Find the slope of the tangent line for the curve r=8+4cosθr=8+4cosθ when θ=π6θ=π/6.

The missing number in the median set is 6.

We are given that;

Median set=18

Now,

To find the missing number, you need to know the number of elements in the set and their order. The median is the middle value of a set when it is arranged in ascending or descending order. If the set has an odd number of elements, the median is the exact middle value. If the set has an even number of elements, the median is the average of the middle two values.

For example, if the set is {2, 4, 6, 8, 10}, the median is 6 because it is the middle value. If the set is {3, 5, 7, 9}, the median is (5 + 7) / 2 = 6 because it is the average of the middle two values.

Therefore, by median the answer will be 6.

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Answer:

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

Step-by-step explanation:

Given:

\(R = (0,0)\)

\(S= (8,4)\)

\(T = (-2,3)\)

First, we have that the line is parallel to RS.

This means that the line has the same slope as RS and the slope of RS is calculated as follows:

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

\(m = \frac{4-0}{8-0}\)

\(m = \frac{4}{8}\)

\(m = \frac{1}{2}\)

So, the line has a slope of \(m = \frac{1}{2}\)

Next, we have that the line passes through \(T = (-2,3)\).

The equation of the line is then calculated using the following formula

\(y - y_1 = m(x - x_1)\)

\(y - 3 = \frac{1}{2}(x - (-2))\)

\(y - 3 = \frac{1}{2}(x +2)\)

Open bracket

\(y - 3 = \frac{1}{2}x +1\)

Make y the subject

\(y = \frac{1}{2}x +1+3\)

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

Answer:

n = (3/8)x+(45/8)

Step-by-step explanation:

3x+5 = 4(n-5)*(6/3)

Is this written correctly?

3x+5 = 4(n-5)*(6/3)

3x+5 = 8(n-5)      [Simplify: {4*(6/3) = 8)]

3x+5 = 8n-40      [Expand the parentheses]

8n-40 = 3x+5      [Rearrange]

8n = 3x+5 + 40    [Rearrange]

8n = 3x+45          [Simplify]

n = (3x+45)/8       [Divide both sides by 8]

n = (3/8)x+(45/8)    [Rearrange]

Answer:

No its correct x=25

Step-by-step explanation:

It is a rectangular region with u and v values ranging from 1 to 2.

To find the Jacobian of the transformation x = 3u, y = 2uv, we need to compute the partial derivatives ∂x/∂u, ∂x/∂v, ∂y/∂u, and ∂y/∂v.

Given:

x = 3u

y = 2uv

Calculating the partial derivatives:

∂x/∂u = 3

∂x/∂v = 0 (since x does not depend on v)

∂y/∂u = 2v

∂y/∂v = 2u

Now, we can construct the Jacobian matrix J:

J = [∂x/∂u   ∂x/∂v]

   [∂y/∂u   ∂y/∂v]

Substituting the partial derivatives we calculated earlier:

J = [3   0]

   [2v  2u]

Therefore, the Jacobian of the transformation is:

J = [3   0]

   [2v  2u]

To sketch the region described by the inequalities g: 3 < 3u < 6, 2 < 2uv < 4, we can consider the ranges of u and v that satisfy these conditions.

From the inequality 3 < 3u < 6, we have:

1 < u < 2

From the inequality 2 < 2uv < 4, we can divide both sides by 2:

1 < uv < 2

Since u and v must both be greater than 1, we can determine the range of v:

1 < v < 2

Now, we can sketch the region in the u-v plane bounded by the conditions:

1 < u < 2

1 < v < 2

It is a rectangular region with u and v values ranging from 1 to 2.

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Answer:

true

Step-by-step explanation:

Go faster 50 for insurance And 40 per hour

Blaster Jet Ski 70 for insurance and 30 per hour

50 + 40x = 70 + 30x

x is the hours

10 x = 20

x = 2

after 2 hours both will charge the same amount of money .

Step-by-step explanation:

Top dashed box:

AC is congruent to itself by: reflexive property of congruence

Bottom left dashed box:

Angles DAC & BCA are congruent, and angles ACD and BAC are congruent by: alternate interior angles

Bottom middle dashed box:

Triangles ACD and CAB are congruent by: ASA

Bottom right dashed box:

Segments AB and CD are congruent, and segments AD and BC are congruent by: CPCTC

Answer:

-2x - 6 < -8

Step-by-step explanation:

when the first one is smiplfid it gives us   x<−2

when the second one is smiplfid it gives us    x>1 which means it's correct because 8 is greater than 1

plz mark brainliest

Answer:

(  −∞  ,  −2  )  ∪  (  1  ,  ∞  )

Step-by-step explanation:

5x + 3 < -7  →  x  <  −2    → (  −∞  ,  −2  )  

-2x - 6 < -8  → x  >  1        →  (  1  ,  ∞  )

5x + 3 < -7 or -2x - 6 < -8 → x  <  −2  or  x  >  1 →  (  −∞  ,  −2  )  ∪  (  1  ,  ∞  )

Graph 1)   5x + 3 < -7

Graph 2)  -2x - 6 < -8

Graph 3)  5x + 3 < -7 or -2x - 6 < -8

Answer:

the unit of length ,mass , and time are same in both the system , thus, the SI system is the extended from of MKS system.

and why is the subject math lol

we can express cos 115 degrees as cos 25 degrees, which is a function of a positive acute angle

To express cos 115 degrees as a function of a positive acute angle, we can use the concept of reference angles.

The reference angle is the positive acute angle formed between the terminal side of an angle and the x-axis. It is the smallest angle between the terminal side and the x-axis.

To find the reference angle for 115 degrees, we subtract 90 degrees from 115 degrees:

Reference angle = 115 degrees - 90 degrees = 25 degrees

Since cosine is an even function, the cosine of the reference angle will be the same as the cosine of the original angle:

cos 115 degrees = cos 25 degrees

Therefore, we can express cos 115 degrees as cos 25 degrees, which is a function of a positive acute angle.

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(a) The curve defined by the parametric equations x = t^2, y = -1/4t (t > 0) represents a parabolic trajectory, the point of intersection between the curve and the hyperbola is (4∛2, -1/(4∛2)).

To find the points on the curve where the tangent line is parallel to the line y = x, we need to determine when the slope of the tangent line is equal to 1.

The slope of the tangent line is given by dy/dx. Using the chain rule, we can calculate dy/dt and dx/dt as follows:

dy/dt = d/dt(-1/4t) = -1/4

dx/dt = d/dt(\(t^2\)) = 2t

To find when the slope is equal to 1, we equate dy/dt and dx/dt:

-1/4 = 2t

t = -1/8

However, since t > 0 in this case, there are no points on the curve where the tangent line is parallel to y = x.

(b) To determine the points on the curve where it intersects the hyperbola xy = 1, we can substitute the parametric equations into the equation of the hyperbola:

\((t^2)(-1/4t) = 1 \\-1/4t^3 = 1\\t^3 = -4\\\)

Taking the cube root of both sides, we find that t = -∛4. Substituting this value back into the parametric equations, we get:

x = (-∛4)^2 = 4∛2

y = -1/(4∛2)

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Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

a. The class width for all intervals in this frequency distribution is 3.

b. Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

c. Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

The number of full oscillations that any wave element performs in one unit of time is how we determine the frequency of a sinusoidal wave.

To find the class width, class midpoints, and class boundaries for the given frequency distribution, let's analyze the temperature intervals and frequencies:

Temperature (°F)    Frequency

32-35                      1

36-39                      3

40-43                      5

44-47                      11

48-51                      7

52-55                      7

56-59                      1

(a) Class width:

The class width is the difference between the upper and lower boundaries of each temperature interval. In this case, all the intervals have the same width.

Class width = Upper boundary - Lower boundary

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class width = 35 - 32 = 3

The class width for all intervals in this frequency distribution is 3.

(b) Class midpoints:

The class midpoint is the average value of the upper and lower boundaries of each interval. It represents the central value of the interval.

Class midpoint = (Upper boundary + Lower boundary) / 2

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35.

Class midpoint = (35 + 32) / 2 = 33.5

Calculating the class midpoints for all intervals, we get:

32-35: 33.5

36-39: 37.5

40-43: 41.5

44-47: 45.5

48-51: 49.5

52-55: 53.5

56-59: 57.5

(c) Class boundaries:

The class boundaries are the values that separate each interval. They are calculated by adding or subtracting half of the class width from the upper and lower boundaries.

For example, in the first interval (32-35), the lower boundary is 32 and the upper boundary is 35, and the class width is 3.

Lower class boundary = Lower boundary - (0.5 * class width) = 32 - (0.5 * 3) = 32 - 1.5 = 30.5

Upper class boundary = Upper boundary + (0.5 * class width) = 35 + (0.5 * 3) = 35 + 1.5 = 36.5

Calculating the class boundaries for all intervals, we get:

32-35: 30.5-36.5

36-39: 34.5-39.5

40-43: 38.5-43.5

44-47: 42.5-47.5

48-51: 46.5-51.5

52-55: 50.5-55.5

56-59: 54.5-59.5

Note: The class boundaries are inclusive of the lower boundary and exclusive of the upper boundary.

These are the calculations for the class width, class midpoints, and class boundaries for the given frequency distribution.

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To find the class width, subtract the lower class limit from the upper class limit. To find the class midpoints, add the lower and upper class limits and divide by 2. To find the class boundaries, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit.

(a) Class width:

To find the class width, we subtract the lower class limit from the upper class limit. For example, the class width for the first class interval (32-35) is 35 - 32 = 3.

(b) Class midpoints:

To find the class midpoints, we add the lower class limit and the upper class limit and divide the sum by 2. For example, the class midpoint for the first class interval (32-35) is (32 + 35) / 2 = 33.5.

(c) Class boundaries:

To find the class boundaries, we subtract 0.5 from the lower class limit and add 0.5 to the upper class limit. For example, the class boundaries for the first class interval (32-35) are (32 - 0.5) and (35 + 0.5).

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Answer: Natasha is 17 and Ravi is 25

Step-by-step explanation:

Let n = Natasha’s age and r = Ravi’s age

We can write an equation then substitute: 42=n+r

We know that Ravi is 8 years older than Natasha, so Ravi’s age is equal to n+8. We can substitute that in, so 42= n+(n+8)

Simplify:

42=n+(n+8)

42= 2n+8

42-8=2n+8-8 (subtract 8 from both sides to isolate n)

34=2n

34/2=2n/2 (divide both sides by two)

17=n

Natasha is 17, and Ravi is 8 years older. 17+8= 25, Ravi is 25. You can double check by adding 25 and 17 together, which brings you back to 42 :]

Answer:

n = x + 8

Step-by-step explanation:

Using the rules of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\((a^m)^{n}\) = \(a^{mn}\)

Then

\(3^{x}\) × \(9^{4}\) = \(3^{n}\)

\(3^{x}\) ×\((3^2)^{4}\) = \(3^{n}\)

\(3^{x}\) × \(3^{8}\) = \(3^{n}\)

\(3^{x+8}\) = \(3^{n}\)

Since bases on both sides are equal, both 3, then equate exponents

n = x + 8

Answer:

\(-\frac{5}{7}\)

Step-by-step explanation:

3--2/-6-1=

3+2/-7

5/-7

Answer:

5/-7

Step-by-step explanation:

y2-y1/x2-x1

3-(-2)/-6-1 = 5/-7

Answer:

\(the \: two\: numbes \: are : \\ 7.777 \: and \: - 2.099\)

Step-by-step explanation:

\(let \: the \: two \: numbers \: be : x \: and \: y \\ x + y = 5.678.....eq(1) \\ x - y = 9.876 .....eq(2)\\ x = 9.876 + y....from \: eq(2) \\ y = 5.678 - x....frm \: eq(1) \\ eq \:...y \: in \: terms \: o f\: x : \\ x = 9.876 + 5.678 - x \\ 2x = 15.554 \\ x = 7.777 \\ y = 5.678 - x = y = 5.678 - 7.777 \\ y= - 2.099.\)

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

I'm pretty sure the answer is F

Answer:

IS F

Step-by-step explanation:

I already did this work.

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

The expression to represent the total area as the sum of the areas of each room would be:

Total area = area of kitchen + area of bathroom + area of remaining space

Total area = 7 x 11 + 4 x 11 + (11 - 7 - 4) x 11

Total area = 77 + 44 + 11

Total area = 132 square feet

(x + 6) (3x - 2)

x (3x - 2) + 6 (3x - 2)

3x² - 2x + 18x - 12

3x² + 16x - 12

Therefore, (x + 6) (3x - 2) as a trinomial is 3x² + 16x - 12

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Researchers must carefully consider their choice of words to avoid bias and ensure a more accurate representation of the responses. 

a. The wordings of the questions contain the word "destroyed" and "80 acres per minute," which could cause the respondent to exaggerate the severity of the issue. Therefore, they may respond with strong negative reactions.

b. The question contains the phrase "vanishing tropical forests," which could cause the respondent to exaggerate the severity of the issue. Therefore, they may respond with strong negative reactions.

c. The question is loaded with the phrase "man-made extinction of animal and plant species," hence, the respondents could lean more towards the idea of the need to prevent it. The question is likely to elicit responses directed toward prevention and preservation.

d. The question contains the phrase "changes in the earth’s atmosphere," which suggests a link between the destruction of tropical forests and changes in the earth’s atmosphere. The question is likely to elicit responses that lean towards agreeing with the statement made in the question. 

Therefore, researchers must carefully consider their choice of words to avoid bias and ensure a more accurate representation of the responses. 

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Answer:

-0.2x

Step-by-step explanation:

-0.2*sqrt(x^2)

-0.2x

The slope of the line m is -2 if the line passes through (4, -3) and (0, 5) the answer is -2.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

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

From the graph:

(4, -3) and (0, 5)

The slope of the line m = (5+3)/(-4)

The slope of the line m = -2

Thus,  the slope of the line m is -2 if the line passes through (4, -3) and (0, 5) the answer is -2.

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Answer:  heres the answer, i just finished the quiz

Therefore, H(t) is increasing on the intervals (-∞, -1/\(\sqrt7\)) and (\(1/\sqrt7\), ∞) and decreasing on the interval (\(-1/\sqrt7\), \(1/\sqrt7\)).and There are no local or absolute maximum values for H(t).

To find the intervals on which the function H(t) is increasing or decreasing, we need to take the first derivative of H(t) and find its critical points.

a.) First derivative of H(t):

\(H'(t) = 12t^11 - 84/7t^13\)

\(= 12t^11(1 - 7t^2)/7t^2\)

The critical points are where H'(t) = 0 or H'(t) is undefined.

So, setting H'(t) = 0, we get:

\(12t^11(1 - 7t^2)/7t^2 = 0\)

\(t = 0\) or t = ±(\(1/\sqrt7\))

H'(t) is undefined at t = 0.

Now, we can use the first derivative test to determine the intervals on which H(t) is increasing or decreasing. We can do this by choosing test points between the critical points and checking whether the derivative is positive or negative at those points.

Test point: -1

\(H'(-1) = 12(-1)^11(1 - 7(-1)^2)/7(-1)^2 = -12/7 < 0\)

Test point: (-1/√7)

\(H'(-1/\sqrt7) = 12(-1/\sqrt7)^11(1 - 7(-1/\sqrt7)^2)/7(-1/\sqrt7)^2 = 12/7\sqrt7 > 0\)

Test point: (1/√7)

\(H'(1/\sqrt7) = 12(1/\sqrt7)^11(1 - 7(1/\sqrt7)^2)/7(1/\sqrt7)^2 = -12/7\sqrt7 < 0\)

Test point: 1

\(H'(1) = 12(1)^11(1 - 7(1)^2)/7(1)^2 = 5/7 > 0\)

Therefore, H(t) is increasing on the intervals (-∞, -1/√7) and (1/√7, ∞) and decreasing on the interval (-1/√7, 1/√7).

b.) To find the local and absolute extreme values of H(t), we need to check the critical points and the endpoints of the intervals.

Critical points:

\(H(-1/\sqrt7) \approx -0.3497\)

\(H(0) = 0\)

\(H(1/\sqrt7) \approx-0.3497\)

Endpoints:

H (-∞) = -∞

H (∞) = ∞

Since H (-∞) is negative and H (∞) is positive, there must be a global minimum at some point between -1/√7 and 1/√7. The function is symmetric about the y-axis, so the global minimum occurs at t = 0, which is also a local minimum. Therefore, the absolute minimum of H(t) is 0, which occurs at t = 0.

There are no local or absolute maximum values for H(t).

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Answer:

No it is not a function.

Step-by-step explanation:

Answer:

No. This is NOT a function.

Step-by-step explanation:

Answer:

C is the anwser

Step-by-step explanation:

divide by flipping everything and rooting it.