A=(1,2,5,7,8)<br> B=(5,9,10,12)<br> How many subset does set B have.

If the length, width, and height of a cube all change by a factor of 7, what happens to the volume of the cube?

Mkey [24]

9514 1404 393

Answer:

The volume is 343 times as large.

The length is 7 times as large.

Step-by-step explanation:

If the original cube has side length s, its volume is given by ...

V = s³

When the side length is changed by a factor of 7, the new volume is ...

V = (7s)³ = 7³×s³ = 343s³

The volume of the cube changes by a factor of 7³ = 343.

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The problem statement tells you the length is 7 times as large.

4 0

3 years ago

What is the area of LMNO ?

emmasim [6.3K]

Should be 60 if you multiply width (base) x height

3 0

3 years ago

Show all worked identify the asymptotes and state the end behavior of the function F(x)=6x over x-36

astraxan [27]

Solution

Asymptote:

Vertical Asymptote

- The vertical asymptotes of a rational function are determined by the denominator expression.

- The expression given is:

$f(x)=\frac{6x}{x-36}$

- The denominator of (x- 36) determines the asymptote line.

- The vertical asymptote defines where the rational function isundefined. Iin order for a rational function to be undefined, its denominator must be zero.

- Thus, we can say:

$\begin{gathered} x-36=0 \\ Add\text{ 36 to both sides} \\ \\ \therefore x=36 \end{gathered}$

- Thus, the vertical asymptote is

$x=36$

Horizontal Asymptote:

- The horizontal asymptote exists in two cases:

1. When the highest degree of the numerator is less han the degree of the demnominator. In this case, the horizontal asymptote is y = 0

2. When the highest degee sof the numerator and tdenominator are the same. In this case, the horizontal asymptote is

$\begin{gathered} y=\frac{N}{D} \\ where, \\ N=\text{ Coefficient of the highest degree of the numerator} \\ D=\text{ Coefficient of the highest degree of the denominator} \end{gathered}$

- For our question, we can see that the highest degrees of the numerator and denominator are the same. Thus, we have the Horizontal Asymptote to be:

$y=\frac{6}{1}=6$

End behavior:

- The end behavior is examining the y-values of the function as x tendsto negative and positive infinity.

- Thus, we have that:

$\begin{gathered} f(x)=\frac{6x}{x-36} \\ \\ \text{ Divide top and bottom by }x \\ f(x)=\frac{6x}{x-36}\times\frac{x}{x} \\ \\ f(x)=\frac{\frac{6x}{x}}{\frac{x-36}{x}}=\frac{6}{1-\frac{36}{x}} \\ \\ As\text{ }x\to-\infty \\ f(-\infty)=\frac{6}{1-\frac{36}{-\infty}}=\frac{6}{1+\frac{36}{\infty}}=\frac{6}{1+0}=6 \\ \\ \text{ Thus, we can say: }x\to-\infty,f(x)\to6 \\ \\ Also, \\ As\text{ }x\to\infty \\ f(\infty)=\frac{6}{1-\frac{36}{\infty}}=\frac{6}{1-0}=6 \\ \\ \text{ Thus, we can also say: }x\to\infty,f(x)\to6 \end{gathered}$

Final Answers

Asymptotes:

$\begin{gathered} \text{ Vertical:} \\ x=36 \\ \\ \text{ Horizontal:} \\ y=6 \end{gathered}$

End behavior:

$\begin{gathered} As\text{ }x\to-\infty,f(x)\to6 \\ \\ As\text{ }x\to\infty,f(x)\to6 \end{gathered}$

7 0

1 year ago

Can someone answer this question please answer it correctly pleas help me if it’s correct I will mark you brainliest

elena-14-01-66 [18.8K]

Answer:

5/39

Step-by-step explanation:

<u>Step 1: Find the probability</u>

Cross country / total

10 / 78

(10/2) / (78/2)

5 / 39

Answer: 5/39

5 0

3 years ago

4) Does the following table show a function?

Alexandra [31]

No i don’t think it does

4 0

3 years ago

A=(1,2,5,7,8) B=(5,9,10,12) How many subset does set B have.