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gogolik [260]
3 years ago
11

Find the domain x^2-25/2

Mathematics
1 answer:
Mumz [18]3 years ago
8 0
For this, I am assuming that -25/2 is not a part of the exponent(although in future questions you should make this clear by using parenthesis.

When I do problems like this, I come to CBAD.  where the variables are y=A(Bx+C)+D

CBAD helps significantly in domain and range problems where there is a well known parent function.  (y=x^2, y=sqrt(x), y=1/x, y=x, etc).  Basically, if there is a parent function with slight additions(y=2*x^2, y=sqrt(x+1), y=1/(5x), y=3x, etc)

This works that in the order, a C term shifts the graph horizontally in the opposite direction expected (a negative number will shift right, a positive number will shift left).  For example, if C is -2, the graph of the parent function will shift right 2.
Then, a B term dilates(changes the horizontal size of the graph) by the factor 1/B(every x value is multiplied by 1/B).  Thus a B >1 will shrink the graph horizontally, and a 0<B<1 with stretch the graph horizontally.  If B is negative, it reflects the graph over the y axis and then either shrinks or stretches horizontally.  If B is 1, nothing changes.
Then, a A term dilates(changes the horizontal size of the graph) by the factor A(every y value is multiplied by A).  Thus a A >1 will stretch the graph vertically, and a 0<A<1 with shrink the graph vertically.  If A is negative, it reflects the graph over the x axis and then either shrinks or stretches vertically.  If A is 1, nothing changes.
Finally, a D term shifts the graph vertically in the direction expected (a negative number will shift down, a positive number will shift up).  For example, if D is -2, the graph of the parent function will shift down 2.

<u>Warning </u><u></u><u>CBAD must be performed in the order C-B-A-D</u>

Now that you know these simple rules and can memorize the few parent functions, you can figure out the domain and range of almost any function.  

In your case, the function x^(2)-25/2 is not much different than x^2, an upwards facing parabola centered at (0,0).  In fact, there is only one transformation, D, because C=0 (it is not shown), B=1(it is not shown), and A=1(it is not shown).  Thus the only difference between your graph and the parent function is that yours is shifted down by 25/2.  

For this reason, because the domain of x^2 is not restricted (it includes all real numbers), the domain of your new function is not restricted (it includes all real numbers).
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2. Wilton drives a taxicab. He charges $40 per hour. One passenger gave Wilton a tip of $30. Write an expression to represent th
ICE Princess25 [194]
Hopefully this is the correct answer! but your expression would be:  y=40x+30
and if he drove for 5hrs then you would plug in 5 for your x value so it would be y=40*5+30 and 40*5 is 200.(the star means multiplying) then add 30 to get a total of $230
so the expression is:  y=40x+30
and if he drove for 5hrs then he sould make a total of: $230
hopefully that helped and was the right answer  :)
3 0
3 years ago
Read 2 more answers
What answer is this?
klemol [59]

Answer:

option B

\frac{31}{50}-\frac{4}{25} i

Step-by-step explanation:

Given in the question a complex fraction

<h3>Step1</h3>

To divide complex numbers, you must multiply by the conjugate. To find the conjugate of a complex number all you have to do is change the sign between the two terms in the denominator.

\frac{5+4i}{6+8i}(\frac{6-8i}{6-8i})

<h3>Step2</h3>

Distribute (or FOIL) in both the numerator and denominator to remove the parenthesis.

\frac{30+24i-40i-32i²}{36-64i^{2} }

<h3>Step3</h3>

Simplify the powers of i, specifically remember that i² = –1.

\frac{62-16i}{36+64}

<h3>Step4</h3>

\frac{62}{100}-\frac{16i}{100}

<h3>Step5</h3>

simply

\frac{31}{50}-\frac{4}{25}i

8 0
3 years ago
we believe that 42% of freshmen do not visit their counselors regularly. For this year, you would like to obtain a new sample to
Maksim231197 [3]

Answer:

A sample of 1077 is required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

42% of freshmen do not visit their counselors regularly.

This means that \pi = 0.42

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.

How large of a sample size is required?

A sample size of n is required, and n is found when M = 0.035. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.035 = 2.327\sqrt{\frac{0.42*0.58}{n}}

0.035\sqrt{n} = 2.327\sqrt{0.42*0.58}

\sqrt{n} = \frac{2.327\sqrt{0.42*0.58}}{0.035}

(\sqrt{n})^2 = (\frac{2.327\sqrt{0.42*0.58}}{0.035})^2

n = 1076.8

Rounding up:

A sample of 1077 is required.

3 0
3 years ago
There are 50 kids at the park 30 of the girls what percent of the kids are boys
Flauer [41]

Answer:

40 %

Step-by-step explanation:

3 0
3 years ago
Triangle A″B″C″ is formed by a reflection over x = −3 and dilation by a scale factor of 3 from the origin. Which equation shows
Allisa [31]

Answer:

  see below

Step-by-step explanation:

Each segment in ΔA"B"C" is 3 times the length of the corresponding segment in ΔABC. This is due to the dilation by a scale factor of 3.

Then you have ...

  \overline{A''B''}=3\overline{AB}\quad\text{or}\\\\\dfrac{\overline{AB}}{\overline{A''B''}}=\dfrac{1}{3}

The latter relation matches the second choice.

5 0
3 years ago
Read 2 more answers
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