Tumblr's stock price is $38 per share. Anjie purchased 600 shares. Assuming a broker's commission of $0.10 per share to purchase the 600 shares, what was Anjie's total cost? A. $22,860 B. $22,740 C. $23,400 D. $22,800

Answer:

vertex (  [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).

Step-by-step explanation:

Given : The equation of a parabola is given.

       y=−14x²+4x−19

To find  : What are the coordinates of the vertex of the parabola.

Solution : We have given that

y = −14x²+4x−19

we will be "completing the square" .

Factor out -14 to make leading coefficient 1

y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}[/tex])

Add and subtract [tex](\frac{-1}{7}) ^{2}[/tex]

y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}+\frac{-1}{7}) ^{2} - (\frac{-1}{7})^{2})[/tex] .

Complete the square

y = -14 ( [tex](x -\frac{1}{7}) ^{2} +\frac{19}{14}- (\frac{-1}{7})^{2})[/tex].

y = -14 ( [tex](x-\frac{1}{7}) ^{2} -\frac{131}{7}[/tex]

Standard form of parabola vertex form y  = a(x - h)²+ k,

Where, ( h, k)  are vertex

On comparing a = -14 , h= [tex]\frac{1}{7}[/tex], k =  [tex]\frac{131}{7}[/tex]

Therefore, vertex (  [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).

The commutative property in mathematics says that the order in which numbers are multiplied doesn't change the product. For example, using the commutative property, the product of 13 x 7 x 21 will be the same as 7 x 21 x 13, which is 1911.

The commutative property is a fundamental concept in Mathematics which states that for multiplication and addition, numbers can be moved around (or commuted) without changing the result. For example, if you have the multiplication problem 13 * 7 * 21, thanks to the commutative property, you can rearrange this problem to: 7 * 21 * 13 or 21 * 13 * 7 or any other arrangement of these three numbers, and the result will remain the same.

Let’s see this in action:
Original arrangement: 13 * 7 * 21 = 1911
Changed arrangement: 7 * 21 * 13 = 1911
As you can see, regardless of how the terms were rearranged, the answer remained the same, thus demonstrating the commutative property.

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The woman's new office has twice the area of her current office. By calculating the side length of the current square office from the perimeter and then finding the area, we determine the new office's area to be 968 square feet.

The question asks about calculating the area of a larger office which is twice the area of the woman's current office. Knowing the current office perimeter allows us to find the side length of the current square office and use it to calculate the area of both the current and the new office.

The area of the new, larger office is 968 ft².

Answer:

Step-by-step explanation:

Given:

1) Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years.

Published data - Already recorded data used

2)  Mia asked 20 random students at her school how many hours they spend on the computer each day.

Survey by Random sampling -- since a small size of whole population selected at random

3) Beatriz recorded the number of customers entering a store for each hour interval.

This is observational data because data was collected after really observing and recording the number of customers entering a store for each hour interval.

Volume is a three-dimensional scalar quantity. The volume of the trash can is 62.8318 ft³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the trash can = π×r²h = π×(2ft)²×(5ft) = 62.8318 ft³

Hence, the volume of the trash can is 62.8318 ft³.

Learn more about Volume:

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The quotient of the expression (x - 1)/(7x² - 3x - 9) cannot be determined

How to determine the quotient of the expression

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

(x - 1)/(7x² - 3x - 9)

From the above, we have

degree of the numerator = 1

degree of the denominator = 2

The degree of the numerator is less than the degree of the denominator

This implies that the quotient of the expression cannot be determined

To determine if a formula represents a length, area, or volume, consider the units used in the formula.

When determining if a formula represents a length, area, or volume, you need to consider the units used in the formula. Length is typically measured in units such as meters or feet. Area is measured in square units, such as square meters or square feet. Volume is measured in cubic units, such as cubic meters or cubic feet.

For example, suppose you have a formula that involves only one variable and it includes units such as meters. This formula would most likely represent a length. If the formula involves two variables and includes units like square meters, then it represents an area. And if the formula involves three variables and includes units like cubic meters, then it represents a volume.

It's important to pay attention to the units to determine whether a formula represents a length, area, or volume.

Answer:

[tex]y=\frac{3}{2}(x+4)[/tex]

Step-by-step explanation:

We are given

[tex]\frac{2}{3}y-4=x[/tex]

Since, we have to solve for y

so, we will isolate y on anyone side

Firstly, we add both sides by 4

[tex]\frac{2}{3}y-4+4=x+4[/tex]

[tex]\frac{2}{3}y=x+4[/tex]

Multiply both sides by 3

[tex]3\times \frac{2}{3}y=3\times(x+4)[/tex]

[tex]2y=3\times(x+4)[/tex]

now, we can divide both sides by 2

and we get

[tex]y=\frac{3}{2}(x+4)[/tex]

The function's formula that represents the number of pages Naoya has left to read at time t would be P(t) = 570 - 55t.

From the information given we know that Naoya reads at a rate of 55 pages per hour. After 4 hours of reading, he still has 350 pages left to read. This means that before he started reading, he had (55 pages/hour * 4 hours + 350 pages) = 570 pages in total. Since he reads at constant rate, the function that describes the remaining pages to read would be P(t) = 570 - 55t, where t represents the time in hours and P(t) is the number of pages left to read.

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We have factorized the expression 'r2 - 6r - 9s2 + 9' into (r - 3)^2 - (3s)^2 and then used the difference of squares formula to find the factorization as (r - 3 + 3s)(r - 3 - 3s). So the correct answer is option A)

The question asked for the complete factorization of the expression r2 - 6r - 9s2 + 9. To factorize this, we can rewrite it into the formula form of a perfect square, which is a^2 - 2ab + b^2 = (a - b)^2.

Our expression fits this form when a = r and b = 3s. Following this, we can rewrite the expression as (r - 3)^2 - (3s)^2 = (r - 3 + 3s)(r - 3 - 3s). Therefore, the correct answer is option A) (r - 3 + 3s)(r - 3 - 3s)

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