A thermometer reading 22° Celsius is placed in an oven preheated to a constant temperature. Through a glass window in the oven door, an observer records that the thermometer read 31° after 39 seconds and 32° after 78 seconds. How hot is the oven?

Answer: It's the 3rd one. Secant line

The solutions of the given equation are x= (√5+3)/2 & x= (-√5+3)/2

If ax²+bx+c = 0 is a quadratic equation ,where a,b,c are real numbers, Then the solution is x = (-b±√(b²-4ac))/2a , where a≠0

The given equation is, 4x²-12x+9 = 5

So, 4x²-12x+9 = 5

⇒ 4x²-12x+9-5 = 0

⇒ 4x²-12x+4 = 0

Comparing this equation with ax²+bx+c = 0 we get,

a = 4, b = -12, c = 4

Applying sridharacharya formula we get,

x = (-(-12)±√((-12)²-4×4×4))/(2×4)

  = (12±√(144-64)/8

  = (12±√80)/8

  = (3±√5)/2

The values of x are (√5+3)/2 & (-√5+3)/2

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Answer:

Step-by-step explanation:

Equation 3.0.

The variables x, y, and z correspond to the entries in the last column. Therefore, the solution to the system of linear equations is x = 1, y = 0, and z = -2 (option d).

To find the solution of the system of linear equations represented by the given augmented matrix, we can perform row operations to bring the matrix into row-echelon form or reduced row-echelon form. By analyzing the resulting matrix, we can determine the values of the variables x, y, and z. In this case, after performing the necessary row operations, we find that the solution to the system of linear equations is x = 1, y = 0, and z = -2 (option d).

Let's perform row operations to bring the given augmented matrix into row-echelon form or reduced row-echelon form. The matrix we have is:

[12 5 -9 | 2]

[-2 4 -6 | 0]

[1 -3 6 | 1]

First, we will divide the first row by 12 to make the leading coefficient of the first row 1:

[1 5/12 -3/4 | 1/6]

[-2 4 -6 | 0]

[1 -3 6 | 1]

Next, we will eliminate the leading coefficient of the second row by adding 2 times the first row to the second row:

[1 5/12 -3/4 | 1/6]

[0 19/6 -15/2 | 2/3]

[1 -3 6 | 1]

Similarly, we will eliminate the leading coefficient of the third row by subtracting the first row from the third row:

[1 5/12 -3/4 | 1/6]

[0 19/6 -15/2 | 2/3]

[0 -19/12 27/4 | 1/6]

Now, we will divide the second row by (19/6) to make the leading coefficient of the second row 1:

[1 5/12 -3/4 | 1/6]

[0 1 -5/4 | 2/19]

[0 -19/12 27/4 | 1/6]

Next, we will eliminate the leading coefficient of the third row by adding 19/12 times the second row to the third row:

[1 5/12 -3/4 | 1/6]

[0 1 -5/4 | 2/19]

[0 0 6 | 9/19]

Finally, we will divide the third row by 6 to make the leading coefficient of the third row 1:

[1 5/12 -3/4 | 1/6]

[0 1 -5/4 | 2/19]

[0 0 1 | 3/38]

Now, we can read off the solution from the row-echelon form. The variables x, y, and z correspond to the entries in the last column. Therefore, the solution to the system of linear equations is x = 1, y = 0, and z = -2 (option d).


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Management by objectives (MBO) is a management system that incorporates goal setting as its central principle.

It emphasizes the establishment of clear, measurable objectives for individuals and teams within an organization, aligning their efforts with overall organizational goals and strategies. MBO provides a framework for performance management and evaluation, allowing managers and employees to work together to define objectives, set targets, and track progress towards achieving those goals.

The goal-setting aspect of MBO is supported by various theories and principles. Firstly, the concept of goal setting itself is a fundamental component of MBO. It is based on the idea that setting specific, challenging, and attainable goals can motivate individuals and enhance performance. The expectancy theory comes into play as well, as MBO assumes that individuals are motivated to achieve their goals when they believe that their efforts will lead to successful performance and desired central outcomes.

Additionally, cognitive dissonance theory suggests that MBO can help reduce cognitive dissonance by providing individuals with clear objectives and performance expectations, minimizing conflicts between their attitudes and behaviors. While hedonism and equity theory are not directly incorporated into MBO, they may indirectly influence individuals' motivation and satisfaction as they work towards their objectives within the MBO framework.

In summary, Management by Objectives (MBO) is a management system that revolves around goal setting. It incorporates various theories and principles such as goal setting theory, expectancy theory, and cognitive dissonance theory. By setting clear objectives, aligning efforts, and tracking progress, MBO provides a structured approach to performance management and encourages individuals and teams to work towards achieving organizational goals.

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Answer: 0%

Step-by-step explanation:

It's impossible for it to be different than 75 or 97

\(y=78^{\circ}\) (alternate interior angles theorem)

\(x=78^{\circ}\) (alternate segment theorem)

\(z=24^{\circ}\) (angles in a triangle add to 180 degrees)

Answer:

Tallahassee

Step-by-step explanation:

Answer:

Hello,

We don't need vw(x) !

\(w^{-1}(x)=\dfrac{x-1}{2}\)

Step-by-step explanation:

\(w(x)=2x+1=y\\\\2y+1=x \ exchanging \ x\ and\ y\\\\y=\dfrac{x-1}{2} \\\\w^{-1}(x)=\dfrac{x-1}{2}\)

Answer:

48

Step-by-step explanation:

It's given that Ava takes 4 breaths every 10 seconds.

4 breaths : 10 seconds. ...(1)

To solve this, first we need to calculate how many seconds there are in two minutes.

As 60 seconds make up one minute, 120 seconds make up two.

Now, to solve for the number of breaths (x), we just multiply (1) by 12. We do this so that we get 120 seconds on the right side, so the left side will give us the answer we need.

4 × 12 breaths : 10 × 12 seconds

48 breaths : 120 seconds.

So, the final answer would be 48 breaths.

Hope this helps! :D

Step-by-step explanation:

The conjugate of the complex root must also be a zero of the function if the complex root is already a zero.

Conjugate of -4 + 3i is -4 - 3i.

Hence -4 - 3i is also a zero of the function.

Answer:

-4 - 3i

Step-by-step explanation:

If a zero of a function is a+bi, there is at least one other zero, a-bi, called the conjugate.

\(f( - 4) = - 122\)

And

\(g(5) = - 21\)

Step-by-step explanation:

Greetings !

For the first expression

\(f(x) = 2x {}^{3} + 6\)

plug in -4 at the variable x and solve the expression.

\(f( - 4) = 2( - 4) {}^{3} + 6\)

Follow the PEMDAS order of operations

calculate the exponents

\(( - 4) {}^{3} = - 64\)

Apply exponent rule

\(( - a) {}^{n} = - a {}^{n} . \: if \: n \: is \: odd\)

Thus,

\(( - 4) {}^{3} = - 4 {}^{3} = - 64\)

Multiply and divide (left to right )

\(2( - 64) = - 128\)

\( = - 128 + 6 \\ = - 122\)

Fairly follow the same. process for the second function

Hope it helps !!

If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒  x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

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Carolyn's garden is in the shape of a parallelogram with a base of 3x^2 + 4x + 5 and a height of 48 - 9. The area of her garden can be calculated by multiplying the base and the height.



To determine the area of Carolyn's garden, we need to use the formula for the area of a parallelogram, which is given by the product of the base and the height. The base of the parallelogram is represented by the expression 3x^2 + 4x + 5, while the height is represented by the expression 48 - 9.

To find the area, we multiply the base and the height:

Area = (3x^2 + 4x + 5) * (48 - 9)

To simplify the expression, we can distribute the values within the parentheses:

Area = 3x^2 * 48 + 3x^2 * (-9) + 4x * 48 + 4x * (-9) + 5 * 48 + 5 * (-9)

Simplifying further, we have:

Area = 144x^2 - 27x^2 + 192x - 36x + 240 - 45

Combining like terms, we get:

Area = 117x^2 + 156x + 195

Therefore, the area of Carolyn's garden is given by the expression 117x^2 + 156x + 195.

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Answer:

Step-by-step explanation:

Nice question!!! It should be ####. and that's the answer that you want

Step-by-step explanation:

what is the difference between the x- values ?

and what is the difference between the y- values ?

a transformation means a simple shift. so, addition of subtraction. no multiplication or such.

1 to -1 ? -2

-1 to -3 ? -2

5 to 3 ? -2

6 to 6 ? 0

3 to 3 ? 0

-2 to -2 ? 0

so, the transformation is (-2, 0)

(0,0)

Step-by-step I took the test

Answer:

hello

the answer is Y>-5x-3

bye

Answer:

suchh harddb

Step-by-step explanation:

Answer:

Since the shape is an corresponding angle, you would work out the question like this:

(3x + 22) = (x + 30)

X = 4

Therefore X is equal to 4. No rounding is needed.

I'm NOT a math teacher, please double check my answer!

Cheers! :)

We would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g by using properties of the normal distribution.

To find the range in which you would expect to find the middle 68% of amounts of nicotine in these cigarettes, we can use the properties of the normal distribution.

Given:
Mean (μ) = 0.946 g
Standard deviation (σ) = 0.289 g

For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, we can expect the middle 68% of amounts of nicotine to fall within the range:

μ ± σ

Substituting the given values:

0.946 ± 0.289

To calculate the range, we have:

Lower bound = 0.946 - 0.289 ≈ 0.657 g
Upper bound = 0.946 + 0.289 ≈ 1.235 g

Therefore, we can expect to find the middle 68% of amounts of nicotine in these cigarettes to be between approximately 0.657 g and 1.235 g.

Now, if we were to draw samples of size 41 from this population, the standard deviation of the sample mean (also known as the standard error) can be calculated as:

Standard error (SE) = σ / √n

where σ is the population standard deviation and n is the sample size.

Substituting the given values:

SE = 0.289 / √41 ≈ 0.045 g

To find the range in which we would expect to find the middle 68% of the sample means, we multiply the standard error by 1 to capture approximately 68% of the data, giving us:

Lower bound = μ - SE ≈ 0.946 - 0.045 ≈ 0.901 g
Upper bound = μ + SE ≈ 0.946 + 0.045 ≈ 0.991 g

Therefore, we would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g.

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When finding local maxima and minima from the graph of a derivative, we need to identify the points where the derivative changes sign. These points represent the locations of local maxima and minima on the original function.

When finding local maxima and minima from the graph of a derivative, we need to understand the relationship between the original function and its derivative. The derivative of a function represents the rate of change of the function at any given point. Local maxima and minima occur where the derivative changes sign from positive to negative or from negative to positive. At these points, the slope of the original function changes from increasing to decreasing or from decreasing to increasing.

By following these steps, we can identify the local maxima and minima from the graph of a derivative.

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Identify the critical points, Determine the intervals, Analyze the sign changes and Check the endpoints

To find the local maximum and minimum points from the graph of a derivative, you can follow these steps:

Identify the critical points: These are the points where the derivative is either zero or undefined. Find the values of x where f'(x) = 0 or f'(x) is undefined.

Determine the intervals: Divide the x-axis into intervals based on the critical points and any other points of interest. Each interval represents a section of the graph where the derivative is either positive or negative.

Analyze the sign changes: Within each interval, observe the sign of the derivative. If the derivative changes sign from positive to negative, there is a local maximum at that point. If the derivative changes sign from negative to positive, there is a local minimum at that point.

Check the endpoints: Also, check the derivative's sign at the endpoints of the graph. If the derivative is positive at the leftmost endpoint and negative at the rightmost endpoint, there is a local maximum at the left endpoint. Conversely, if the derivative is negative at the leftmost endpoint and positive at the rightmost endpoint, there is a local minimum at the left endpoint.

By following these steps and analyzing the sign changes of the derivative within intervals, as well as checking the endpoints, you can identify the local maximum and minimum points from the graph of the derivative.

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answer:

\(x - y =4\)

steps shown below:

Answer:

the answer is d.8(/)(w)

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Mode: 60

Median: 30

Mean: 36.666

Step-by-step explanation:

Answer: (8.5, 8)

Step-by-step explanation:

The equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

What is Equation in Spherical Coordinates?

A mathematical equation that is represented in terms of the spherical coordinates of a point is known as an equation in spherical coordinates. A three-dimensional coordinate system known as spherical coordinates makes use of two angles, typically represented by symbols and a radial distance (r), and a coordinate system to find points in space.

\($r^2 = 81$\)

To represent the equation in spherical coordinates, we substitute the Cartesian coordinates \($x = r\sin(\phi)\cos(\theta)$, $y = r\sin(\phi)\sin(\theta)$, and $z = r\cos(\phi)$\) into the equation. After substitution and simplification, we have:

\($r^2\sin^2(\phi)\cos^2(\theta) + r^2\sin^2(\phi)\sin^2(\theta) + r^2\cos^2(\phi) = 81$\)

Since \(r^2 = 81,\) we can substitute it into the equation:

\($81\sin^2(\phi)\cos^2(\theta) + 81\sin^2(\phi)\sin^2(\theta) + 81\cos^2(\phi) = 81$\)

Finally, we divide the equation by 81 to simplify:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

So, the equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

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