1. Let f(x) be defined by the linear function graphed below and
g(x) = x2 - 9x + 14.
I
A. Describe the right end behavior of g(x).

1. Let F(x) Be Defined By The Linear Function Graphed Below Andg(x) = X2 - 9x + 14.IA. Describe The Right

Answers

Answer 1

Answer:

Step-by-step explanation:

A). g(x) = x² - 9x + 14

     Since coefficient of highest degree term (x²) is positive, parabola will open upwards.

    For any parabola opening upwards,

    Right end behavior,

    y → ∞ as x → ∞

B). Let the equation of the linear function is,

    f(x) = mx + b

    Where m = slope of the function

    b = y-intercept

    From the graph attached,

    Slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{-(2+1)}{(0+1)}[/tex]

    m = -3

    b = -1

    Therefore, function 'f' will be,

    f(x) = (-3)x - 1

    f(x) = -3x - 1    

    g(x) = x² - 9x + 14

           = x² - 7x - 2x + 14

           = x(x - 7) - 2(x - 7)

           = (x - 2)(x - 7)

    If h(x) = f(x)g(x)

    h(x) = -(3x + 1)(x -2)(x - 7)

    For h(x) ≥ 0

    -(3x + 1)(x - 2)(x - 7) ≥ 0

     [tex]x\leq -\frac{1}{3}[/tex] Or 2 ≤ x ≤ 7

    Therefore, for 2 ≤ x ≤ 7, h(x) ≥ 0

C). If k(x) = [tex]\frac{h(x)}{(x-2)}[/tex]

    k(x) = [tex]\frac{-(3x+1)(x-2)(x-7)}{(x-2)}[/tex]

    k(x) = -(3x + 1)(x - 7)

    For k(x) = -56

    -(3x + 1)(x - 7) = -56

     3x² -20x - 7 = 56

     3x² - 20x - 63 = 0

     3x² - 27x + 7x - 63 = 0

     3x(x - 9) + 7(x - 9) = 0

     (3x + 7)(x - 9) = 0

     [tex]x=-\frac{7}{3},9[/tex]


Related Questions

Three cats and three dogs, A, B, C, D, E, and F, live on a street in three different-coloured houses. Each house hosts one cat and one dog. One house is red. A is a cat and does not live in the red house. B is a dog and does not live in the same house as C (even though they could). D lives in the blue house. D does not live with A or F (even though it could). E does not live with A and does not live in the yellow house.


Indicate whether each letter correspond to a cat or a dog, and match each cat and each dog with a colored house.

Answers

Answer:

1) A is a cat; B is a dog; C is a cat; D is a dog; E is a dog; F is a cat

2) A lives with B in a yellow house; C lives with D in a blue house; E lives with F in a red house.

Step-by-step explanation:

Step 1: First we identify the animals as cats or dogs

A is a cat

B is a Dog

Since B can live with C, C is a cat

Since D can live with A, D is a dog

F is a cat since it can live with D

E is therefore, a dog

Step 2: We then identify the house each two animals live in pairs of a cat and a dog

D lives in a blue house

A lives in a yellow house since it does not live with D or in a red house

C lives with D in a blue house since D does not live with either A or F

E lives in a red house since it does not live with A or in a yellow house

F lives with E in a red house since E does not live with A

Therefore, B lives with A in a yellow house

Help me please help

Answers

I think it’s roast beef

An investor wants to save money to purchase real estate. She buys an annuity with monthly payments that earn 5.6% interest, compounded monthly. Payments
will be made at the end of each month, Find the total value of the annuity in 16 years if each monthly payment is $65.
Do not round any intermediate computations, and round your final answer to the nearest cent

Answers

Answer:

1040

Step-by-step explanation:

just took 65 and mutiply 65$

Answer:

1040

Step-by-step explanation:

just took 65 and mutiply 65$

The following data represent the​ high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts​ (a) through​ (c).

Temperature Lower Limit Upper Limit Days
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9

Required:
Approximate the mean and standard deviation for temperature.

Answers

Answer:

The mean is  [tex]\= x  = 79.7 [/tex]

The standard deviation  [tex]\sigma =7.81[/tex]

Step-by-step explanation:

From the question we are told that

  The data given is  

Temperature                Lower Limit           Upper Limit               Days

50-59                               50                             59                          2

60-69                                 60                            69                        313

70-79                                  70                           79                          1419

80-89                                   80                          89                         1503

90-99                                   90                          99                          319

100-109                                100                         109                         9        

Generally the average of each limit is evaluated as

Temperature    Lower Limit   Upper Limit         Average[tex](x_i)[/tex]                    Days[tex](f_i)[/tex]

50-59                 50                   59              ( 50 + 59 )/2 =54.5                 2

60-69                 60                   69              (60+69)/2 = 64.5                    313

70-79                 70                    79               (70+79)/2 =74.5                    1419

80-89                 80                   89                (80+89)/2 =84.5                  1503

90-99                 90                   99                 (90+99)/2 = 94.5                319

100-109             100                  109                 (100+109)/2 = 104.5            9  

Generally the mean is  evaluated as

     [tex]\mu  =  \frac{\sum x_i f_i}{\sum f_i}[/tex]

=>  [tex]\mu  =  \frac{ (54.5 * 2) + (64.5 * 313) +\cdots +(104.5 *  9)}{2 + 313 +\cdots + 9}[/tex]

=> [tex]\= x  = 79.7 [/tex]

Generally the standard deviation  is  evaluated as

    [tex]\sigma = \sqrt{ \frac{\sum[ f_i * ( x_i^2 - \= x^2)] }{\sum f_i}}[/tex]

=>   [tex]\sigma =\sqrt{ \frac{[2 * [(54.5)^2) - 79.7^2 ]]+[313 *[ (64.5)^2)-79.7^2] +\cdots +[9 *[ (104.5)^2)- 79.7^2]  }{2 + 313 +\cdots + 9}}[/tex]

=>  [tex]\sigma =7.81[/tex]

   

The mean and Standard deviation for the given data would be as follows:

μ [tex]= 79.7[/tex]

б [tex]= 7.81[/tex]

Frequency Distribution

Given that,

Temperature       Lower Limit           Upper Limit             Days([tex]f_{i}[/tex])

50-59                       50                           59                          2

60-69                       60                           69                         313

70-79                         70                           79                          1419

80-89                        80                          89                          1503

90-99                        90                          99                           319

100-109                    100                         109                            9  

Average([tex]x_{i}[/tex])    

[tex]( 50 + 59 )/2 =54.5[/tex]

[tex](60+69)/2 = 64.5[/tex]

[tex](70+79)/2 =74.5[/tex]

[tex](80+89)/2 =84.5[/tex]

[tex](90+99)/2 = 94.5[/tex]

[tex](100+109)/2 = 104.5[/tex]

As we know,

Mean (μ) [tex]=[/tex] ∑[tex](x_{i} f_{i}) /[/tex]∑[tex]f_{i}[/tex]

[tex]= [(54.5[/tex] × [tex]2) + (64.5[/tex] ×[tex]313)+....(104.5[/tex]× [tex]9)][/tex][tex]/(2 + 313 + 1419 + ....9)[/tex]

∵ μ [tex]= 79.7[/tex]

As we know,

Standard Deviation:-

[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{f_{i} }}}[/tex]

by putting the values, we get

∵ б [tex]= 7.81[/tex]

Thus, μ [tex]= 79.7[/tex] and б [tex]= 7.81[/tex] are the correct answers.

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What is the unit rate for meters per second if a car travels 414 meters in 23 seconds?

Answers

Answer:

18 meters per second

Step-by-step explanation:

414/23=18

Not trying to be rude but you should know how to do this with or without a calculator

Please help! Thank you

Answers

Answer:

-294

Step-by-step explanation:

If cost of 3 kg of sugar is Rs 240. What is rate of cost of sugar​

Answers

Rs80 for each 1kg sugar

The company is interested in which confidence intervals associated with 1 (very satisfied) contain the proportion 0.25, or 25%. Determine which confidence levels satisfy this. (Select all that apply.)

Answers

Hi, you've asked an incomplete question. However, I provided a brief explanation about confidence interval and confidence level.

Explanation:

The term confidence interval and confidence level are not the same but they are related. Confidence interval refers to a range of values that makes up part of the statistic's mean data which contains an unknown population parameter.

However, the Confidence level is the level of certainty that the confidence interval would contain the true population parameter if a random sample is drawn.


Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are written on a separate piece of paper and
placed in a hat. One piece of paper is randomly selected from the hat. Use the Venn diagram shown
to help you determine the probability that the number selected is odd or less than 5.

Answers

Step-by-step explanation:

i dont see a venn diagram but i think the number is probably more than 5

The probability that the number selected is odd or less than five will be 0.20 or 20%.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are written on a separate piece of paper and placed in a hat.

One piece of paper is randomly selected from the hat.

Then the probability that the number selected is odd or less than 5 will be

Total event = 10

Favorable event = 2 {1, 3}

Then the probability will be

[tex]\rm P = \dfrac{2}{10}\\\\P = 0.2 \ or \ 20\%[/tex]

More about the probability link is given below.

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I mark as brainliest ​

Answers

Answer:

D

Step-by-step explanation:

Its d Reason is if she has 5 and he has 10 he has twice as much

Please Solve as Fast as You Can
If the point (3, -2) is reflected across the y-axis, what are the coordinates of the reflected point?

Answers

Answer:

flips the sign of the opposing coordinate (-3,-2)

Step-by-step explanation:

In which of the following stores would you pay the least amount for an item that is priced $360?
Store A: Sale of 10% off and a successive discount of 10% off.
Store B: Sale of 15% with no additional discount.
Store C: Sale of $35 off and a successive discount of 10% off.
a.
All of the stores have the same discounted price.
b.
You can get the lowest price at Store A.
c.
You can get the lowest price at StoreB.
d.
You can get the lowest price at Store C.


Please select the best answer from the choices provided

A
B
C
D

Answers

I think answer should be a. Please give me brainlest let me know if it’s correct or not okay thanks bye I appreciate it bye

''Store A'' has the least amount to pay for an item at price of 291.60.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Price : 360

Hence,

Store A: Sale of 10% off and a successive discount of 10% off.

360 x (100-10)% = 360 x 90% = 324

324 x (100-10)% = 324 x 90% = 291.60

Store B: Sale of 15% with no additional discount

360 x (100-15)% = 360 x 85% = 306

Store C: Sale of $35 off and a successive discount of 10% off

360 - 35 = 325

325 x (100-10)% = 325 x 90% = 292.50

Hence, Store A has the least amount to pay for an item at price of 291.60

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The number 49 has exactly three factors Since 98 is a multiple of 49, which must be tue of 982
It must have only two factors
tmusthave fewer than three factors
It must have exacty three factors
t must have more than three factors

Answers

Must have more than three factors

Answer:

it must have more than 3 factors

Step-by-step explanation:

that factors are 1,2,491,982

The Fashion Store has $6000 available each month for advertising. Newspaper ads cost $200 apiece and no more than 20 can be run per month. Radio ads cost $100 each and no more than 30 can run per month. TV ads cost $800 a piece, with a maximum of 7 available each month. Approximately 1000 women will see each newspaper ad, 800 will hear each radio ad, and 14,000 will see each TV ad. How much of each type of advertising should be used if the store wants to maximize exposure?

Answers

9514 1404 393

Answer:

7 TV ads4 radio ads

Step-by-step explanation:

The audience per dollar is ...

  Newspaper: 1000/$200 = 5/$

  Radio: 800/$100 = 8/$

  TV: 14000/$800 = 17.5/$

So, TV gives the greatest exposure. As much of the budget as possible should be spent on TV ads. That amount is the lesser of $6000 and ...

  (7 ads)($800/ad) = $5600

With $5600 spent on TV ads, the remaining advertising budget is ...

  $6000 -5600 = $400

The next most cost-effective medium is radio. The remaining $400 budget allows for ...

  $400/($100/ad) = 4 ads

__

To maximize exposure, the advertising budget should be spent this way:

TV: 7 ads for $5600, exposure of 98000Radio: 4 ads for $400, exposure of 3200

Sharon invests $2000 in a savings
account with a fixed annual interest rate of
7% compounded monthly. What is the amount in her saving account after 5 years?

Help :(

Answers

Answer: 0.07

Step-by-step explanation:

Use the given functions to set up and simplify 5years. 7% = 0.075 years = 0.07

A Cessna 172 plane that is used to transport up to four VIPs is 2 km in the air if the potential energy of the VIP plane with three VIPs on board is 860 J what is the combined mass of the Cessna and passengers

Answers

Answer:

0.0438 kg

Step-by-step explanation:

We are given;

Potential energy; U = 860 J

Height; h = 2 km = 2000 m

Formula for potential energy is;

U = mgh

Where g is acceleration due to gravity = 9.81 m/s²

Thus;

860 = m × 9.81 × 2000

m = 860/(9.81 × 2000)

m = 0.0438 kg

Simplify the following expression, 3/8 divided by 1/4

Answers

The correct answer is 1.5 in decimal form but in fraction form it’s 3/2

The required simplified product is 3/2.

Given that fractions  3/8 ÷ 1/4.

To divide two fractions by multiplying the first fraction with the reciprocal of the second fraction.

Let a, b, c and d be any real numbers. Consider a/b ÷ c/d that gives

[tex]\frac{a}{b}[/tex]  ÷  [tex]\frac{c}{d}[/tex] = [tex]\frac{a}{b}[/tex] ×  [tex]\frac{c}{d}[/tex].

That implies, [tex]\frac{3}{4}[/tex]  ÷  [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{8}[/tex] ×  [tex]\frac{4}{1}[/tex] = [tex]\frac{3}{2}[/tex].

Hence, the required simplified product is 3/2.

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Restless Leg Syndrome and Fibromyalgia
People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent study indicates that people with fibromyalgia are much more likely to have restless leg syndrome than people without the disease. The study indicates that, for people with fibromyalgia, the probability is 0.33 of having restless leg syndrome, while for people without fibromyalgia, the probability is 0.03. About 2% of the population has fibromyalgia. Create a tree diagram from this information and use it to find the probability that a person with restless leg syndrome has fibromyalgia.

Answers

Answer:

The probability that a person with restless leg syndrome has fibromyalgia is 0.183.

Step-by-step explanation:

Denote the events as follows:

F = a person with fibromyalgia

R = a person having restless leg syndrome

The information provided is as follows:

P (R | F) = 0.33

P (R | F') = 0.03

P (F) = 0.02

Consider the tree diagram attached below.

Compute the probability that a person with restless leg syndrome has fibromyalgia as follows:

[tex]P(F|R)=\frac{P(R|F)P(F)}{P(R|F)P(F)+P(R|F')P(F')}[/tex]

            [tex]=\frac{(0.33\times 0.02)}{(0.33\times 0.02)+(0.03\times 0.98)}\\\\=\frac{0.0066}{0.0066+0.0294}\\\\=0.183333\\\\\approx 0.183[/tex]

Thus, the probability that a person with restless leg syndrome has fibromyalgia is 0.183.

Deandre pays $15.20 for a pack of 8 towels.
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.
Please help

Answers

Answer: Each towel costs $1.90

Step-by-step explanation:

$15.20 divided by 8 = $1.90

A table marked at ₹ 15,000 is available for ₹ 14,400. Find the discount given and the discount percentage.

Answers

Answer:  ₹ 600 and 15% discount rate i believe

Step-by-step explanation:

Can u please helppppppp !!!!!!!!!

Answers

Answer:

yes i can help you

Step-by-step explanation:

Answer:

The height is the water wheel diameter so if you have 9' of head but are only running a 6 foot diameter wheel the height for this calculation is 6 feet. Most people use 12v batteries to store their electricity and an inverter

Step-by-step explanation:

Sorry if I cant help but that's number 2 answer.

A directed segment ST¯¯¯¯¯ is partitioned from S (−5,0) to T in a 32 ratio at point M (10, 15). What are the coordinates of point T? (20, 25) (15, 20) (7, 3) (5, 15

Answers

Answer:

[tex]T = (20,25)[/tex]

Step-by-step explanation:

Given

[tex]S = (-5,0)[/tex]

[tex]M = (10,15)[/tex]

[tex]Ratio = 3:2[/tex]

Required

Determine the coordinate of T

Line division by ratio is calculated using:

[tex]M(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where:

[tex](x_1,y_1) = (-5,0)[/tex]

[tex](x,y) = (10,15)[/tex]

[tex]m:n = 3:2[/tex]

So, we have:

[tex](10,15) = (\frac{3 * x_2 + 2 * -5}{3+2},\frac{3 * y_2 + 2 * 0}{3+2})[/tex]

[tex](10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5})[/tex]

Multiply through by 5

[tex]5 * (10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5}) * 5[/tex]

[tex](50,75) = (3x_2 -10,3y_2)[/tex]

By comparison:

[tex]3x_2 - 10 = 50[/tex]

[tex]3y_2 = 75[/tex]

[tex]3x_2 - 10 = 50[/tex]

[tex]3x_2 = 50 + 10[/tex]

[tex]3x_2 = 60[/tex]  --- Divide through by 3

[tex]x_2 = 20[/tex]

[tex]3y_2 = 75[/tex]

[tex]y_2 =75/3[/tex] --- Divide through by 3

[tex]y_2 =25[/tex]

Hence:

The coordinates of T is

[tex]T = (20,25)[/tex]

A cookbook originally cost $13.00. Yesterday, Marta bought it at 40% off.
Horn
40%
OFF
How much was deducted from the original price? (4 pt.)
А
$0.40
B
$5.20
$7.80

Answers

The answer is A, just so you know this was the best math class I’ve ever been in

A percentage is a way to describe a part of a whole. The amount paid by Marta for the cookbook is $7.80.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

As it is given that the original price of the cookbook was $13, Marta bought it for 40% off. Therefore, Marta only paid 60% of the original cost,

[tex]\text{Amount paid by Marta} = \text{60\% of the original cost}\\\\\text{Amount paid by Marta} = \dfrac{60}{100} \times \$13\\\\\text{Amount paid by Marta} = \$7.8[/tex]

Thus, the amount paid by Marta for the cookbook is $7.80.

Learn more about Percentages:

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find an equation for the line that passes through the point (7,1) and is perpendicular to the line x-3y+25=0​

Answers

Answer:

y + 3x = - 20

Step-by-step explanation:

x - 3y + 25 = 0

- 3y = - 25 - x

3y = 25 + x

y = ( 25 + x )/3

y = ( 1/3 )x + 25/3

Y= mX+ c

m= gradient= 1/3

The perpendicular gradient should be the negative reciprocal of the gradient we have now.

which is : -1÷(1/3) = -3

Now for the perpendicular line equation, we have:

y = 1

x= 7

m= -3

y - y1 = m ( x - x1 )

y - 1 = -3 ( x + 7 )

y-1 = -3x -21

y + 3x = -20

An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower

Answers

Answer:

415 ft/s

Step-by-step explanation:

I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.

From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.

The constant elevation remains 4090 ft while the value of x and s varies with time.

Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.

Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s

Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.

This means that we want to find ds/dt when x = 3010 ft

From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;

s = √(4090² + 3010²)

s = √25788200

s ≈ 5078.21 ft

Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;

x² + 4090² = s²

Differentiating x and s with respect to t, we have;

2x(dx/dt) = 2s(ds/dt)

2 will cancel out to give;

x(dx/dt) = s(ds/dt)

ds/dt = (x/s)(dx/dt)

Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;

ds/dt = (3010/5078.21) × 700

ds/dt ≈ 415 ft/s

what is 3/7 × 3 3/7?​

Answers

= 3/4 × 3 3/7

= 3 3/7 as an improper fraction = 24/7

= 3/4 × 24/7

= 3 × 24 / 4 × 7

= 72/28

Let us try to simplify it .

We know that both 72 and 28 is divisible by 4 . Hence ,

72 ÷ 4 / 28 ÷ 4

= 18/7

Therefore , 3/7 × 3 3/7 = 72/78 or 18/7 ( simplest form ) .

Answer: 1²³⁄₄₉

Step-by-step explanation:

Convert any mixed numbers to fractions

3³⁄₇ x ²⁴⁄₇

Applying the fractions formula for multiplication

3 x 24

_____

7   x  7

= ⁷²⁄₄₉

Simplifying fraction

1²³⁄₄₉

i need help please help me

Answers

Answer:

use a contractor or protractor or whatever theyre called

Step-by-step explanation:

i just need points to ask another question

Help me plsss! I'll give u 10 points​

Answers

Answer:

1.02n

Step-by-step explanation:

We just have to simply the expression already given which will give you the equivalent expression.

n + 0.02n since these are like terms because of the variable "n", we can just add them together

n+0.02n

1.02n

How is 5 represented in 6.75

Answers

Answer:

5 is in the hundreths place :))

Step-by-step explanation:

Answer:

0.05

Step-by-step explanation:

since the place value of the five is beyond the decimal point, and it is the second number beyond the decimal point, so it is in the hundredths place.

(5/6) 2 x (1 1/10) 2

Answers

Answer:

11/3x

your welcome

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