What is the length of the midsegment of this trapezoid?
(In units, please!) :)

In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

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Answer: 0.5

Step-by-step explanation:

Given

Line passes through \((-10,-30), (0,-25), (10,-20), \text{and}\ (20,-15)\)

The slope of the line is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

Taking any two points: (0, -25) and (20,-15)

Slope is

\(\Rightarrow m=\dfrac{-15-(-25)}{20-0}=\dfrac{10}{20}\\\\\Rightarrow m=0.5\)

The value of x and y that will prove triangle ABC is congruent to DEF is 5 and 20 Respectively.

Congruent triangles have both the same shape and the same size. This means that if two angles have equal angles and equal length they are congruent.

Therefore;

48 = 9x+3

9x = 48 -3

9x = 45

divide both sides by 9

x = 45/9

x = 5

Angle D = angle C

angle D = 180-( 54+ 88)

= 180- 142

= 38

therefore ,

1.9y = 38

y = 38/1.9

y = 20

Therefore,the value of x and y that will prove triangle ABC is congruent to DEF is 5 and 20 Respectively.

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Answer: I need to see the picture of the shaded part to awnser

Step-by-step explanation:

The following formula is used: P(n,r) = n! / (n - r)! to the calculate  the number of permutations.

The formula used to calculate the number of permutations when a permutation is any arrangement of r objects

selected from n possible objects is P(n,r).

P(n,r) is the formula used to calculate the number of permutations.

Let us try to understand the concept of permutations first.

Permutations refer to the different ways of arranging elements.

It is represented as nPr called as n-permute-r.

Here, n represents the total number of elements present, and r represents the number of elements taken for each

permutation.

To calculate the number of permutations, the following formula is used:

P(n,r) = n! / (n - r)!

Where n! is equal to n-factorial that refers to the product of all numbers starting from 1 up to n.

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Answer:

the width of the path is 24m²

Answer:

Subtract 1 from both sides.

Answer:

subtract 1 from both sides. because taking out the 1 from 1 and 1 from 17 will equal 16. which leaves t/4=16

The domain of f is the range of f^-1, and the domain of f^ −1 is the range of f.

The domain of a function f consists of all possible input values that can be used as arguments for f to generate output values.

If we consider the inverse function of f, denoted as f^−1, it will swap the roles of the input and output values of f. In other words, if f(x) = y, then f^−1(y) = x.

Therefore, the domain of f^−1 is equal to the range of f, which consists of all possible output values generated by f for any valid input value. This is because any output value of f can be used as an input value for f^−1.

Similarly, the range of f^−1 is equal to the domain of f, which consists of all possible input values that can be used as arguments for f to generate output values. This is because any valid input value of f can be used as an output value for f^−1.

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-16  is the of x in the given expression.

To solve for x in the equation:

16x + 24/4 = -5(2 - 3x)

We can start by simplifying the equation using the order of operations (PEMDAS) and basic algebraic properties.

16x + 6 = -10 + 15x (distribute -5)

6 = -10 - x (move 15x to the left, and 16x to the right)

16 = -x (subtract 6 from both sides)

x = -16 (multiply both sides by -1)

Therefore, the solution to the equation is x = -16.

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The Ramsey Regression Equation Specification Error Test (RESET) test is a general specification test for the linear regression model. More specifically, it tests whether non-linear combinations of the fitted values help explain the response variable.

The test's underlying assumption is that the model is misspecified if non-linear combinations of the explanatory variables have any effect on explaining the response variable, suggesting that a polynomial or other non-linear functional form might be a better approximation for the process of generating the data.

If the functional form of the regression is acceptable, it will pass Ramsey's RESET test. To put it another way, we examine if a linear relationship between the dependent variable and the independent factors is indeed necessary or whether a non-linear form would be preferable.

Hence for the above reasons ramsey regression specification error test (reset) test is one of the ideal way for identifying the nonlinearity.

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To determine the number of steps on the stepper motor, we can divide the total rotation angle (6480°) by the step angle (3°).

Number of steps = Total rotation angle / Step angle

Number of steps = 6480° / 3°

Number of steps = 2160

Therefore, the stepper motor has 2160 steps if each step angle is 3°.

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Answer:

Step-by-step explanation:

A reflection across the line y = x will not carry the square onto itself, since the vertex (0, 2) would be reflected to (2, 0) which is not a vertex of the original square.

A reflection across the line y = -x would also not carry the square onto itself, since the vertex (0, 2) would be reflected to (−2, 0) which is not a vertex of the original square.

However, a reflection across the x-axis would carry the square onto itself since all of the vertices lie in the same quadrant, and reflecting across the x-axis does not change their signs.

A 45° or 90° rotation about the origin would also carry the square onto itself since the square has rotational symmetry of order 4.

Therefore, the correct answers are C, D, and E.

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

The length of the base edge of the square pyramid is 6 feet.

The surface area of a square pyramid is 96 square feet. The height is two thirds of the length of the base edge.

The length of the base edge can be found as follows:

Hence,

surface area of square pyramid = a² + 2al

where

Therefore,

using Pythagoras's theorem, let find the slant height of the pyramid.

c² = a² + b²

where

Hence,

height = 2 / 3 a

Therefore,

l² = (2 / 3 a)² + (1 / 2a )²

l² = 4 / 9 a² + 1 / 4 a²

l² = 25 / 36 a²

square root both sides

l = 5 / 6 a

Hence,

surface area of square pyramid = a² + 2a(5 / 6 a)

surface area of square pyramid = a² + 10 / 6 a²

surface area of square pyramid = 16 / 6 a²

96 = 16 / 6 a²

96 = 8 / 3 a²

cross multiply

96 × 3 = 8a²

288 / 8 = a²

a² = 36

a = √36

a = 6 feet

Therefore, the base length is 6 feet.

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Using the monthly payment formula, it is found that the amount he will have to pay each month is of $649.45.

It is given by:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

In this problem, considering that the down payment does not count for interest, the parameters are given as follows:

P = 130000, r = 0.0438, n = 30 x 12 = 360.

Then:

r/12 = 0.0438/12 = 0.00365 -> 1+r = 1.00365.

Then the monthly payment is given by:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

\(A = 130000\frac{0.00365(1.00365)^{365}}{(1.00365)^{365} - 1}\)

A = 649.45.

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Answer:The square below represents one whole.

What percent is represented by the shaded area?

Step-by-step explanation:

Answer: Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.

m(slope)=7/10 or (7,10)

General form y= ax^2+bx+c

standard form y = a(x-h)^2+k

where

(h,k)= vertex = (7,2)

Since the zero are at -1 and 15 we have the points

(-1,0) and (15,0)

We will use one of the points (-1,0) and the vertex in the general form:

0= a(-1-7)^2+2

0= a(-8)^2+2

0= a64+2

-2 =a64

-2/64 =a

-1/32 =a

y= -1/32 (x-7)^2+2

y =-1/32 (x-7)(x-7)+2

y= -1/32 (x^2-14x+49)+2

y= -1/32 x^2+7/16x-49/32+2

y= -1/32x^2+7/16x-113/32

The derivative of y with respect to x, dy/dx, is equal to 2xye^(x^2y).The given expression is e^(x^2y) - e^y = y. To find dy/dx, we differentiate both sides of the equation implicitly.

To find the derivative dy/dx, we differentiate both sides of the given equation. Using the chain rule, we differentiate the first term, e^(x^2y), with respect to x and obtain 2xye^(x^2y).

The second term, e^y, does not depend on x, so its derivative is 0. Differentiating y with respect to x gives us dy/dx.

Combining these results, we have 2xye^(x^2y) = dy/dx. Therefore, the derivative of y with respect to x, dy/dx, is equal to 2xye^(x^2y).


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Answer:80

Step-by-step explanation:

first, we can find out angle dbf which is 80 as angles on a straight line sum to 180, then we can enforce the alternate angles concept

Answer:

$2.90 %Step-by-step explanation:

because if you round it it would be close to 90 and if you mutiply 2 x 2 =4 x 89

point B is located in quadrant II (option B)

Point A: (6, 3) = (x, y)

reflection of point A across the y axis:

The x coordinate will be negative and the y coordinate will remain the same

reflection of point A across the y axis = (-6, 3)

Attaching the graph showing the point after reflection:

Since point B is the reflection of point A.

Hence, point B is located in quadrant II (option B)

The function f(x) = -6.7sin(x)5.8cos(x) represents a periodic function with a combination of sine and cosine terms. Tthe maximum value of the given function f(x) is 38.86, and the minimum value is -38.86.

1. To find the maximum and minimum values of this function, we need to examine the behavior of both the sine and cosine functions.

2. In the given function, the sine and cosine terms are multiplied together. Since the maximum absolute value of the sine function is 1 and the maximum absolute value of the cosine function is also 1, the maximum absolute value of their product is 1.

3. Therefore, the maximum value of the function occurs when the product of the sine and cosine terms is positive and equal to 1. In this case, the maximum value of the function is 6.7 * 5.8 = 38.86.

4. Similarly, the minimum value of the function occurs when the product of the sine and cosine terms is negative and equal to -1. In this case, the minimum value of the function is -6.7 * 5.8 = -38.86.

5. In summary, the maximum value of the given function f(x) is 38.86, and the minimum value is -38.86. These values are obtained when the product of the sine and cosine terms is equal to 1 and -1, respectively.

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Answer:

Step-by-step explanation:

We had a rectangle with dimensions 12 in x 6 in

We cut 2 in x 2 in squares from each corner and fold up.

We end up with the rectangle with dimensions:

a) It gives us one side which is x. If we assume x is the length, then the width is x - 6.

The area is:

b) The small square with side of y, has an area:

c) We subtract the side length of y from the both sides.

The sides of smaller rectangle are:

The area:

Answer:

This is going to be deleted but thanks for the points

Step-by-step explanation:

Answer:

thank u so much !!!!

have a blessed day !!!

Answer:

PQ ≈ 9.4 cm

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = P(- 4, - 2) and (x₂, y₂ ) = Q(4, 3)

PQ = \(\sqrt{(4+4)^2+(3+2)^2}\)

     = \(\sqrt{8^2+5^2}\)

     = \(\sqrt{64+25}\)

     = \(\sqrt{89}\)

     ≈ 9.4 cm ( to 1 dec. place )

Answer:

the square root of 89 is 9.4 so thats your answer

Step-by-step explanation: