Determine the slope of a function with the following two solutions:
(-1.5, 2) and (7.5, 5)

The function f(x) = x^6(x-5)^7, defined for x ∈ [-14, 15], is increasing on the intervals [-14, 0] and [5, 15], positive on (-14, 0) ∪ (5, 15), and achieves its minimum at x = 5.

The function f(x) = x^6(x-5)^7 is defined for x ∈ [-14, 15]. To determine where the function is increasing, we need to find the intervals where its derivative is positive. The derivative of f(x) can be obtained using the product rule and simplifying it as f'(x) = 6x^5(x-5)^7 + 7x^6(x-5)^6.

For the function to be increasing, its derivative should be positive. By analyzing the sign of the derivative, we find that f'(x) is positive on the intervals [-14, 0] and [5, 15]. Thus, f(x) is increasing on these intervals.

To find the region where the function is positive, we need to consider the sign of f(x) itself. Since f(x) is a product of two terms, x^6 and (x-5)^7, we need to determine the sign of each term separately.

The term x^6 is positive for all values of x, except when x = 0, where it evaluates to 0. On the other hand, the term (x-5)^7 is positive for x > 5 and negative for x < 5. Combining these two conditions, we find that f(x) is positive on the intervals (-14, 0) ∪ (5, 15).

Finally, to locate the minimum of the function, we can examine the critical points. By setting the derivative f'(x) equal to 0, we can solve for x and find that the only critical point is x = 5. To confirm it is a minimum, we can check the sign of the second derivative or evaluate f(x) at the critical point. In this case, f(5) = 0, so x = 5 is the point where the function achieves its minimum value.

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This is a horizonal line going through y = 4.

Horizontal lines are of the form

Where

a is a number

Slope is rise over run, or, the change in y divided by change in x.

No matter what the change in x is, the change in y is always zero (horizontal line). Thus, the slope is always 0 as well.

1.

The slope of the line is 0

2.

The slope intercept form is:

Since the slope is zero, m = 0 and y intercept (b) is 4, we have:

Answer:

D

Step-by-step explanation:

Which is x < -3

Answer:

D. x < -3

Step-by-step explanation:

-8x - 15 > 9

-8x > 9 + 15

-8x > 24

-x > 24 ÷ 8

-x > 3

x < -3

If λ is an eigenvalue of matrix A and x is the corresponding eigenvector, then for any positive integer m, λ^m is an eigenvalue of A^m, and x is the corresponding eigenvector of A^m.

Let λ be an eigenvalue of matrix A with eigenvector x. This means that Ax = λx. Now, consider the matrix A^m, where m is a positive integer. By multiplying both sides of the eigenvector equation by A^(m-1), we have A^(m-1)Ax = A^(m-1)(λx), which simplifies to A^mx = λA^(m-1)x.

Since A^mx = (A^m)x and A^(m-1)x = λ^(m-1)x, we can rewrite the equation as (A^m)x = λ^(m-1)(Ax). Using the initial eigenvector equation Ax = λx, we have (A^m)x = λ^(m-1)(λx), which further simplifies to (A^m)x = λ^m x.

Therefore, we have shown that if λ is an eigenvalue of A with eigenvector x, then for any positive integer m, λ^m is an eigenvalue of A^m with the same eigenvector x. This result demonstrates the relationship between eigenvalues and matrix powers, illustrating that raising the matrix to a power corresponds to raising the eigenvalue to the same power while keeping the eigenvector unchanged.

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Answer:

Step-by-step explanation:

20% of 1150 is 230, so 1150-230=920

if the tax is applied after the discount, you find 10% of 920 (which is 92)

you add that to the discounted price 920+92= 1012, so they could go to florida.

The option that best describes the experiment is accurate and reproducible.

All the values from the experiment are close in value to the accepted value. This indicates that the experiment is accurate. Two experiments yield the same values. This indicates that the experiment is reproducible.

Here is the table used in answering the question:

Accepted Value: 130

Experiment 1 129

Experiment 2 131

Experiment 3 129

Experiment 4 132

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Answer:

(A)They are precise and reproducible

Step-by-step explanation:

Answer:

$39

Step-by-step explanation:

3 x 9 = 27

3 x 4 = 12

27 + 12 = 39

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Answer: 35:15

Step-by-step explanation:

7 times 5 = 35

3 times 5 = 15

35+15 = 50

Answer:3^2

Step-by-step explanation:

I think it is 3 with exponent of 3 because if its asking for side length of 9 then 3 x 3=9

The rule of the rotation to the right is a rotation by 90° clockwise about the origin.

We need to describe the rule of the rotation to the right.

A figure and its rotation keep the same shape and size but face in a new direction. A figure can be rotated in either a clockwise or counterclockwise direction. The angle of rotation is the measure of how far a figure is rotated about its centre of rotation. The angle of rotation is often expressed in degrees. We specify the rotation's degree measure and direction.

If the rotation is applied to the right, it means a rotation of 90° in a clockwise direction about the origin.

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The absolute maximum and absolute minimum of the function `f(x) = 2x² – 3x² – 12x – 5` on the closed interval `[-2, 4]` are `-39` and `-73` respectively.

Given the function `f(x) = 2x² – 3x² – 12x – 5`, we are to find the absolute maximum and absolute minimum on the closed interval `[-2, 4]`.

To find the absolute maximum and minimum values of a function, we have to follow the steps given below:

Find the derivative of the function and equate it to zero to get the critical points of the function.

Once we have the critical points, we need to determine the nature of the critical points as maximum, minimum, or neither.

Find the values of the function at these critical points as well as the values of the function at the endpoints of the given interval.

Compare these values to find the absolute maximum and minimum values.

Let's follow these steps to find the absolute maximum and minimum values of the given function `f(x) = 2x² – 3x² – 12x – 5`.

First, we need to find the derivative of `f(x)`.`f(x) = 2x² – 3x² – 12x – 5`

Differentiate the function f(x) with respect to x.

`f'(x) = 4x - 6x - 12`

Simplify the expression.

`f'(x) = -2x - 12`

Equate `f'(x)` to zero to find the critical points.`-2x - 12 = 0`

=> `-2x = -12`

=> `x = 6`

We have only one critical point, i.e., x = 6.

Now, let's find the nature of this critical point by taking the second derivative of the function.

`f(x) = 2x² – 3x² – 12x – 5`

Differentiate `f'(x)` with respect to x.

`f''(x) = -2`

Since the second derivative of the function is negative, the function has a maximum at `x = 6`.

Now, let's find the value of the function at the critical point x = 6.

`f(6) = 2(6)² – 3(6)² – 12(6) – 5`

=> `f(6) = -73`

The interval we are working with is `[-2, 4]`.

Therefore, we need to find the values of the function at the endpoints of this interval as well as at the critical point.

`f(-2) = 2(-2)² – 3(-2)² – 12(-2) – 5`

=> `f(-2) = -39`

And

`f(4) = 2(4)² – 3(4)² – 12(4) – 5`

=> `f(4) = -61`

Comparing the values, we can say that:

Absolute maximum value of `f(x)` is `f(-2) = -39`

Absolute minimum value of `f(x)` is `f(6) = -73`

Therefore, the absolute maximum and absolute minimum of the function `f(x) = 2x² – 3x² – 12x – 5` on the closed interval `[-2, 4]` are `-39` and `-73` respectively.

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Answer:

Step-by-step explanation:

Given, A car travels 330 miles in 6 hours.

total time = 330 miles.

total distance = 6 hours

It travels at 50 mph for the first two hours.

The distance in the first 2 hours = 2*50 = 100 miles.

It travels the last 180 miles at 60 miles per hour.

The time taken = 180/60 = 3 hours.

Distance travelled = 180 miles.

The balance time = 6-2-3 = 1 hour

The balance distance = 330-100-180 = 50 miles

It travels at constant speed for the remaining time.

a) Time taken by the car to travel the first 100 miles = 2 hours

Time taken by the car to travel the next 50 miles = 1 hours

So the time taken by the car to travel the first 150 miles = 2+1 = 3 hours

b) The car was at a distance of 150 miles from the starting point after 3 hours.

Answer:

see explanation

Step-by-step explanation:

An ordered pair is a set of coordinates (x, y )

This can be o point on a graph or the solution to a system of equations or values from a table

Answer: It's a point on a graph (y,x)

Step-by-step explanation:

Answer:

C and D are are the true statements

closed circles are at negative 2 and positive 8. everything between the points is shaded.

We have the equation:

|h - 3| \(\leq\) 5

Remember that the equation:

|f(x)| = A

with A > 0

means that:

f(x) = A

or

f(x) = -A

Then for our case, we can rewrite:

|h - 3| \(\leq\) 5

as:

(h - 3) \(\leq\) 5

or

-(h - 3) \(\leq\) 5

Now we can solve these two equations to find the two possible values of p.

From the first one, we get:

h \(\leq\) 8

Now from the other equation, we can get the other solution:

h \(\geq\) -2

Then the correct option is:

closed circles are at negative 2 and positive 8. everything between the points is shaded.

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Answer:

12.35

Step-by-step explanation:

Just multiply

\(19\)

and

\(0.65\)

Because

Orginal Price x Sale Cost= Sale of the Price.

\(19 \times 0.65 = 12.35\)

Answer: The measure of the missing angle is 115∘.

Step-by-step explanation: To find missing interior angles, you have to add the two angles that are known and see how much they add up.  The work is done below:

40∘ + 75∘ = 115∘.

In order to find out the missing interior angle, we have to subtract 115∘ from 180∘ to find that angle:

180∘ - 115∘ = 65∘, which is the missing angle that is inside the triangle.

Now, you're probably wondering how any of this has to do with finding the angle that has a ? on it.  Well, us finding the missing interior angle inside of the triangle is what's going to help us find that angle with a ? on it.  To find that angle, you need to subtract 65∘ from 180∘ to find the angle that you need:

180∘ - 65∘ = 115∘.

Therefore, 115∘ is your answer.

Let me know if this is right! :)

Minimizing the Sum of Squared Deviations

In statistics, the objective of many analyses is to identify the values of parameters that minimize the sum of squared deviations between observed and expected values. A common example of this is finding the mean (average) of a set of values. In this context, the deviations are calculated as the difference between each observed value and the mean.

In the problem stated above, we have a sum of squared deviations given by the expression (x_1 - c)^2. The goal is to find the value of c that minimizes this expression. To do this, we will take the derivative of the expression with respect to c, set it equal to 0, and solve for c.

Taking the derivative with respect to c:

The derivative of (x_1 - c)^2 with respect to c is 2 * (x_1 - c) * (-1) = 2 * (c - x_1). Setting this equal to 0 and solving for c:

2 * (c - x_1) = 0

c = x_1

So, the value of c that minimizes the expression (x_1 - c)^2 is equal to x_1.

Comparing Sum(x_i - mu)^2 and Sum(x_i - x_1)^2:

Now, let's consider the two quantities Sum(x_i - mu)^2 and Sum(x_i - x_1)^2. Assuming that mu is the population mean and x_1 is a sample mean, we can say that Sum(x_i - mu)^2 will always be equal to or larger than Sum(x_i - x_1)^2. This is because the sample mean is an unbiased estimator of the population mean and has a smaller variance than the population mean. In other words, the sample mean will be closer to the observed values, on average, than the population mean, leading to smaller deviations and a smaller sum of squared deviations.

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Answer:

Step-by-step explanation:

The number of items sold that gives the max profit is found in the vertex of this quadratic, (h, k). Lucky for us we have a formula for k that will give us exactly what we are looking for, and nothing else.

\(k=c-\frac{b^2}{4a}\) where a = -.5, b = 50, and c = -300:

\(k=-300-\frac{50^2}{4(-.5)}=-300+1250=950\)

The max profit is $950 per week

Answer:

-1

Step-by-step explanation:

the awnser is -1

Hi there!

55 is greater than 7.874007874. Therefore:

55 > 7.874007874

Or

7.874007874 < 55

I hope this helps!

a. The point where the tangent is horizontal is (-7, -32).

b. The points where the tangent is vertical are (5, -16) and (5, 16).

To find the points on the curve where the tangent is horizontal, we need to find where the derivative dy/dx equals zero.

First, we need to find dx/dt and dy/dt using the chain rule:

dx/dt = -2t

dy/dt = 3t² - 12

Then, we can find dy/dx:

dy/dx = dy/dt ÷ dx/dt = (3t² - 12) ÷ (-2t) = -(3/2)t + 6

To find where dy/dx equals zero, we set -(3/2)t + 6 = 0 and solve for t:

-(3/2)t + 6 = 0

-(3/2)t = -6

t = 4

Now that we have the value of t, we can find the corresponding value of x and y:

x = 9 - t²= -7

y = t³ - 12t = -32

So the point where the tangent is horizontal is (-7, -32).

To find the points on the curve where the tangent is vertical, we need to find where the derivative dx/dy equals zero.

First, we need to find dx/dt and dy/dt using the chain rule:

dx/dt = -2t

dy/dt = 3t² - 12

Then, we can find dx/dy:

dx/dy = dx/dt ÷ dy/dt = (-2t) ÷ (3t² - 12)

To find where dx/dy equals zero, we set the denominator equal to zero and solve for t:

3t² - 12 = 0

t² = 4

t = ±2

Now that we have the values of t, we can find the corresponding values of x and y:

When t = 2:

x = 9 - t² = 5

y = t³ - 12t = -16

When t = -2:

x = 9 - t² = 5

y = t³ - 12t = 16

So the points where the tangent is vertical are (5, -16) and (5, 16).

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Answer:

y = 1/5x + 9/5.

Step-by-step explanation:

x = -3 + 5y - 6

5y - 3 - 6 = x

5y - 9  = x

5y = x + 9

y = 1/5x + 9/5.

Hope this helps!

Function describes the graph of the transformed function is  4*e^(x-1)+3.

What is Function?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Adrienne is close, but she mixed up left and right

The x-1 in the exponent means we shift 1 unit right, and not left.

It's a bit confusing since it seems backwards.

But you can think of it like this: replacing x with x-1 shifts the xy axis 1 unit to the left, so we have the illusion the curve moved 1 unit to the right.

Here's one way to write out the transformation steps

f(x) = e^x

4*f(x) = 4*e^x .... vertical stretch by factor of 4

4*f(x-1) = 4*e^(x-1) ... shift 1 unit right

4*f(x-1)+3 = 4*e^(x-1)+3 ... shift 3 units up

g(x) = 4*e^(x-1)+3

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Function describes the graph of the transformed function is  4*e^(x-1)+3.

What is Function?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Adrienne is close, but she mixed up left and right

The x-1 in the exponent means we shift 1 unit right, and not left.

It's a bit confusing since it seems backwards.

But you can think of it like this: replacing x with x-1 shifts the xy axis 1 unit to the left, so we have the illusion the curve moved 1 unit to the right.

Here's one way to write out the transformation steps

f(x) = e^x

4*f(x) = 4*e^x .... vertical stretch by factor of 4

4*f(x-1) = 4*e^(x-1) ... shift 1 unit right

4*f(x-1)+3 = 4*e^(x-1)+3 ... shift 3 units up

g(x) = 4*e^(x-1)+3

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The numeric value of the inverse function at x = 0 is of y = 3.

An original function is composed by a set of points in the following format:

(x,y).

On the graph, we have that:

On the inverse function, the input and the output are exchanged, hence the format of the point is:

(y,x).

To find the numeric value of the inverse function at x = 0, we need to identify the value of x on the original function where y = 0.

From the graph of the function, it crosses the x-axis at x = 3, hence the numeric value of the inverse function at x = 0 is of y = 3.

The graph of the function is given by the image at the end of the answer.

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The graph for the equation of each diagonal line from upper left to lower right are shown in the image attached below.

In Mathematics, the slope-intercept form of an equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

At (0, 0.5) and (0.5, 0), the slope and equation of the diagonal line can be written as follows;

Slope = (0 - 0.5)/(0.5 - 0)

Slope = -1.

Equation: y = -x + 0.5

At (0, 1.5) and (2, 0), the slope and equation of the diagonal line can be written as follows;

Slope = (0 - 1.5)/(2 - 0)

Slope = -0.75.

Equation: y = -0.75x + 1.5

At (0, –2) and (3, 0), the slope and equation of the diagonal line can be written as follows;

Slope = (0 + 2)/(3 - 0)

Slope = 2/3.

Equation: y = 2x/3 + 1.5

At (0, –3) and (3, 0), the slope and equation of the diagonal line can be written as follows;

Slope = (0 + 3)/(3 - 0)

Slope = 1.

Equation: y = x - 3

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A  no   = 1/5

B no   = 4

C  no   = 1/3

D   yes

E     no = 17/50

26/104

the correct option is 26/104 because if 26 divides 26/104 it will give 1/4 because

26÷26= 1

104÷26=4

therefore, the correct option is 26/104