Find the average rate of change of the function on the interval specified for real number h in the simplest form: f(x)=2x−5 on [2,2+h]

Answer: x=2

Step-by-step explanation:

Given AC = 2x+9 and BD = 7x-1

AC=BD,

2x+9 = 7x-1

10=5x

x=10/5 = 2

Answer:

$1.79

Step-by-step explanation:

h + 5f = 8.74 → (1)

2h + 3f = 7.75 → (2)

Multiplying (1) by 3 and (2) by - 5 and adding will eliminate f

3h + 15f = 26.22 → (3)

- 10h - 15f = - 38.75 → (4)

Add (3) and (4) term by term to eliminate f

- 7h = - 12.53 ( divide both sides by - 7 )

h = 1.79

The hamburger cost $1.79

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

Yes, it can. Triangles [in order for them to be one] must equal 180. If you add all of these angles together, since a triangle only has three angles anyway, it equals to 180, so you know it's a triangle.

If this was confusing, I am happy to help further!

The new limits of integration for the given integral are L = ∫∫L = ∫∫(u, v) ∈ unit circle.

To evaluate the given integral using the given transformation, we need to find the new limits of integration (L) after performing the transformation.

The transformation provided is:

x = √(8/11)u - √(8/29)v

y = √(8/11)u - √(8/29)v

We are given that the region R is bounded by the ellipse equation: \(10x^2 - 9xy + 10y^2 = 8.\)

Substituting the values of x and y from the transformation into the equation of the ellipse, we have:

\(10(√(8/11)u - √(8/29)v)^2 - 9(√(8/11)u - √(8/29)v)(√(8/11)u - √(8/29)v) + 10(√(8/11)u - √(8/29)v)^2 = 8.\)

Simplifying this equation, we get:

8u^2 + 8v^2 = 8.

Dividing both sides by 8, we have:

\(u^2 + v^2 = 1.\)

This represents the unit circle in the uv-plane. Thus, the transformed region L corresponds to the unit circle.

Therefore, the new limits of integration for the given integral are L = ∫∫L = ∫∫(u, v) ∈ unit circle.

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Answer:  Decreasing, if it "Halves (cuts in half)". If it was increasing, it would probably say double.

Step-by-step explanation:

So, if it was being cut in half every two days, we would only be counting days 2, 4, and 6.

So days 2, it would be cut in half, and go from 500 to 250. Day 4, it would go from 250 to 125. The day 6, it would go from 125 to 62.5.

In 6 days, the investment will be worth $62.50

To find the partial sum S₁7 for the arithmetic sequence with a first term (a) of 3 and a common difference (d) of 2, we can use the formula for the sum of an arithmetic sequence. Therefore, the partial sum S₁7 for the arithmetic sequence with a first term of 3 and a common difference of 2 is 323.

The formula for the sum of an arithmetic sequence is given by:

Sn = (n/2)(2a + (n-1)d)

In this case, we want to find the partial sum S₁7, which means we need to substitute n = 17 into the formula.

Plugging in the values, we have:

S₁7 = (17/2)(2(3) + (17-1)(2))

Simplifying the equation inside the parentheses, we get:

S₁7 = (17/2)(6 + 16(2))

Simplifying further:

S₁7 = (17/2)(6 + 32)

S₁7 = (17/2)(38)

Finally, evaluating the expression, we have:

S₁7 = 17(19)

S₁7 = 323

Therefore, the partial sum S₁7 for the arithmetic sequence with a first term of 3 and a common difference of 2 is 323.

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The equations that are equivalent to the equation 3x - 4 = 5 are -

3x = 9

3x - 4 + 4 = 5 + 4

- 4 = 5 - 3x

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given is the following equation -

3x - 4 = 5

The given is a linear equation in one variable.

We can write it the following possible ways -

3x = 9

3x = 5 + 4

3x - 4 = 5

3x - 4 + 4 = 5 + 4

3x = 9

3x - 4 = 5

- 4 = 5 - 3x

Rearranging -

3x - 4 = 5

Therefore,  the equations that are equivalent to the equation 3x - 4 = 5 are -

3x = 9

3x - 4 + 4 = 5 + 4

- 4 = 5 - 3x

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Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

To determine which point is a solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2, we can test each point to see if it satisfies both inequalities.

a) Point E at (4, -2):

Substituting the coordinates into the inequalities:

-2 > -2(4) + 10 -> -2 > -8 + 10 -> -2 > 2 (False)

-2 > (1/2)(4) - 2 -> -2 > 2 - 2 -> -2 > 0 (False)

b) Point K at (2, 3):

Substituting the coordinates into the inequalities:

3 > -2(2) + 10 -> 3 > -4 + 10 -> 3 > 6 (False)

3 > (1/2)(2) - 2 -> 3 > 1 - 2 -> 3 > -1 (True)

c) Point B at (4, 7):

Substituting the coordinates into the inequalities:

7 > -2(4) + 10 -> 7 > -8 + 10 -> 7 > 2 (True)

7 > (1/2)(4) - 2 -> 7 > 2 - 2 -> 7 > 0 (True)

d) Point D at (-7, 1):

Substituting the coordinates into the inequalities:

1 > -2(-7) + 10 -> 1 > 14 + 10 -> 1 > 24 (False)

1 > (1/2)(-7) - 2 -> 1 > -3.5 - 2 -> 1 > -5.5 (True)

Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

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Answer:

(-18, 0)

Step-by-step explanation:

The x intercept has a y value of 0. So, to find the x intercept, plug in 0 as y into the equation, and solve for x:

y = 2/3x + 12

0 = 2/3x + 12

-12 = 2/3x

-18 = x

So, the x intercept is (-18, 0)

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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Step-by-step explanation:

\( \underline{ \underline{ \text{Given}} }: \)

\( \underline{ \underline{ \text{To \: find}}} : \)

Let E ( -3 , 2 ) be ( x₁ , y₁ ) & H ( 1 , -1 ) be ( x₂ , y₂ )

\( \underline{ \underline{ \text{Solution}}} : \)

\( \sf{Midpoint = ( \frac{x_{1} + x_{2}}{2} \: , \frac{ y_{1} + y_{2}}{2} )}\)

⟶ \( \sf{( \frac{-3 + 1}{2} \: , \frac{2 + ( - 1)}{2} )}\)

⟶ \( \sf{( \frac{-2}{2} \:, \frac{2 - 1}{2} )}\)

⟶ \( \sf{( -1 \: ,\frac{1}{2} )}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{(-1 \: , \: \frac{1}{2} )}}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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The approximation for the integral using five equal subintervals is 88.

To approximate 5 ∫ -5 (2+x²) dx using five equal subintervals, we can use the midpoint rule. This rule states that the integral can be approximated by the sum of the areas of rectangles whose heights are the function evaluated at the midpoint of each subinterval and whose widths are the subinterval lengths.

First, we need to find the width of each subinterval. The total interval width is 10 (from -5 to 5) and we want to divide it into five equal subintervals, so each subinterval has a width of 2.

Next, we need to find the midpoints of each subinterval. Starting from the left endpoint, the midpoints are -4, -2, 0, 2, and 4.

Now we can evaluate the function at each midpoint and calculate the area of the corresponding rectangle. The height of each rectangle is the function evaluated at the midpoint, which gives us:

f(-4) = 18, f(-2) = 6, f(0) = 2, f(2) = 6, f(4) = 18

The area of each rectangle is the height times the width, which is 2. Therefore, the total approximation is:

(18)(2) + (6)(2) + (2)(2) + (6)(2) + (18)(2) = 88

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Answer:  C

Step-by-step explanation:

A. is wrong, only 6 students liked pineapple and 12 bacon, so they did not prefer pineapple to bacon

B. is wrong,  the most students liked was not cheese, it was pepperoni

C. is correct, pineapple is the least liked at 6 student

D. is wrong, not all the students liked pepperoni, some students liked other things

Answer:\(98.13\ \text{or}\ 261.87^{\circ}\)

Step-by-step explanation:

Given

\(\cos \beta =-\dfrac{\sqrt{2}}{10}\)

As the value of cosine is negative, therefore the angle must lie in II or III quadrant

\(\Rightarrow \beta =\cos^{-1}(-\dfrac{\sqrt{2}}{10})\\\Rightarrow \beta=\cos^{-1}(-0.14142)\\\Rightarrow \beta =98.13^{\circ}\ \text{or}\ 270^{\circ}-8.13\\\Rightarrow \beta=98.13^{\circ}\ \text{or}\ 261.87^{\circ}\)

Oregon has 5 golf course per 100,000 people.

The butterfly method for adding or subtracting fractions is:

Write the fractions side by side as you normally would, but this time draw two wings along the diagonals formed by the numerator of one fraction and the denominator of the other fraction.

Multiply the numbers in each wing as shown by the wings, which resemble a multiplicand.

To give it a body, join the lower halves of the wings together to form a loop that resembles a body. Then, multiply the two denominators it joins to place the result within the body.

Adjust the numbers in the antennas in accordance with how fractions are being altered, then add or subtract the resulting value from the body number.

If required, simplify or minimize the outcome.

Given that the golf course for 4301089 people is 190.

4201089 = 190

100000 = x

Using the butterfly method for multiplication we have:

x = 190 * 100000 / 4201089

x = 5

Hence, Oregon has 5 golf course per 100,000 people.

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Answer: The correct answer is C. It represents a function only.

A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.

In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.

Step-by-step explanation:

Answer:

D. It represents both a relation and a function

Hope this helps!

Step-by-step explanation:

All functions are relations, but not all relations are functions. The equation given is an Exponential function.

Point F=(3;2) I think so

The value of the piecewise function f(x) at x = 5 is (b) 29

From the question, we have the following parameters that can be used in our computation:

Part 1:

f(x) = x cubed for x less than negative 3

Part 2:

f(x) = 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4,

Part 3

f(x) = 5 times x plus 4, for x greater than or equal to 4

When the above statements are represented properly, we have the following equations

Part 1: f(x) = x³ for x < -3

Part 2: f(x) = 2x² - 9 for -3 ≤ x < 4

Part 3: f(x) = 5x + 4, for x ≥ 4

To calculate the function f(5), we use the domain

x ≥ 4

So, we have the following function

f(x) = 5x + 4

Substitute the known values in the above equation, so, we have the following representation

f(5) = 5(5) + 4

Evaluate the expression

f(5) = 29

Hence, the value is (b) 29

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The marginal revenue function is R'(z) = -0.092 dollars, the marginal cost function is C'(z) = 75 - 0.16z dollars, and the marginal profit function is P'(z) = 0.16z - 75.092 dollars.

The given revenue function is R(z) = 1052 - 0.092z dollars.

Differentiating R(z) with respect to z, we get the marginal revenue function:

R'(z) = -0.092

The given cost function is C(z) = 1000 + 75z - 0.08z² dollars.

Differentiating C(z) with respect to z, we get the marginal cost function:

C'(z) = 75 - 0.16z

The profit function is given by P(z) = R(z) - C(z).

Differentiating P(z) with respect to z, we get the marginal profit function:

P'(z) = R'(z) - C'(z)

      = -0.092 - (75 - 0.16z)

      = -0.092 - 75 + 0.16z

      = 0.16z - 75.092

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Answer:

2 imaginary solutions

Step-by-step explanation:

No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.

The SSS congruence theorem  expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.

Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.

From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.

Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.

So, given triangle is proved to congruent by SAS congruency not by SSS congruency.

Hence, enough information is not given.

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Answer:

52 degrees

Step-by-step explanation:

a line is 180 degrees so just subtract 128 from 180 which is 52

Answer:

b)

Step-by-step explanation:

i hope this help you

Sigma factors are necessary in the initiation phase of transcription. This phase requires a complex called RNA polymerase to locate the DNA's start site and begin the synthesis of a new RNA strand.

RNA polymerase recognizes promoters, which are DNA sequences adjacent to the transcription start sites that define the start site for RNA synthesis. Sigma factors are subunits of RNA polymerase that help it recognize promoters.Sigma factors regulate the initiation of RNA synthesis by RNA polymerase.

The sigma factor is a DNA-binding protein that recognizes specific promoter sequences and recruits RNA polymerase to the DNA molecule at the appropriate location. When the sigma factor binds to a promoter, RNA polymerase becomes anchored and initiates transcription. There are several sigma factors, each of which recognizes a different promoter sequence.

They are required for transcription of different sets of genes in response to environmental cues or other cellular stimuli.It is worth noting that the promoter sequence that sigma factors bind to can vary in terms of its similarity to the consensus sequence recognized by the sigma factor.

Sigma factors can also recognize alternative promoter sequences that bind to the RNA polymerase core enzyme with lower affinity than the consensus sequence. In general, a promoter with a perfect match to the consensus sequence is more effective than one with a non-perfect match in initiating transcription.

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Answer:

\((a)\ 257 * [-1] =-257\)

\((b)\ (-30) * [9] =-270\)

(c) The additive inverse of -21 is 21

\((d)\ 918 *[0]=0\)

\((e)\ (-56) * [(-9)+(-1)] = 560\)

Step-by-step explanation:

Required

Fill in the blanks

Represent all blanks with x

\((a)\ 257 * x =-257\)

Divide both sides by 257

\(x =\frac{-257}{257}\)

\(x = -1\)

So:

\((a)\ 257 * [-1] =-257\)

\((b)\ (-30) * x =-270\)

Divide both sides by -30

\(x =\frac{-270}{-30}\)

\(x = 9\)

So:

\((b)\ (-30) * [9] =-270\)

(c)The complete question here is to determine the additive inverse of (-21)

The \(additive\) \(inverse\) of a \(number\) x is -x

So:

\((-21) \to -(-21)\)

\((-21) \to 21\)

\((d)\ 918 *x=0\)

Divide both sides by 918

\(x=\frac{0}{918}\)

\(x = 0\)

So:

\((d)\ 918 *[0]=0\)

\((e)\ (-56) * [(-9)+(-1)] = x\)

Solve the inner brackets

\((-56) * [-9-1] = x\)

\((-56) * [-10] = x\)

Multiply

\(560 = x\)

So:

\((e)\ (-56) * [(-9)+(-1)] = 560\)