The length of a rectangle is given by 5t+4sqrt(t), and its height is sqrt(t), where t is time in seconds and the dimensions are in centimeters. Fine the rate of change of the area of the rectangle with respect to time when the length of the rectangle is 9 centimeters.

Answer:

g(x) = |2(x+5)|

Step-by-step explanation:

To translate a function left 5 units, replace x with (x+5). In this function, that means

  2x ⇒ 2(x+5) . . . . . matches the last choice

The distributive property is demonstrated in the equation.

The algebraic property demonstrated in the equation is the distributive property. The distributive property states that when a number is multiplied by the sum or difference of two other numbers, you can distribute the multiplication to each term inside the parentheses.

In the given equation, 3(2x - 7) means multiplying 3 by both terms inside the parentheses. This results in 6x - 21. Therefore, the equation can be simplified to 5 + 6x - 21.

To simplify the given expression, factor out the common factors from the denominator and rewrite the expression using the factored form.

To simplify the given expression, we first need to simplify the denominator. This can be done by factoring out a common factor of 4 from each term:

(4a + 2)(2a - 3)

Next, we can rewrite the expression using the factored form:

1 / (4a + 2)(2a - 3)

This is the simplified form of the given expression.

The answer is c. [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex]

Separate the cube root: We can break down the cube root of a fraction into the cube root of the numerator divided by the cube root of the denominator:

[tex]\sqrt[3]{\frac{4 x}{5}} = \frac{\sqrt[3]{4 x}}{\sqrt[3]{5}}[/tex]

Simplify the cube root of 5: Since 5 is a perfect cube (5 = 1 * 5 * 5), its cube root is simply 5:

[tex]\frac{\sqrt[3]{4 x}}{\sqrt[3]{5}} = \frac{\sqrt[3]{4 x}}{5}[/tex]

Rationalize the denominator: To make the expression look more simplified, we can eliminate the cube root in the denominator. We do this by multiplying both the numerator and denominator by the cube root of 5:

[tex]\frac{\sqrt[3]{4 x}}{5} \times \frac{\sqrt[3]{5}}{\sqrt[3]{5}} = \frac{\sqrt[3]{4 x} \times \sqrt[3]{5}}{5 \times \sqrt[3]{5}}[/tex]

This simplifies to:

[tex]\frac{\sqrt[3]{20 x}}{5}[/tex]

Therefore, the simplified form of the expression is [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex].

Complete Question:

What is the simplified form of the following expression?

[tex]\sqrt[3]{\frac{4 x}{5}}[/tex]

a. [tex]$\frac{\sqrt[3]{4 x}}{5}$[/tex]

b. [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex]

c. [tex]$\frac{\sqrt[3]{100 x}}{5}$[/tex]

d. [tex]$\frac{\sqrt[3]{100 x}}{125}$[/tex]

Answer:

Andrew has 30 goldfish and Todd has 10 goldfish

Step-by-step explanation:

Lets call A the number of goldfish Andrew has and T the number of goldfish Todd has.

Andrew has 10 more goldfish than Todd:

A = T + 10

Together they have 50 goldfish:

A + T = 50

Lets replace A = (T + 10) in the las equation:

T + 10 + T = 50

Lets solve T in this equation:

2T + 10 -10 = 50 -10

2T /2 = 40 /2

T = 20

Todd has 20 goldfish

Now lets calculate A = T + 10 = 20 + 10 = 30

Andrew has 30 goldfish

The equation in standard form with a constant of proportionality greater than 1 is p=40h.

Given that, Tiesha enjoys reading in her spare time. She reads 4 pages every 1/10 of an hour.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other. That constant is known as the "constant of proportionality".

Now, p∝h

⇒p=kh-----(i)

So, 4∝1/10

⇒4=k/10

⇒k=40-----(ii)

Substitute equation (ii) in equation (i).

That is, p=40h

Therefore, the equation in standard form with a constant of proportionality greater than 1 is p=40h.

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Answer:

Step-by-step explanation:

A rolling pin has a cylindric shape, which is a revolution surface. This means that the rolling pin is symmetric about a line or axis, therefore, it can be rotated around it.

A rolling pin has rotational symmetry about its longitudinal axis, making it the correct answer, while a car, a set of rectangular stairs, and a stapler do not demonstrate this symmetry.

The question relates to the concept of rotational symmetry in three-dimensional objects, which is a part of the study of Physics, specifically dealing with rotational motion. The answer to which of the listed objects has rotational symmetry about a line is C. a rolling pin. A rolling pin has rotational symmetry because when it rotates about its longitudinal axis, its appearance is unchanged after a certain angle of rotation. In contrast, objects like a car, a set of rectangular stairs, and a stapler do not exhibit this symmetry because their appearance changes visibly when they are rotated about any line.

Answer:

The median age is 9 years old

Step-by-step explanation:

We can find the median by getting the average of the center number of the middle two numbers

8 and 10 are the two middle numbers in this scenario.  8 + 10 = 18

18/2 = 9

The graph of the function f(x) = x² + 2x − 6 is an upward-opening parabola with the vertex at (-1, -7) and a y-intercept at (0, -6). There are no asymptotes for this quadratic function.

To find the graph of the function f(x) = x² + 2x − 6, we need to look at the characteristics of this quadratic equation. This is a parabola that opens upward because the coefficient of x² is positive. We can find the vertex of this parabola by using the formula -b/2a for the x-coordinate of the vertex.

Here, a = 1 and b = 2. Applying the formula, we get the x-coordinate of the vertex as -b/2a = -2/(2×1) = -1. Now, we plug this value back into the function to get the y-coordinate of the vertex: f(-1) = (-1)² + 2(-1) − 6 = 1 - 2 - 6 = -7. Therefore, the vertex of the parabola is at (-1, -7). The parabola will intersect the y-axis when x = 0, which gives us the y-intercept f(0) = -6. No asymptotes are present in this quadratic function.

The graph of f(x) is symmetrical about the line x = -1 and has a y-intercept at (0, -6). The vertex at (-1, -7) is the lowest point on the graph since the parabola opens upwards. Thus, we are looking for a graph with these characteristics to represent the function f(x) = x² + 2x − 6.

The accounting profit for Gomez's pottery firm is $37,500, calculated by subtracting explicit costs from total revenue. The economic profit is $6,000, figured out by subtracting both explicit costs and implicit costs from total revenue.

To calculate the accounting profit for Gomez's pottery firm, we subtract all explicit costs (money spent) from the total revenue. In this case, we subtract the salary of the helper ($15,000), the rent of the shop ($6,500), and the amount spent on materials ($23,000) from the total annual revenue from pottery sales ($82,000). Therefore, the accounting profit is $82,000 - $15,000 - $6,500 - $23,000 = $37,500.

On the other hand, to obtain the economic profit, we need to also subtract implicit costs, which are the opportunity costs of using the resources in one way rather than the next best alternative way. Gomez could have made $6,000 by investing his own $40,000 elsewhere, and he could have earned $20,500 by working for a competitor, so these are both implicit costs. Additionally, he estimates his entrepreneurial talents to be worth $5,000. Therefore, "the economic profit is $37,500 (accounting profit) - $6,000 (returns from alternative investment) -  $20,500 (salary from competitor) - $5,000 (value of his entrepreneurial talents) = $6,000".

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Answer:

R

Step-by-step explanation:

A vertical line has slope that is "undefined". Line R is the vertical line on your graph.

_____

The slope of a vertical line is "undefined" because of the way slope is defined. Slope is the vertical change divided by the horizontal change. When the line is vertical, there is no horizontal change, so the computation of slope involves division by zero. The result of division by zero is "undefined."

Answer:

C. R

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