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4 years ago

What is the missing value

Mathematics

1 answer:

Vikentia [17]4 years ago

4 0

If A is equal to 30, and A+B equals 42. That means B equals 12. So, if the value increased with the same rate of change, it would be 54. This is because 30 plus 12 is 42. 42 plus 12 would equal 54.

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Simplify. 12 24 A) 3 2 B) 6 2 C) 1 2 D) 2 2

AleksandrR [38]

12/24 simplifies to 1/2, seeing as 12 is half of 24. :) Your answer is C.

5 0

4 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

The ratio of the side lenghths of two cubes is 3:7. find the ratio of their volumes

babunello [35]

27:343 because since the side lengths are like cm or in, it's always to the power of 1, but it is invisible, so since you want to know the ratio of the volume, volume is always inches cubed or centimeters cubed etc. So you get the original ratio of the side lengths to the first power, and do each number to the third power which gives you that ratio.

8 0

3 years ago

A club has 15 girls and 20 boys as members. The president wants to break the club into groups, with each group containing the sa

Alenkasestr [34]

Answer:

you can make 8 groups with 2 girls and 1 boy in each group or you can make 4 groups with 4 girls and 2 boys in each group

Step-by-step explanation:

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4 years ago

Study the number line shown. Match the question with the correct letter on the number line.

RideAnS [48]

Answer:

C,B,D,A

Step-by-step explanation:

Start at 3(X) and move based on the question

5 0

3 years ago