A circular rug has a radius of 4.5 feet. What is the circumference of the rug? Use 3.14 for .

The volume of the pencil is approximately 4.05 cm³.

To determine the volume of the pencil, we need to calculate the volumes of the cylindrical body and the conical tip separately and then add them together.

Volume of the cylindrical body:

The formula for the volume of a cylinder is [tex]V = \pi r^2h[/tex], where r is the radius and h is the height.

[tex]V_{cylinder} = \pi (0.5 cm)^2 * 15 cm[/tex]

Volume of the conical tip:

The formula for the volume of a cone is [tex]V = (1/3)\pi r^2h[/tex], where r is the radius and h is the height.

[tex]V_{cone} = (1/3) * \pi (0.5 cm)^2 * 2 cm[/tex]

Now, we can calculate the volumes:

[tex]V_{cylinder} = \pi * (0.5 cm)^2 * 15 cm = 3.53 cm^3\\\\V_{cone} = (1/3) * \pi * (0.5 cm)^2 * 2 cm = 0.52 cm^3[/tex]

Finally, we can add the volumes of the cylindrical body and the conical tip to get the total volume of the pencil:

[tex]Total\ volume = V_{cylinder} + V_{cone} = 3.53 cm^3 + 0.52 cm^3 = 4.05 cm^3[/tex]

Therefore, the volume of the pencil is approximately 4.05 cubic centimeters ([tex]cm^3[/tex]).

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Answer:

It is a rhombus.

Step-by-step explanation:

To identify the type of polygon, we will first determine if the opposite sides are parallel.  To do this, we find the slope of each line segment.  (Parallel lines have the same slope.)

For WX, m = (5-2)/(1-5) = 3/-4 = -3/4

For XY, m = (2--1)/(5-1) = 3/4

For ZY, m = (2--1)/(-3-1) = 3/-4 = -3/4

For ZW, m = (2-5)/(-3-1) = -3/-4 = 3/4

Since the slopes of WX and ZY are the same, these two sides are parallel.  Since the slopes of XY and ZW are the same, these two sides are parallel.  Since opposite sides are parallel, the figure is a parallelogram.

In order to be a rectangle, the angles would have to be right angles.  Since perpendicular lines have slopes that are negative reciprocals of each other, the slopes of adjoining sides would have to be opposite signs and flipped.  This is not the case, so the angles are not right; this means it is not a rectangle.

The only other option for a parallelogram without right angles would be a rhombus.  This is the case if the length of each side is the same.  We will use the distance formula for this:

[tex]WX=\sqrt{(5-2)^2+(1-5)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\XY=\sqrt{(2--1)^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\YZ=\sqrt{(2--1)^2+(-3-1)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\ZW=\sqrt{(2-5)^2+(-3-1)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Since the length of each side is the same, this figure is a rhombus.

Answer:

Temperature t > -15 degrees.

Step-by-step explanation:

Let t denote the temperature.

The inequality sign for above or greater is >. The inequality sign for less than is <.

It is given temperature stayed above -15 degrees.

This can be written in inequality form as t> -15 °(degrees)

The inequality to represent the temperature is t > -15°C

Given data:

To represent the situation where the temperature stayed above -15 degrees, the inequality symbol used is ">".

In an inequality, the ">" symbol means "greater than." By using this symbol,  the temperature needs to be greater than -15 degrees.

The inequality representing this situation is:

Temperature > -15°C

So, t > -15°C

If the temperature is higher than -15 degrees, the inequality is true.

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The expression that can be simplified by combining like terms is 16 c^2 + 8cd + 7c - 8d, where 8cd and -3dc are like terms and can be combined to simplify the expression to 16c^2 + 5cd + 7c - 8d.

The expression 16 c2 + 8cd + 7c - 8d can be simplified by combining like terms. Like terms in an algebraic expression are terms that have the same variable raised to the same power. Here, the terms 8cd and -3dc are like terms and can be combined.

Here's the step-by-step simplification:

This process of combining like terms helps in simplifying algebraic expressions, making them easier to work with.

After combining like terms, it's important to always check the answer to see if the simplification is reasonable and if there are any other like terms that can be combined.

So, the simplified expressions are:

1. [tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]

2. [tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]

3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]

4. [tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]

Let's simplify each expression by combining like terms:

1. [tex]\(6d^2 + 5cd - 3dc + 8\)[/tex]

  Combine like terms:

  [tex]\(6d^2 + (5cd - 3dc) + 8\)[/tex]

 [tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]

2. [tex]\(12c^2 - 8d^2c + 3dc + 4\)[/tex]

  Combine like terms:

[tex]\(12c^2 - (8d^2c - 3dc) + 4\)[/tex]

  [tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]

3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]

  No like terms to combine.

4. [tex]\(16c^2 + 8cd + 7c - 8d\)[/tex]

  Combine like terms:

  [tex]\(16c^2 + (8cd + 7c) - 8d\)[/tex]

  [tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

Step-by-step explanation:

Given :

[tex]\dfrac {c-4}{c-2} = \dfrac {c-2}{c+2} - \dfrac{1}{2-c}[/tex]                   --------- (1)

Calculation :

[tex]\dfrac {c-4}{c-2} = \dfrac {(c-2)^2+(c+2)}{(c+2)(c-2)}[/tex]

[tex]c-4 = \dfrac {(c^2-4c+4)+(c+2)}{(c+2)}[/tex]

[tex](c-4)(c+2) = (c^2-3c+6)[/tex]

[tex](c^2-2c-8) = (c^2-3c+6)[/tex]

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

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Answer:

14 and Zero

Step-by-step explanation:

y = k/x

Step-by-step explanation:

Answer:

11.18

Step-by-step explanation:

General Idea:

There are few exponent rules that need to be used to simplify the rational exponent to get to the answer.

Exponent rules:

[tex] Rule\; 1: a \cdot a \cdot a \cdot a =a^4\\ \\ Rule\; 2: (a^m)^n=a^{m \times n} [/tex]

Applying the concept:

Rewriting 81 as a number with an exponent using prime factorization.

[tex] 81=3 \times 3 \times 3 \times 3 = 3^4\\ \\ Applying \; Rule \; 1, \; we\; get\; \\\\81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}} \\ \\ Applying \; Rule \; 2,\; we\; get\\ \\ 3^{4 \times\frac{3}{4} } = 3^{\frac{12}{4} }=3^3=3 \times 3 \times 3 = 27 [/tex]

Conclusion:

The above explanation explains why [tex] 81^{\frac{3}{4}} =27 [/tex]