Mathematics College

The graph of F(x), shown below, resembles the graph of G(x) = x^2?, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?

The Graph Of F(x), Shown Below, Resembles The Graph Of G(x) = X^2?, But It Hasbeen Changed Somewhat.

Answers

Answer 1

Answer:

D

Step-by-step explanation:

Slope is negative, derivative of x shows that -3 is the maximum in C/D but C is not negative

Answer 2

The function F(x) = -3(x + 3)^2 + 3.

The correct option is (D).

What is a Function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A variable y is said to be a function of the independent variable x if there is a relationship between them.

As per the given data:

We are given the equation of the functions G(x) and we have to find out the equation of the function F(x).

Equation of G(x) = x^2

For a left shift of 3 units x → x + 3.

⇒ y = (x + 3)^2

For a change in concavity, if the curve, multiply by -3.

⇒ y = -3(x + 3)^2

For an up shift of 3 units y → y -3.

⇒ y - 3 = -3(x + 3)^2

The function F(x) comes out to be:

F(x) = -3(x + 3)^2 + 3

Hence, The function F(x) = -3(x + 3)^2 + 3.

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Related Questions

Simplify:
3^x-1 × 27^x+1
___________
81^x​

Answers

Answer:

3^x-1×27^x+1

___________

81^x

81^x+x-1+1

_________

81^x

81^2x

_____

81^x

81^2x-1x

81^1x

find the slope intercept form of the equation of the line that passes through (-1,5) and is parallel to the line y=2x+4

Answers

Answer:

y = 2x + 7

Step-by-step explanation:

Which number line correctly shows -3-(1.5) ​

Answers

The first choice is correct because negative goes left and both numbers are negative!

Element X is a radioactive isotope such that every 40 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 110 grams, how much of the element would remain after 29 years, to the nearest whole number?

Answers

Answer:67 or 66.549674907

Step-by-step explanation:

Man women baby

Which container holds more, a half-gallon milk jug or a 2-liter juice bottle

Answers

Answer:

1 gallon=3.79 liters  2 liter juice bottle would hold more

Step-by-step explanation:

Write a cubic function whose graph is shown

Answers

Answer:

f(x) = x³ - 2x² - x + 2

Step-by-step explanation:

Since, the graph attached has three zeros (x-intercepts) at x = -1, 1 and 2,

Equation of the given function will be,

f(x) = (x + 1)(x - 1)(x - 2)

By solving this equation,

f(x) = (x² - 1)(x - 2)

     = x²(x - 2) - 1(x - 2)

     = x³ - 2x² - x + 2

Therefore, answer  will be f(x) = x³ - 2x² - x + 2.

The cubic function will be "f(x) = x³ - 2x² - x + 2".

According to the given graph,

Three zeros,

x = -1, 1, and 2

The function will be:

→ [tex]f(x) = (x+1)(x-1)(x-2)[/tex]

By solving this, we get

          [tex]= (x^2-1)(x-2)[/tex]

          [tex]= x^2(x-2)-1(x-2)[/tex]

          [tex]= x^3-2x^2-x+2[/tex]

Thus the function above is right.

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Rob is setting up a model train track that is 3 and 3 over 8 feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole every 3 over 8 foot apart. How many telephone poles does he need? (Input number values only.

Answers

Answer:

9?

Step-by-step explanation:

Answer:

sorry dont understaand

Step-by-step explanation:

easy question if your having big problem

Answers

Answer:

whats the problem

Step-by-step explanation:

Answer:

yup

Step-by-step explanation:

In an arithmetic sequence, the seventh term is −9 and the nineteenth term is 39.
Find the common difference. Give only the exact value as your answer.

Answers

Answer:

37.5% that is the answer

Step-by-step explanation:

The required common difference is 4.

What is an arithmatic progression?

An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.

Now it is given that,

the seventh term, T₇ = −9 and

the nineteenth term, T₉ =  39.

Let a be the first term, d is the common difference and n is the number of term.

Since Tn of the series is given as,

Tn = a + (n-1)d

Therefore,

T₇ = a + (7-1)d

⇒ -9 = a + 6d ...(i)

and,

T₉ = a + (19-1)d

⇒ 39 = a + 18d  ...(ii)

Subtracting equation (ii) by (i) we get,

48 = 12d

or, d = 48/12

⇒ d = 4

Thus, the required common difference is 4.

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Mrs. Dimitri purchased a case of yogurt cups. Out of every 10 yogurt cups, 6 are strawberry. There are 30 yogurt cups in the case. How many yogurt cups are strawberry?

Answers

Answer:

18

Step-by-step explanation:

The ratio of strawberry yogurt cups to all of the yogurt is 6:10.  We know that there are 30 total yogurt cups, which is the same as 3 times 10.  to find the number of strawberry cups, 6 should be multiplied by 3 as well to equal 18.  18:30 is still the same ratio as 6:10

Please helpp I’ll give brainleist

Answers

Answer:

87 for lo and om is 56

Step-by-step explanation:

Answer:

<LON= 98 Degrees

Step-by-step explanation:

180-55(2)=70

70+28=98

(b) 25% of what number is 17?

Answers

Answer:

68

Step-by-step explanation:

derive that 25 percent of 68 equals 17.

Answer:

25 percent of 68 equals 17.

Step-by-step explanation:

find the lowest common multiple (LCM) of 15 and 30.

A) 5
B) 15
C)30
D)60​

Answers

Answer:

L.C.M of 15 and 30 is 30.

please help UwU
if correct you get Brainiest

Answers

Answer: C

Step-by-step explanation:

Always choose c When in doubt

Mrs. Savino runs 3 miles in 28 minutes. At this rate, how many minutes would it take her to run 15 miles? * Need it ASAP​

Answers

Answer:

she would take 140 minutes to run 15 miles

Step-by-step explanation:

28 X 5 os equal to 140

Answer:

139.95

Step-by-step explanation:

28 divided by 3 is 9.33 so 9.33x 15=139.95

HELP ME PLEASEEEEEEEEEE

Answers

the photo isnt loading

PLEASE HELP WILL GIVE BRAINLIEST

Does the following table represent a linear function? If so, find the linear equation that models the data.​

Answers

Y=-5x -2 should be the equation I’ll go check tho

A bag of marbles contains three blue, one black, and four
yellow marbles. If two marbles are chosen at random
without replacement, what is the probability that both
marbles will be yellow?

Answers

Answer:

3/14

Step-by-step explanation:

Blue = 3Black = 1Yellow = 4

Total = 3 + 1 + 4 = 8

Probability of two yellows:

4/8*3/7 = 3/14

Simplify 18 - 6x + 5x - 11

Answers

Answer:

7-x

Step-by-step explanation:

18-11=7

-6x+5x=-x

therefore, the answer is 7-x

The solution of the expression is,

⇒ - x + 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 18 - 6x + 5x - 11

Now, We can solve the expression as;

⇒ 18 - 6x + 5x - 11

Rearrange as;

⇒ - 6x + 5x + 18 - 11

Combine like term as;

⇒ - x + 7

Thus, The solution of the expression is,

⇒ - x + 7

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What is the difference between ploting (2, 3) and (3, 2)
on a coordinate plane? Explain.

Answers

The X and Y values are different, they have to be equal and in the right order to be plotted the same.

. The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.† Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night. For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes. Suppose that the sample standard deviations were 25 minutes for the U.S. sample and 49 minutes for the Mexico sample. The report concludes that on average, adults in the United States get less sleep on work nights than adults in Mexico. Is this a reasonable conclusion? Support your answer with an appropriate hypothesis test. (Use
= 0.05.
Use 1 for Mexico and 2 for the United States.)

Answers

Answer:

Yes the conclusion in the question  is a reasonable conclusion

Step-by-step explanation:

From the question we are told that

    The sample size is  [tex]n_1 = n_2 = n = 250[/tex]

     The sample mean for USA is  [tex]\= x_1 = 391 \ minutes[/tex]

     The sample mean for Mexico is [tex]\= x_2 = 426 \ minutes[/tex]

     The sample standard deviation for USA is  [tex]s_1 = 25 \ minutes[/tex]

    The sample standard deviation for Mexico is  [tex]s_2 = 49 \ minutes[/tex]

     

The null hypothesis is  [tex]H_o : \mu_1 = \mu_2[/tex]

The alternative hypothesis is  [tex]H_a : \mu_1 < \mu_2[/tex]

Generally the test statistics is mathematically represented as

        [tex]z = \frac{\= x_1 - \= x_2 }{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2 } } }[/tex]

=>     [tex]z = \frac{ 391 - 426 }{ \sqrt{ \frac{25^2}{250} + \frac{49^2}{250} } }[/tex]

=>     [tex]z = -10[/tex]

From the z table  the area under the normal curve to the left corresponding to   -10  is

    [tex]p-value = P(Z < -10 ) = 0.00[/tex]

Generally from the value obtained we see that

  The p-value is  <  [tex]\alpha[/tex]  hence

The decision rule is

Reject the null hypothesis

The conclusion is  

 The is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico

Hence the conclusion in the question is a  reasonable conclusion

The p-value is less than [tex]\alpha[/tex] hence reject the null hypothesis. This is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico and hence it is a reasonable conclusion given in the problem.

Given :

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits.Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night.For the United States, the sample mean was 391 minutes, and for Mexico the sample mean was 426 minutes.Suppose that the sample standard deviations were 25 minutes for the U.S. sample and 49 minutes for the Mexico sample.

According to the given data the sample size of the US and Mexico is [tex]\rm n_1=n_2=250[/tex].

The hypothesis are as follows:

Null Hypothesis is [tex]\rm H_0 : \mu_1=\mu_2[/tex]

Alternate Hypothesis is [tex]\rm H_1 : \mu_1<\mu_2[/tex]

Now, the mathematical representation of test statistics is:

[tex]\rm z = \dfrac{\bar{x_1}-\bar{x_2}}{\sqrt{\dfrac{\sigma^2_1}{n_1}+\dfrac{\sigma^2_2}{n_2}} }[/tex]

[tex]\rm z = \dfrac{391-496}{\sqrt{\dfrac{25^2}{250}+\dfrac{49^2}{250}} }[/tex]

z = -10

According to the z-table:

p - value = p (Z < -10) = 0

The p-value is less than [tex]\alpha[/tex] hence reject the null hypothesis.

This is sufficient evidence to conclude that adults in the United States get less sleep on work nights than adults in Mexico and hence it is a reasonable conclusion given in the problem.

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Solve this equation 5x -7 = -12

Answers

Answer:

The answer is x = -1

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

5x-7=-12

5x=-5

x=-1

A classroom is painting the classrooms. Each classroom takes 1/3 of a gallon of
paint. If the school buys 6 gallons of paint, how many classrooms can they paint?
Plz help

Answers

Answer: try 18

Step-by-step explanation:


Could someone answer this I am a bit confused I will give a brainlist for the right answer I promise :)

Answers

The answer to NP is 14

Answer:

NP=14

BC=44

Step-by-step explanation:

[tex]60-24-22=14\\NP=14\\MN=BP=PC\\BC=2(MN)\\BC=44[/tex]

If a wagon is accelerating at a rate of 2 m/s and the
force acting on it is 20 N, what is the mass of the
wagon?

Answers

Answer:

40kg

Explanation:

a=2m/s^

f=20N

M=?

we know

f=m*a

or, 20=m*2

or, 2m=20

or, m= 20/2

:. m=10 kg

4(2x-15)+7(3x+2)=70?

Answers

Answer:

the answer is [tex]x=4[/tex]

Step-by-step explanation:

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.

hope this helps :)

4(2x-15) +7(3x+2) =70
8x -60 +21x +14 =70
29x -60 +14 =70
29x -46 =70
29x =24
29x/29 = 24/29
x= 1.208333333

does that help?

which point of the number line represents negative 4/5?
A

B

C

D​

Answers

c i believe since your counting the negative one as well

Answer:

the answer is A

Step-by-step explanation:

Please answer, will give brainliest.

Answers

Answer:

third one

Step-by-step explanation:

Answer:

I think one solution

Step-by-step explanation:

*Sorry if this did not help. I'm only in 5th grade*

For every 24 cookies, there are 12 students. Which ratio does not represent cookies to students?

Answers

Answer: 12:24

Step-by-step explanation:

You can’t have 12 students to each cookie

Answer:

D: 2 students for every cookie

Step-by-step explanation:

D does not represent the ratio of cookies to students because it claims there are 2 students to every cookie, where there are 2 cookies for every student.

A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. Answer parts a and b.
a. To what percent of its capacity is the large container filed?
The container is filled to % of the maximum capacity.

Answers

Answer:

The container is filled to 87.5% of the maximum capacity.

Step-by-step explanation:

Given

Maximum capacity of container = m = 64 ounces

Filled capacity=> as it is 8 less than maximum capacity = 64-8 = 56 ounces

The container is 56 ounces full.

To find the percentage:

[tex]percentage = \frac{56}{64}*100\\= 0.875*100\\=87.5\%[/tex]

Hence,

The container is filled to 87.5% of the maximum capacity.

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