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yarga [219]
2 years ago
9

Mrs. Galicia has a cupcake company. The amount of money earned is represented by

Mathematics
1 answer:
sashaice [31]2 years ago
6 0

Using the profit function, it is found that:

a) She earns $36 after 25 years.

b) The function was shifted right 4 units and up 1 units.

<h3>What is the profit function?</h3>

The profit, in x years after 2015, is given by:

p(x) = 12\sqrt[3]{x + 2}

Item a:

She earns $36 after x years, considering x for which p(x) = 36, hence:

p(x) = 12\sqrt[3]{x + 2}

36 = 12\sqrt[3]{x + 2}

\sqrt[3]{x + 2} = 3

(\sqrt[3]{x + 2})^3 = 3^3

x + 2 = 27

x = 25

She earns $36 after 25 years.

Item b:

The new function is:

h(x) = 12\sqrt[3]{x - 2} + 1

At the domain, we have that x + 2 \rightarrow x - 2, that is, x \rightarrow x - 4, hence it was shifted right 4 units.

At the range, we have that h(x) = h(x - 4) + 1, hence it was shifted up 1 unit.

You can learn more about functions at brainly.com/question/24380382

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A tree cast a shadow of 30m long and a 2m stick casts one that is 3m long. As show in the below diagram how tall is the tree?​
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Step-by-step explanation:

<u>We have similar triangles here.</u>

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A 2X2 square is centered at the origin. It is dilated by a factor of 3. What are coordinates of the vertices of the square?
Vesna [10]

Answer:

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B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

Step-by-step explanation:

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

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C(1, 1) = 3(1, 1) = C'(3, 3)

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To most closely estimate the difference below, would you round the numbers to the nearest ten thousand, the nearest thousand, or
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Answer:

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I would round 49,625 to the nearest thousand, since it would make the subtraction easier and 49,625 is only 375 units away from 50,000.

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