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2 years ago

2/3 of a plot is garden.1/5 of the garden is lawn find the fraction of the plot of land that is lawn

Mathematics

1 answer:

Marina CMI [18]2 years ago

5 0

Answer:

2/3 + 1/5 = 13/15

Step-by-step explanation:

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Draw the graph for f(x)=x-1/x^2-x-6 and state:a. the x-intercept(s).b. the y-intercept.c. the equation(s) of any vertical asympt

Zigmanuir [339]

ANSWER:

a. (1, 0)

b. (0, 1/6)

c. x = -2. x = 3

d. y = 0

e. The asymptotes have the form of a line and divide the function into 3 parts.

$\begin{equation*} \text{Domain: }\left(-\infty\:,\:-2\right)\cup\left(-2,\:3\right)\cup\left(3,\:\infty\:\right) \end{equation*}$

$\text{Range}(-\infty,\infty)$

STEP-BY-STEP EXPLANATION:

We have the following function:

$f\left(x\right)=\frac{x-1}{x^2-x-6}$

The graph corresponding to the function is the following:

We determine in each case what the statement asks for, like this:

a. the x-intercept(s):

$\begin{gathered} \text{ in this case y = 0, therefore:} \\ \\ \frac{x-1}{x^2-x-6}=0 \\ \\ x-1=0\cdot(x^2-x-6) \\ \\ x=1 \\ \\ \text{The x-intercept is \lparen1, 0\rparen} \end{gathered}$

b. the y-intercept:

$\begin{gathered} \text{ in this case x = 0, therefore } \\ \\ y=\frac{0-1}{0^2-0-6} \\ \\ y=\frac{-1}{-6} \\ \\ y=\frac{1}{6} \\ \\ \text{ The y-intercept is }\:\left(0,\frac{1}{6}\right) \end{gathered}$

c. the equation(s) of any vertical asymptote(s). The horizontal asymptotes are the values that x cannot take since the function would be discontinuous for those values.

In this case, since it is a rational function, it would be when the denominator is 0, therefore, we solve the following:

$\begin{gathered} x^2-x-6=0 \\ \\ (x-3)(x+2)=0 \\ \\ x-3=0\rightarrow x=3 \\ \\ x+2=0\operatorname{\rightarrow}x=-2 \\ \\ \text{ The equation\lparen s\rparen of any vertical asymptote are:} \\ \\ x=3,x=-2 \end{gathered}$

d. the equation of the horizontal asymptote. If the degree of the denominator is greater than that of the numerator, the horizontal asymptote is the x-axis, that is:

$y=0$

e. information about the behavior at the asymptote(s).

In this case the behavior of the asymptotes are straight lines that represent values that the function cannot take or cannot reach, divide the function into 3 parts.

f and g.

In this case, the domain is the interval of values that x can take and the range is the interval of values that y can take.

Therefore:

$\begin{gathered} \text{Domain: }\left(-\infty\:,\:-2\right)\cup\left(-2,\:3\right)\cup\left(3,\:\infty\:\right) \\ \\ \text{Range:}\:\left(-\infty\:,\:\infty\:\right) \end{gathered}$

8 0

1 year ago

If f(2)=pi+7 then f^-1(pi+7)=?

stepladder [879]

Hello,

$f(2)=\pi + 7\\\\
2=f^{-1}\ o\ f(2)=f^{-1} (f(2))=f^{-1}( \pi + 7 })$

6 0

3 years ago

Read 2 more answers

Please answer me as soon as possible

adell [148]

Answer:????

Step-by-step explanation:

8 0

2 years ago

More people leave Anytown, AL each year than move into it. The population over the past 20 years is shown in the table. Use tech

Phoenix [80]

The equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

Let's suppose the equation that models the exponential decline is:

$\rm y = a(b^x)$

From the data given, we can calculate the value of a and b:

a = 46348587109809610

b = 0.9861

y = 46348587109809610(0.9861)ˣ

Thus, the equation that models the exponential decline is y = 46348587109809610(0.9861)ˣ if the population over the past 20 years is provided.

Learn more about the line of best fit here:

brainly.com/question/14279419

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6 0

1 year ago

Please help i don’t understand this

swat32

Similar polygons only differ by a scaling factor. In other words, two polygons are similar if one is the scaled version of the other.

In particular, this implies that the angles are preserved, and the correspondent sides are in proportion.

These two polygons are both rectangles, so the angles are preserved. We must check the sides, and we have to check if the smaller sides are in the same proportion as the bigger sides.

So, the two rectangles are similar if the following is true.

$4\div 5 = 11\div 12$

In any proportion, the product of the inner terms must be the same as the product of the outer terms:

$4\cdot 12 = 5\cdot 11 \iff 48=55$

This is clearly false, and thus the two rectangles are not similar.

5 0

2 years ago