Provide the correct justifications for each statement in the derivation of the tangent difference identity.
1.

identity

2. Trigonometric

identities

3. Divide numerator and denominator by


4. Factor out common factors using the quotient identity.

The midpoint of the line segment is the average of the respective coordinates.

So the x-value of the midpoint if the average of the two individual x-coordinates.

    (-3.5 + 4)/2 = 0.5/2 = 0.25

And the y-value of the midpoint if the average of the two individual y-coordinates.

    (2 + (-2.5))/2 = -0.5/2 = -0.25

So, the midpoint is (0.25, -0.25) or (1/4, -1/4) or "C".

Answer:

multiply the diameter of the circle with π (

Step-by-step explanation:

Answer: 8.118 / 0.615 = 13.2

Based on the data, the mean would be the best measure of center to describe a typical value in the data set.

To create a dot plot, we can list the numbers in order and place a dot above the corresponding value on the number line.

20 ••

21 ••

22 •

23 ••••

24 •••••

25 ••

26 ••

27 •

The dot plot shows a relatively symmetric distribution of the data, with the majority of values clustered around the middle. Therefore, the mean would be a good measure of center to describe a typical value of the data set.

Learn more about dots plot in: https://brainly.com/question/22746300

#SPJ1

Answer:

Find the perimeter of a park that measures 7 miles by 910 miles. Get the answers you need, now! ... Advertisement tasha005111 is waiting for your help. Add your answer and earn points. kaylapoo34 kaylapoo34 Answer: the answer is 130. Step-by-step explanation: ... 15 Niles and Bob sailed at the same time for the same length of time.

Step-by-step explanation:

Answer:B

Step-by-step explanation:

the value of variable x in the rhombus is Option (c) 25.

A parallelogram is a particular instance of a rhombus. opposite sides and angles of the rhombus are parallel and equal. The rhombus has equal-length sides on each side, and its diagonals meet at right angles to form its shape as square. The rhombus is sometimes called as a diamond or rhombus.

Let O be the intersection point of the line AC and the line BD in the rhombus.

This two lines intersect at a 90° angle in the center. ( Property of Rhombus)

∠AOD=90°

∠AOD+∠OAD+∠ODA=180° (triangle sum property)

90°+x+x+40°=180°

2x=180°-130°

x=25

Hence the value of x=25.

To know more about parallelogram, visit:

https://brainly.com/question/19187448

#SPJ1

Answer:

6x -16

Step-by-step explanation:

f(x) = 6x + 2

f(x-3) =

Replace x with x-3

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

   Distribute

    = 6x - 18 +2

    = 6x -16

The right answer is 6x-16

please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

5 5/6

Step-by-step explanation:

Change the mixed numbers to improper fractions, and you get -9/2 + 31/3, which adds up to 35/6, then divide 35 by 6, which changes it back to a mixed number, 5 5/6.

On solving the provided question, we got to know that - the  cost of common equity is 11.84

Equity in mathematics education is defined by the National Council of Teachers of Mathematics as high standards and rewarding opportunities for everyone, addressing disparities to assist all kids learn mathematics, and making sure that all classrooms have resources and support for students.

here, the above question we have  -

D0 = $0.85;

P0 = $22.80;

g = 7.00%

  = 700

Answer is  -  The  cost of common equity is 11.84

To know more about equity visit:

https://brainly.com/question/13580545

#SPJ1

Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

Learn more about pollution here,

https://brainly.com/question/24704410

#SPJ1

Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ1

Step-by-step explanation:

The answer im just guessing but teachers like to do false false true true so sorry if im wrong

The formula of the function, where x is entered in radians is   y = -3sin(πx/5) -6

The key components: amplitude, period, phase shift, and vertical shift.

Amplitude is the distance between the midline and max/min points. Midline at (0, -6), so distance to min point (2.5, -9) is 3. Amplitude: 3.

Vertical shift: Displacement along y-axis. Midline at y = -6, vertical shift is -6. Period: distance between max/min points. Graph intersects midline at (0, -6) and minimum point at (2.5, -9).  Period is 5 (2 * 2.5). Freq: Reciprocal of period, 1/5.

Phase shift: Horizontal shift of graph. Graph intersects midline at x=0, no phase shift.

Hence:

The general form of the sinusoidal function is y = A sin (B(x-C)) + D

So, Substituting the known values into the general formula:

y = 3 x  sin((1/5)x - 0) - 6

Hence: Simplifying it will be:

y = 3 x sin(πx/5) - 6

Then, the formula of the function, where x is entered in radians, is: y = -3sin(πx/5) - 6

Based on the image attached, the first given point is one that informs one that the function is a sine (not a cosine) function, and that it is one that has its offset as -6.

Also, the second given point is one that informs you of the first peak is at x=2.5, hence the argument of the sine function is π/2 if x=2.5: (πx/5).

Based on the fact that the peak is 3 units smaller than the midline, the amplitude is said to be -3.

Therefore the  formula for the function is  seen as:  y = -3·sin(πx/5) -6

Learn more about sinusoidal function from

https://brainly.com/question/16300816

#SPJ1

The inequality is given as

To solve, we multiply both sides by 5.

Hence, we have

The solution to the inequality is

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

Find out more on fractions here: https://brainly.com/question/78672

#SPJ1

Answer:

To determine whether Kyle will arrive in time for the baseball game, we need to calculate how long it will take him to travel the 130 miles to the baseball field.

Using the formula:

distance = rate × time

We can rearrange the formula to solve for time:

time = distance / rate

Plugging in the given values, we get:

time = 130 miles / 50 miles per hour

time = 2.6 hours

This means that it will take Kyle 2.6 hours to travel the 130 miles to the baseball field at the speed limit of 50 miles per hour.

Since Kyle has 2 hours to get to the baseball game, he will not arrive in time if he drives at the speed limit. He would need to drive faster than the speed limit to make it to the game on time. However, it's important to note that speeding is illegal and dangerous, so Kyle should not exceed the speed limit. He may need to consider leaving earlier or finding alternative transportation to ensure that he arrives at the baseball game on time.

Step-by-step explanation:

Answer:

ormal blood pressure for most adults is defined as a systolic pressure of less than 120 and a diastolic pressure of less than 80. Elevated blood pressure is defined as a systolic pressure between 120 and 129 with a diastolic pressure of less than 80.

Step-by-step explanation:

Step-by-step explanation:

sin A = opposite/ Hypotenuse

Sin A = 5/7

Hello !

sin(A) = opposite/hypotenuse = 5/7

arcsin(5/7)  ≈ 45,58°

sin(A) = 5/7

the angle A ≈ 45,58°

Answer:

volume=60cm3, surface area=96cm2

Step-by-step explanation:

volume=1/3×(6×6)×5

=60cm3

surface area= 4(1/2×6×5)+(6×6)

=96cm2

Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

Answer:

  2

Step-by-step explanation:

You want to know the mode of a dot plot that could be represented as ...

  1 | x x

  2 | x x x x x

  3 | x x x

  4 | x x x x

  5 | x x

The mode is the data element that appears most often in the data set.

The 5 xs above the 2 is the largest number of xs that appear anywhere, so 2 is the mode.

<95141404393>

Answer:

When you divide both sides of an inequality, you need to flip the inequality sign.

Step-by-step example:

-8x > 72

Divide both sides by -8

x < -9

Using the triangular inequalities we can get:

7/4 < x < 11/2

The image of the triangle is in the image at the end.

A triangle with sides A, B, and C must meet the triangular inequality, it says that the sum of any two sides is larger than the other side.

Now, see the triangle attached at the end, the triangular inequalities say that:

18 + 6x > 2x + 4

18 + 2x + 4 > 6x

6x + 2x + 4 > 18

Now simplify these, for each one we will get:

4x > -14 -----> x > -7/2

22 > 4x -----> 11/2 > x

8x > 14 -----> x > 7/4

Using the second two we can get:

7/4 < x < 11/2

Learn more about triangles at:

https://brainly.com/question/2217700

#SPJ1

Answer:

The scale factor is 3/5.

The image is a(n) reduction.

Step-by-step explanation:

First, it's important to know that whatever shape has an apostrophe after it is the shape after dilation. This means that shape P is the original and shape P' is after dilation. Since P to C is 15 and P' to C is 9, the shape must have shrunk and is an example of a reduction. Now, we need to figure out what the reduction, or scale factor, is. To find scale factor, you need to take the length of the new shape and divide it by the length of the original shape. Since the new shape is 9 and the original shape is 15, the scale factor must be 9/15, or 3/5.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer: -2x + 12

Step-by-step explanation:

2A + B = 2(-2x + 8) + (2x - 4) = -4x + 16 + 2x - 4 = -2x + 12