Suppose that the functions g and f are defined as follows.

g(x)=-3+2x^2
f(x)=9-6x

a. Find (g/f)(2)
b. Find all values that are NOT in the domain of g/f

If there is more than one value, separate them with commas.

Answers

Answer 1

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Given:

[tex]\to g(x)= -3+2x^2 \\\\\to f(x)=9-6x[/tex]

Calculating the value of [tex](\frac{g}{f})(2)[/tex]:

[tex]\to (\frac{g}{f}) (2)= (\frac{g(x)}{f(x)}) \times (2)[/tex]

               [tex]=\frac{2x^2-3}{9-6x} \times 2\\\\=\frac{2\cdot 2^2-3}{3(3-2\cdot 2)} \\\\=\frac{2\cdot 4-3}{3(-1)}\\\\ =\frac{8-3}{-3}\\\\ =\frac{5}{-3}\\\\ = - \frac{5}{3}\\\\[/tex]

x=[tex]- \frac{\sqrt{3}}{2}[/tex] and x=[tex]\frac{\sqrt{3}}{2}[/tex] are not in the domain.

Domain: [tex]x \belong (- \infty, -\frac{\sqrt{3}}{2})\cup (- \frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{2} )\cup (\frac{\sqrt{3}}{2}, \infty)[/tex]


Related Questions

A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed.Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals.What is the value of the test statistic to see if the correlation is statistically significant

Answers

Answer:

Hello your question has a disjointed equation attached to it and it is also incomplete attached below is the correct and complete question

A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below

answer :

y-intercept = 25.9047

 slope = 2.8420

Step-by-step explanation:

Determine the slope for the regression equation and y intercept

The regression equation ( gotten using excel ; attached below is the excel sample on how the equation was gotten )

y = 25.9047 + 2.8420x

from the equation gotten above

y-intercept = 25.9047

slope = 2.8420

10cm 3mm - 4.8cm
I do not understand that well can someone please help no need to explain

Answers

Answer:

60mm   or   6cm

Step-by-step explanation:

108mm - 48mm = 60mm

The answer is 60mm or 6cm

Explanation: i gotchu and leave a like if it helped you

20−5(4/2)^2=? /= fraction

Answers

Answer:

0

Step-by-step explanation:

=20−5(2^2)

=20−(5)(4)

=20−20

=0

10 MINUTES UNTIL I HAVE TO TURN TEST IN
HELP PLS :)

Answers

Answer:

10) Total Discount = $15 dollars; New Amount = $60 dollars.

11) Total Markup = $3,750 dollars; New Amount = $28,750 dollars.

12a) Percent Increase from $100 to $150: 50% increase.

12b) Percent Decrease from $150 to $100: 33.33% decrease.

Step-by-step explanation:

I would be more than happy to show my work, but I see that you have to submit your test soon, so I will just leave it at this for now. If you need any clarification, I am more than happy to help. Feel free to give me Brainliest if you feel this helped! Have a good day, and good luck on your test. :)

. A system may become infected by some spyware through the internet or e-mail. Seventy percent of the time the spyware arrives via the internet, thirty percent of the time via email. If it enters via the internet, the system detects it immediately with probability 0.6. If via e-mail, it is detected with probability 0.8. What percentage of times is this spyware detected

Answers

Answer:

This spyware is detected 66% of the time.

Step-by-step explanation:

We have these following percentages:

70% of the time, the spyware arrives via the internet, and in this case, is detected 60% of the time.

30% of the time, the spyware arrives via e-mail, and in this case, is detected 80% of the time.

What percentage of times is this spyware detected

Sum of 60% of 70%(arrived via spyware, detecte) and 80% of 30%(arrive via e-mail, detected). So

[tex]0.6*0.7 + 0.8*0.3 = 0.42 + 0.24 = 0.66[/tex]

This spyware is detected 66% of the time.

60% of what number is 33?

Answers

60 percent (calculated percentage %) of what number equals 33? Answer: 55.

Answer:

55 :)

Step-by-step explanation:

The area of a rectangle is 2- 3/4 inch. ^2 If the length of the rectangle is 1/2 inch, what is the measurement of the width?

Answers

Answer:

The width of the rectangle = 1.15 inches

Step-by-step explanation:

Explanation:-

Given that the length of the rectangle = [tex]\frac{1}{2} inch[/tex]

The area of the rectangle = [tex]\frac{2.3}{4}[/tex] inch²

We have to find the width of the rectangle

The area of the rectangle = length × width

                                  [tex]\frac{2.3}{4} = \frac{1}{2} X width[/tex]

                    ⇒     2 × 2.3 = 4× width

                   ⇒      4.6 = 4 w

                  ⇒      w = 1.15 inches

Final answer:-

The width of the rectangle = 1.15 inches

Solve Question 2 for x, the number of bracelets Tasha bought:

Question 2: (Tasha bought some bracelets that cost $5 each and 2 hats that cost $12 each. The cost of her total purchase was $39. Which equation can be used to find x, the number of bracelets she bought?)

Answer: x = bracelets

Answers

Answer:

x=3 bracelets

Step-by-step explanation:

5(X)+2(12)=39

5X=39-24

5X=15

X=3

What is -1/2+-1/5+-5x+3/10+3/2=

Answers

Answer:

-5x + 11/10

Step-by-step explanation:

Two cities are 252 miles apart. How far are the two cities from one another on a map with a scale of 1/4 inches: 18 miles?

Answers

Answer:

3.5 inches

Step-by-step explanation:

create a proportion:

inches / miles = inches / miles

let 'x' = distance in inches

1/4 = x

18    252

18x = 252(1/4)

18x = 63

x = 63 / 18

x = 3.5

Find the vertex and focus of the parabola.
x^2 + 4x - 8y + 12 = 0​

Answers

The Vertex is (-2,1)

And the focus is  (-2,3)

Find a solution to the linear equation y=6x−18 by filling in the boxes with a valid value of x and y.

Answers

Y= 6x-18
(Substitute y= 0)
0=6x-18
(Move the variable to the left)
-6x=-18
(Divide both sides)
The answer is X= 3

Answer:

So, (0,−18), (4,6), and (3,0) are some solutions to y=6x−18.

Step-by-step explanation:

Here are the first four terms of a number sequence.
8
14
20
26
Write down the next term of the number sequence and explain how you found your answer

Answers

8,14,20,26

8 to 14 is 6
14 to 20 is 6
20 to 26 is 6


The next term will be 26 + 6 = 32

Because there is a gap of 6 between each number

Raul has 6 shoeboxes on his bookshelf. If he has 9 toy robots in each shoebox, how
many toy robots does Raul have?
A. 63
B. 54
C. 36
D. 15
< Back
Clear Answer
Next >

Answers

Raul has 54 toy robots

Ally made 60 donuts on Friday. She made 3x donuts on Wednesday and 2x donuts on Thursday. How much donuts did she make in all?

Answers

Answer:

Step-by-step explanation: 60 x 3= 380

2 x 60= 270

270 + 380= 810

I have to determine whether the sides of the triangle form a pythagorean triple.​

Answers

Answer:

Step-by-step explanation:

How do you know if side lengths form a Pythagorean triple?

Pythagorean triples may also help us to find the missing side of a right triangle faster. If two sides of a right triangle form part of a triple then we can know the value of the third side without having to calculate using the Pythagorean theorem. From the ratio, we know that it is a Pythagorean triple.

a scientist recorded the temperature of the first day of spring for 24 hours starting from Midnight their hours the scientist recorded a low of 44°f and a high of 67°f.

Answers

Answer:

so what is the question?

Can the Pythagorean Theorem be used to find a distance in the coordinate plane?

Answers

Answer:

Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem, a2+b2=c2 a 2 + b 2 = c 2 , is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse.

Step-by-step explanation:

hope it help

Answer:

Yes it can be used because there is a right angle and by using 3 points u form a right triangle and then u will can find distance

What’s 57.036 in word form

Answers

Fifty seven point thirty six
fifty seven and thirty six hundredth

The city of Gainesville is trying to determine the average price for a gallon of gas. They randomly sampled 28 gas stations and found the sample mean to be $2.58 with a standard deviation of $0.09. Assume that all of the assumptions are met. Calculate a 95% confidence interval for the population mean gas price in Gainesville.

Answers

Answer:

The 95% confidence interval for the population mean gas price in Gainesville is between $2.54 and $2.62.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 28 - 1 = 27

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0.52

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.052\frac{0.09}{\sqrt{27}} = 0.04[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is $2.58 - $0.04 = $2.54

The upper end of the interval is the sample mean added to M. So it is $2.58 + $0.04 = $2.62.

The 95% confidence interval for the population mean gas price in Gainesville is between $2.54 and $2.62.

hat is the product of 4.01 × 10-5 and 2.56 ×108?

Answers

Answer:

35.1 and 276.48

Step-by-step explanation:

Answer:

The correct answer is: 1.0266 ×104

Step-by-step explanation:

Please help with this I really need it

Answers

Answer:

Step-by-step explanation:

calculate the pay for the following day of a weekly time card given a wage of $16/hr

Answers

Answer:

24x16x7

Step-by-step explanation:

Answer:

$2,688 a week

Step-by-step explanation:

16 x 7 x 24 would be 2,688

You develop an app to help students complete their homework. To earn money, you sell advertising space on the app’s main screen. An advertiser pays you $20 per month and an additional $0.005 each time the app is opened. Graph the linear equation that represents your monthly income y (in dollars) when the app is opened x times.

Answers

Answer:

y ⇒⇒⇒ monthly income

x ⇒⇒⇒ number of times app is opened

$20 per month and an additional $0.005 each time the app is opened

∴ y = 0.005 x + 20

The attached figure represents the graph of y

Step-by-step explanation:

What is the answer 2/3 + 5/12 =

Answers

Answer:

then answer is 13/12

Step-by-step explanation:

(8+5)/12

13/12

someone help please !

Answers

9514 1404 393

Answer:

  no, the triangles are not similar

Step-by-step explanation:

The given ratios tell you corresponding side ratios are ...

  ED : DC : EC = 8 : 10 : 12 = 4 : 5 : 6

  AB : BC : AC = 12 : 15 : 21 = 4 : 5 : 7

Corresponding sides do not have the same ratios. The given information can be used to prove the triangles are NOT similar.

In one particular suburb, there are 5 families that own a boxer. If there are a total of
25 families that own a dog in general, then what percentage of dog owners have a boxer?
Round your answer to the nearest whole number if necessary.

Answers

Answer:

60%

Step-by-step explanation:

Explanation:

To get percentages, take the part of a population that is being specified and divided that by the whole population and multiply that value by  

100

%

.

So there are  

30

people that own boxers, this is the specific population that is being compared to the whole dog-owning population, which is comprised of  

50

total families. So

30

50

can be reduced to  

3

5

and that gives us  

.6

When that value is multiplied by  

100

%

, it gives us our percentage of

.6

100

%

=

60

Which point is a solution to the equation 2x - y = 4?

Answers

Answer:

2x=  1 /2 y+ 2

Step-by-step explanation:

Solve for x.

2x−y=4

Add y to both sides.

2x−y+y=4+y

2x=y+4

Divide both sides by 2.

2x /2  =  y+4 /2

x= 1/ 2 y+2

The required point that is the solution to the equation 2x - y = 4 is at (2, -4)

In order to get the solution to the equation, we will need to get its x and y-intercept.

x- intercept is the point where y is zero.

Given the equation 2x - y = 4

If y = 0

2x - 0 = 4

2x = 4

x = 4/2

x = 2

Get the y-intercept

y intercept is the point where x = 0

if x = 0

2(0) - y = 4

-y = 4

y = -4

Hence the y-intercept is -4

The required point that is the solution to the equation is at (2, -4)

Learn more here: https://brainly.com/question/24609929

Which is the graph of y=3/4 x -3?

Answers

It would be graph A.

Answer:

graph A.

Step-by-step explanation:

Suppose you have $20 in your bank account. You start saving $5 each week. Your friend has $5 in his account and is saving $10 each
week. Assume that neither you nor your friend makes any withdrawals.
After how many weeks will you and your friend have the same amount of money in your accounts? How much money will each of you
have?

Answers

Answer:

The answer is after 3 weeks you will have the same amount of money

Step-by-step explanation:

5x + 20 = 10x +5

5x - 10x = 5 -20

-5x = -15

x = -15/-5

x = 3

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