The measure of <ACD is 120. Find the measure of <ACB, <BCD, and <ACE.Explain how you found the measure of <ACE.

Mathematics High School

The measure of <ACD is 120. Find the measure of <ACB, <BCD, and <ACE.

Explain how you found the measure of <ACE.

Answers

Answer 1

Answer:

m∠ACB = 39°

m∠BCD = 81°

m∠ACE = 60°

Step-by-step explanation:

From the picture attached,

m∠ACD = 120°

Since, m∠ACD = m∠ACB + m∠BCD

x + (2x + 3) = 120°

3x + 3 = 120

3x = 117

x = 39

Therefore, m∠ACB = 39°

m∠BCD = (2x + 3) = 2(39) + 3

= 81°

Since, m∠ACE + m∠ACB + m∠BCD = 180° [Angles formed at a point on a straight line]

m∠ACE + 39 + 81 = 180

m∠ACE = 180 - 120

m∠ACE = 60°

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Answer:

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Step-by-step explanation:

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Joshua was offered a job that paid a salary of $77,500 in its first year. The salary was set to increase by 2% per year every year.
If Joshua worked at the job for 5 years, what was the total amount of money earned over the 5 years, to the nearest whole
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Answers

Answer:

if you want it as dollars and cents it is $77.50 but in nearest whole number it would be 78 dollars

Step-by-step explanation:

step 1: multiply the 2 by 5 and you get 10%

step two: you put 10 over 100 and multiply 77,500

10/100 x 77,500/1= $77.50

but when you roung it off you get 78 dollars

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

Angle 1 = 52

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Step-by-step explanation:

Use the theorems

Line b is a straight line which is 180 degrees.

Angle 5 plus angle 6 need to equal 180

Angle 5 = 180 - 128 = 52

Angle 1 is the same as angle 5 because they are located in the same place on a straight line.

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Angle 3 is a vertical angle to angle 1, which means they are identical so angle 3 is also 52 degrees.

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Answers

Answer:

a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

Step-by-step explanation:

Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

P(x, y, z) =

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

The explanation to the answers is now given as follows:

p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)

q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)

r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)

C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z

P(x, y, z) = profit function

x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively

Therefore, we have:

TR = Total revenue = px + qy + rz …………………………….. (1)

Substituting the relevant values into equation (1), we have:

TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z

TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2

Also,

P(x, y, z) = TR – C ……………………………………… (2)

Substituting the relevant values into equation (2), we have:

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z

P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)

Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.

As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:

In America

From equation (3), we have:

Px = 24 – 0.4x = 0

Therefore, we have:

24 – 0.4x = 0

24 = 0.4x

x = 24 / 0.4

x = 60

In Europe

From equation (3), we have:

Py = 12 – 0.2y = 0

Therefore, we have:

12 – 0.2y = 0

12 = 0.2y

y = 12 / 0.2

y = 60

In Asia

From equation (3), we have:

Pz = 16 - 0.2z = 0

Therefore, we have:

16 - 0.2z = 0

16 = 0.2z

z = 16 / 0.2

z = 80

Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Answer:

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Answers

Answer:

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Step-by-step explanation:

Since DB =36, and AC is the same line, then AC = 36. The new equation is 36 = 3x - 3. Do inverse operation. Add 3 to both sides of the equation: 36+3=39 & -3+3=0. New equation is 39=3x. Finally divide. 39/3= 13.

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Answers

Answer:

Step-by-step explanation:

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Answers

answer:

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Step-by-step explanation:

Answer:

188.65

Step-by-step explanation:

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B.
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Answers

Answer:

Step-by-step explanation:

100% is 1-

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Answer:

Step-by-step explanation:

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Answers

Answer:

selling price= $9.9

Step-by-step explanation:

Giving the following information:

During the third week, all remaining basketballs were marked down an additional 30%.

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answer:

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Answers

Answer:

Step-by-step explanation:

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Answer:

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The measure of <ACD is 120. Find the measure of <ACB, <BCD, and <ACE.Explain how you found the measure of <ACE.​

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The measure of <ACD is 120. Find the measure of <ACB, <BCD, and <ACE.

Explain how you found the measure of <ACE.