 180\degree \\ \\ = > 57\degree + (3x + 6)\degree = 180\degree - 90\degree \\ \\ = > 57\degree + (3x + 6)\degree = 90\degree \)

Two Angles are Complementary when they add up to 90° (a Right Angle).

\( = > 57 \degree + (3x + 6) \degree = 90 \degree \\ \\ = > 57 \degree + 3x \degree + 6 \degree = 90 \degree \\ \\ = > 63 \degree + 3x \degree = 90 \degree \\ \\ = > 3x \degree = 90 \degree - 63 \degree \\ \\ = > 3x \degree = 27 \degree \\ \\ = > x\degree = \frac{27}{3}\degree \\ \\ = > x\degree = 9\degree\)

Answer:

x-intercept = 9/5 = 1.80000

 y-intercept = 9/3 = 3

Step-by-step explanation:

x-intercept = 9/1 = 9.00000

 y-intercept = -9/3 = -3

Answer:

x = 7

Step-by-step explanation:

3(2x + 4) - x = 47

Multiply out the brackets:  6x + 12 - x = 47

Collect like terms:              6x - x + 12 = 47

Combine like terms:               5x + 12 = 47

Subtract 12 from both sides:          5x = 35

Divide both sides by 5:                     x = 7

Step-by-step explanation:

Open the bracket by using the number outside the bracket to multiply the ones inside.

Opening the bracket, we have that; 6x+12 - x =47

6x-x+12=47

5x+12=47

Collect like terms,

5x=47-12

5x=35

d.b.s by 5 to make x the subject

5x/5=35/5

x=7

Answer:

x+6 and x+7

Step-by-step explanation:

Given the quadratic equation;

x^2 + 13x + 42

Factorize

x^2+13x+42 = 0

x^2 + 7x + 6x + 42 = 0

x(x+7)+6(x+7) = 0

(x+6)(x+7) =0

Hence the required binomials are x+6 and x+7

Answer:

49 degrees could be an interpolation.

Step-by-step explanation:

For an interpolation, the data point in question needs to be in the middle of the given data points of the graph. Only the value 49 is in between all the points in our graph. The rest of the choice fall outside of the points.

The area of a rectangle is given by the product of its length and width. Therefore, we need to factor the given polynomial into two factors that represent the length and width of the table. We can do this by using the quadratic formula or by factoring the polynomial by grouping. Here, we will use factoring by grouping.

First, we group the terms in pairs:

7x^2 + 75x + 50 = (7x^2 + 35x) + (40x + 50)

Next, we factor out the greatest common factor from each pair of terms:

7x(x + 5) + 10(4x + 5)

We now have a common binomial factor of (x + 5), which we can factor out:

(7x + 10)(x + 5)

Therefore, the dimensions of the table are 7x + 10 and x + 5. We can check this by multiplying the dimensions:

(7x + 10)(x + 5) = 7x^2 + 35x + 10x + 50 = 7x^2 + 75x + 50

This confirms that the given polynomial represents the area of a rectangular table with dimensions of 7x + 10 and x + 5.

Answer:

Hello,

1/37

Step-by-step explanation:

Explanation on the picture

Answer:

134

Step-by-step explanation:

9×268 =2412

2412÷3= 804

804÷6=134

Susan has more candy in weight compared to Isabel.

To compare the candy weights between Susan and Isabel, we need to ensure that both weights are in the same unit of measurement. Let's convert Isabel's candy weight to ounces for a fair comparison.

Given:

Susan: 4 bags x 6 ounces/bag = 24 ounces

Isabel: 1 bag x 16 ounces/pound = 16 ounces

Now that both weights are in ounces, we can see that Susan has 24 ounces of candy, while Isabel has 16 ounces of candy. As a result, Susan is heavier on the candy scale than Isabel.

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g(X) to f(x) horizontal  compression by factor of 1/2  in graph transformation.

What is transformation from a graph?

The system of altering a graph to produce a different interpretation of the bone that came ahead is known as graph transformation. The graphs can be moved about thex-y aeroplane or restated. They may also be stretched, or they may suffer a blend of these changes.

                                  A drastic change in shape or appearance is called a metamorphosis. An pivotal occasion, similar as entering your motorist's licence, enrolling in council, or getting wedded, might change the course of your life. similar dramatic, drastic change is appertained to as a metamorphosis.

from g(X) to f(x) horizontal  compression by factor of 1/2 .

points (-2 , -4) and ( -4 , - 4 )

f(x) = (X+4)² - 4

G(x) = (2x + 4)² - 4

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3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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Use the section formula to get the coordinates of a point that separates a line segment outside or internally in a specific ratio.

By building two right triangles and applying AA similarity, the section formula can be obtained. After determining the ratio of the triangle's side lengths in terms of the supplied ratios, we may solve for x and y to determine the coordinates of the point that divides the line segment.

To determine the coordinates of a point that splits a line segment externally or internally in a certain ratio, apply the section formula. A line segment's midpoint can be determined using this technique as well.

By section formula, we have, if (x, y) divides the line segments joining \($\left(x_1, y_1\right)$\) and \($\left(x_2, y_2\right)$\) internally in the ratio m: n then,

\($x=\frac{m x_2+n x_1}{m+n}$\) and \($y=\frac{m y_2+n y_1}{m+n}$\)

Here,

\(\left(x_1, y_1\right)=(8,-1) \\\\ \left(x_2, y_2\right)=(2,5) \\\\ (x, y)=(4, 3) \\\)

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\( \frac{1}{5} x - 2= 4 \\ \)

Add sides 2

\( \frac{1}{5} x - 2 + 2 = 4 + 2 \\ \)

\( \frac{1}{5} x = 6 \\ \)

Multiply sides by 5

\(5 \times \frac{1}{5} x = 5 \times 6 \\ \)

\(x = 30\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\( \frac{1}{5x} - 2 = 4 \\ \)

Add sides 2

\( \frac{1}{5x} - 2 + 2 = 4 + 2 \\ \)

\( \frac{1}{5x} = 6 \\ \)

Inverse both sides

\(5x = \frac{1}{6} \\ \)

Divide sides by 5

\( \frac{5x}{5} = \frac{1}{6} \div 5 \\ \)

\(x = \frac{1}{6} \times \frac{1}{5} \\ \)

\(x = \frac{1}{30} \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

x=1/3

Step-by-step explanation:

The particular solution that satisfies the initial condition is:

\(xy - 3y^2 = -2.\)

To find the particular solution of the given differential equation, we can use the method of integrating factors.

First, we need to rearrange the equation in the standard form:

(x - 6y)dx - (2x - 9y)dy = 0

Multiply both sides by a suitable integrating factor, which is given by:

IF = e(-∫(6/x - 9/2)dy) = e\(^(9/2 ln(x)\)- 6y) = x\(^(9/2)e^(-6y)\)

Using this integrating factor, we can rewrite the equation as:

\(x^(9/2)e^(-6y)(x - 6y)dx - x^(9/2)e^(-6y)(2x - 9y)dy = 0\)

The left-hand side of this equation is the product rule of (xy - 3y^2), so we can rewrite it as:

\(d(xy - 3y^2) = 0\)

Integrating both sides, we get:

\(xy - 3y^2 = C\)

To find the particular solution that passes through the point (1, 1), we can substitute x = 1 and y = 1 into the above equation and solve for C:

\(1(1) - 3(1)^2 = C\)

C = -2

Therefore, the particular solution that satisfies the initial condition is:

\(xy - 3y^2 = -2.\)

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The provided equation is true for any y = f(x), which makes any function a solution. However, given the specific points x = 1 and y = 1, we find that the particular solution to the equation is y = x.

The given equation is a first order homogeneous differential equation that we can solve using a substitution method. Let's substitute v = y/x, or y =vx, such that dy = vdx+ xdv.

Therefore, the particular solution of the equation is y = 1x, or y = x.

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The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

A closed, two-dimensional, flat or planar structure with straight sides is referred to as a polygon. Its sides do not bend in any way. A polygon's sides are also referred to as its edges. A polygon's vertices (or corners) are the places where two sides converge. Polygons and polyhedrons are two names for geometric shapes having three or more sides. The names of a few polygons are listed below. In order to link and develop projects and blockchains that are compatible with Ethereum, Polygon (MATIC), a cryptocurrency and technological platform, was introduced. A fully closed polygon is a flat, two-dimensional form with straight sides. They must have straight sides. Any number of sides can be found in polygons.

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A summary of data that shows the number of observations in each of several non-overlapping bins is called a histogram.

A histogram is a graph used to visualize the distribution of a dataset. The x-axis represents the different ranges of the data being observed, which are usually called bins. The y-axis displays the frequency or count of data values that fall into each bin.

The shape of a histogram can provide valuable insights into the underlying data distribution. For example, if a histogram is bell-shaped, it indicates that the data follows a normal distribution, which is a symmetrical distribution with most values clustered around the mean. If a histogram is skewed to the left, the data has a long tail on the left-hand side and is concentrated on the right-hand side. If a histogram is skewed to the right, the data has a long tail on the right-hand side and is concentrated on the left-hand side. In conclusion, a histogram is a useful tool for summarizing data and providing insights into its distribution.

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