Let f be the function defined as follows:1. If a = 2 and b = 3, is f continuous at x = 1? Justify your answer.2. Find a relationship between a and b for which f is continuous at x = 1.Hint: A relationship between a and b just means an equation in a and b.3. Find a relationship between a and b so that f is continuous at x = 2.4. Use your equations from parts (ii) and (iii) to find the values of a and b so that f is continuous at both x = 1 and also at x = 2?5. Graph the piece function using the values of a and b that you have found. You may graph by hand or use your calculator to graph and copy and paste into thedocument

Let F Be The Function Defined As Follows:1. If A = 2 And B = 3, Is F Continuous At X = 1? Justify Your

Answers

Answer 1

Answer:

1. not continuous, as the function definitions deliver different function values at x=1 when approaching this x from the left and from the right side.

2.

2 = a + b

3.

0 = 2a + b

4.

a = -2

b = 4

Step-by-step explanation:

the function is continuous at a specific point or value of x, if the f(x) = y functional value is the same coming from the left and the right side at that point.

1. that means that for x=1

3 - x = ax² + bx

so,

3 - 1 = a×1² + b×1 = a + b

2 = a + b

we have to use a=2 and b=3

2 = 2 + 3 = 5

2 is not equal 5, so the assumed equality is false, so the function is not continuous there.

2. point 1 gave us already the working relationship between a and b.

2 = a + b

only if that is true, is the function continuous at x=1.

3. now for x=2

5x - 10 = ax² + bx

5×2 - 10 = a×2² + b×2 = 4a + 2b

10 - 10 = 4a + 2b

0 = 4a + 2b

0 = 2a + b

4. to find a and b to be continuous at both locations x=1 and x=2 both expressions in a and b must apply.

so, they establish a system of 2 equations with 2 variables.

2 = a + b

0 = 2a + b

a = 2 - b

0 = 2×(2-b) + b = 4 - 2b + b = 4 - b

b = 4

therefore

a = 2 - 4 = -2

5. I cannot draw a graph here.

just use now the function

3 - x, x < 1

‐2x² +4x, 1 <= x < 2

5x - 10, x >= 2


Related Questions

Help find the equivalent fraction with the correct steps please !

-2/5 x 6/-1 ÷ 5/-2

What’s the equivalent fraction ? Please help! Tysm (:

Answers

Answer:

: = ÷

[tex]\frac{-2}{5}*\frac{6}{-1} : \frac{5}{-2} = \frac{-12}{-5} : \frac{5}{-2} = \frac{12}{5}*\frac{-2}{5}=\frac{-24}{25}[/tex]

An equivalent fraction is -24 over 25.

evaluate expression: evaluate each expression when a = "-2" b=4 and c=-10

2a+b

ac-b

a+b/a

8a+5b

-4a-b

3c/-5

Answers

Answer:

2a+b=0

ac-b=16

a+b/a=-4

8a+5b=-4

-4a-b =4

3c/-5=6

Select the best answer to describe the parabola

Answers

Answer:

B

Step-by-step explanation:

It opens downwards, so the parabola is negative. This also means the vertex of the parabola is the highest point, therefore it is a maximum.

(t + 1)(t2 + 2t + 4)
find the product.

Answers

Answer:

5+5t

Step-by-step explanation:

The answer you are looking for is t^3+3t^2+6t+4.

Solution:

(t+1)(t^2+2t+4)

t^3+2t^2+4t+t^2+2t+4

t^3+3t^2+6t+4

Find the surface areas of each figure. Round your answers to the nearest tenth, if necessary​

Answers

Answer:

345.6 mi^2

Step-by-step explanation:

S.A = 2πrh+2πr^2

= 2π(5)(6) + 2π(5)^2

= 345.6 mi^2

Answered by G a u t h m a t h

Express 4 in simplest radical form.

Answers

Answer:

2

Step-by-step explanation:

What is the tenth term in the sequence 9, 13, 17, 21, 25…?


A. 29
B. 35
C. 45
D. 49

Answers

Answer:

45

Step-by-step explanation:

9, 13, 17, 21, 25

We are adding 4 each time

9+4 = 13

13+4 =17

17+4 = 21

The common difference =4

a1 = 9

The formula is

an = a1+d(n-1) where n is the term number

an = 9+4(n-1)

We want the 10th term

a10 = 9+4(10-1)

     = 9+4(9)

    = 9+36

   = 45

what is the total cost

Answers

Answer:

u watch Naruto

Step-by-step explanation:

.....................,....,...

Planes X and Yand points J, K, L, M, and N are shown.

Exactly how many planes contain points J, K, and N?

X

O 0

O 1

O 2

03

K

Υ

2

.M

.N

Answers

Answer:

0

Step-by-step explanation:

0

Number planes contain points J, K and N is 0. Therefore, option A is the correct answer.

What is a plane?

A plane in geometry is a level surface that never ends. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature.

Given that, X and Y are planes.

In the given figure, point J lies outside the X and Y planes.

Points K and N are lies on plane X.

So, J, K and N are not lying in the same plane.

Therefore, option A is the correct answer.

Learn more about the coordinate plane here:

https://brainly.com/question/24134413.

#SPJ7

The revenue, in dollars, of a company that manufactures televisions can be modeled by the polynomial 3x²+180x . The cost, in dollars of producing the televisions can be modeled by 3x² - 160x +300. The variable x is the number of televisions sold. If 150 televisions are sold, what is the profit?

Answers

We use the profit concept, and doing this, it is found that if 150 televisions are sold, the profit is $50,700.

-------------------------------------------

Profit is given by revenue subtracted by cost.

In this question:

Revenue: [tex]R(x) = 3x^2 + 180x[/tex]Cost: [tex]C(x) = 3x^2 - 160x + 300[/tex]

Thus, the profit of selling x televisions is:

[tex]P(x) = R(x) - C(x)[/tex]

[tex]P(x) = 3x^2 + 180x - (3x^2 - 160x + 300)[/tex]

[tex]P(x) = 3x^2 + 180x - 3x^2 + 160x - 300[/tex]

[tex]P(x) = 340x - 300[/tex]

-------------------------------------------

For 150 televisions, we have P(150), so:

[tex]P(150) = 340(150) - 300 = 50700[/tex]

If 150 televisions are sold, the profit is $50,700.

A similar question is given at https://brainly.com/question/14469903

Fifthteen of student took a math test. Eight student scored 75, five scored 82 and two scored 95. What was the average of there score

Answers

Answer:

84

Step-by-step explanation:

To find the average of the data or the mean, add 75, 82, and 95 which is 252, then 252 divided by 3 = 84. Hopefully, this helps :)

Please answer before 2:30!!!
There are 189 apples in a basket. How many children can share them equally?
List all numbers that apply.

Answers

For the equal distribution each child can take either 1 or 3 or 7 or 9 or 21 or 27 or 63 or 189 apple.

What is equal distribution?

The distribution of a something in a way that each will get same amount.

How 189 can be divided equally?

If the distribution is equally then each child should take, either 1 or 2 or 3 an so on means same amount.

For this we will check that 189 is divisible by which numbers.

Now we can see that 189 is divisible by 1, 3, 7, 9, 21, 27, 63, 189. It is clear that each child can take either 1 or 3 or 7 or 9 or 21 or 27 or 63 or 189 apple then the distribution will be equal means every child will have same amount of apple.

Therefore, the correct answer is 1, 3, 7, 9, 21, 27, 63, 189.

Learn more: https://brainly.ph/question/4734029

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Find the missing side of triangle

Answers

Answer:

30.

Step-by-step explanation:

x^2 = 24^2 + 18^2

x^2 = 576 + 324 = 900

x = sqrt900 = 30.

A room is twice as long as it is broad and its height is 8 m. if the cost of painting its walls at Rs. 20 per m² is Rs 9600 , find the cost of carpeting its floor at Rs. 400 per m²​​

Answers

let breadth be X

length = 2x

height = 8m

rate of painting the four wall= 20/m^2

cost of painting=9600

Area of four wall= cost of painting / rate

= 9600/20

= 480m^2

again,

Area of four wall = 2 h(l+b)

or, 480=2×8(X+2x)

or, 480/16=3x

or, 30/3=X

or, X= 10m

again,

2x= 2×10m=20m

again,

Area of floor = length × breadth

= 20×10

=200m^2

again,

rate of carpeting the floor= 400/m^2

cost of carpeting the floor = rate × area

= 400× 200

= Rs. 80000

What describes the correct way to convert minutes to an hour

Answers

Answer:

Yo mean correct way??

yo can divide minute by 60 to convert minute into hour

For example

To convert 10 minute into hour. then we should divide 10 by 60. 10/60

Answer:

In any conversion you have to establish  ratios (or rates) for the different units being converted.

The process will be performed by a series of multiplications that will cancel out the "unwanted" units.

multiplication by one (1) does not change the value in an equation.

you have to multiply by a "series of ones" that take into account the units being converted..

for example  

1 minute/60 seconds   or  1 inch = 2.54 cm   or  1 day = 24 hours

in your problem you have minutes... lets say you have 100 minutes

100 minutes * 1 hour             minutes cancel and you have  100/60 = 1 [tex]\frac{2}{3}[/tex] hrs

                       60 minutes

Step-by-step explanation:

What should the equations look like for each number? 17-20

Answers

Answer:

See below.

Step-by-step explanation:

17.)

[tex]x+100+120+100=360\\x+320=360\\x=40[/tex]

18.)

[tex]x+150+77+48=360\\x+275=360\\x=85[/tex]

19.)

[tex]x+122+92+76=360\\x+290=360\\x=70[/tex]

20.)

[tex]x+115+85+60=360\\x+260=360\\x=100[/tex]

if a = 4 b = 5 find the value of a^2+ab^2+y^2​

Answers

Answer:

121

Step-by-step explanation:

Given,

a = 4

b = 5

a² + ab² + b²

= 4² + 5 x 4² + 5²

= 16 + 80 + 25

= 121

If angle DCA measures 65 degrees, then angle ACB measures _____ degrees.

90
25
65

Answers

DCB form a right angle which is 90 degrees.

The two inside angles need to equal 90

ACB = 90-65 = 25

Answer: 25

Answer:

25

Step-by-step explanation:

its correct

three consecutive even numbers add up to 105 determine the product of the three numbers​

Answers

Answer:

34 + 35 + 36 = 105

Step-by-step explanation:

Help me with this pls IM FAILING PYTHAGOREAN THEOREM

Answers

Answer: 33

Work Shown:

Apply the pythagorean theorem to get

[tex]a^2 + b^2 = c^2\\\\x^2 + 44^2 = 55^2\\\\x^2 + 1936 = 3025\\\\x^2 = 3025 - 1936\\\\x^2 = 1089\\\\x = 33[/tex]

A bookstore is selling books for $10 each. Which graph shows the relationship between the number of books, x, the store sold and the total amount of money, y, paid from the book sales?

Answers

Answer:

Graph B

Explanation:

f(x) = 2[tex]x^{2}[/tex]+ x − 4 for x ∈R, a ≤ x ≤ a+3. If the range of the function f is −2 ≤ f(x) ≤ 16, find the possible values of a.

Answers

Answer:

No answer is possible

Step-by-step explanation:

First, we can identify what the parabola looks like.

A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.

Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.

This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.

Given these, we can then solve for when the endpoints of the interval are reached and go from there.

The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying

2x²+x-4 = -2

add 2 to both sides to put everything on one side into a quadratic formula

2x²+x-2 = 0

To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2  * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so

x= (-b ± √(b²-4ac))/(2a)

x = (-1 ± √(1-(-4*2*2)))/(2*2)

= (-1 ± √(1+16))/4

= (-1 ± √17) / 4

when f(x) = -2

Next, we can solve for when f(x) = 16

2x²+x-4 = 16

subtract 16 from both sides to make this a quadratic equation

2x²+x-20 = 0

To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so

x = (-1 ± √(1-(-20*2*4)))/(2*2)

= (-1 ± √(1+160))/4

= (-1 ± √161)/4

Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that

(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.

(2.75 x 107) + (1.23 x 108) simplify

Answers

Answer:

427.09

Step-by-step explanation:

(2.75 x 107) + (1.23 x 108)

294.25 + 132.84 = 427.09

HELP PLEAAASEEEEE
Can someone find the domain and range of this function PLEASE
y = 2/x + 3

Answers

Answer:

The domain is the whole R-{0} and the range is R

Need answer asap algebra 2 math

Answers

Answer:

B

Step-by-step explanation:

f(x) = 2x^2 - 4x + 5                   Put brackets around the first 2 terms.

f(x) = (2x^2 - 4x) + 5                 Take out the common factor of 2

f(x) = 2(x^2 - 2x) + 5                 1/2 the second term and square.

f(x) = 2(x^2 -2x + (2/2)^2) + 5   Express brackets as a perfect square.

f(x) = 2(x - 1)^2 + 5                     Multiply 2 * 1 (the term without an x. Subtract.

f(x) = 2(x - 1)^2 + 5 - 2                Combine

f(x) = 2(x - 1)^2 + 3

What is the midpoint of the segment shown below?
10
O A. (-1,-1)
(-11, 0)
O B. (-2, -3)
O C. (-1, -3)
- 10
10
(9,-1)
- 10
D. (-2, -1)

Answers

Answer:

(-1,-0.5)

Step-by-step explanation:

Find the solution to this problem by using the midpoint formula which is (x1+x2/2,y1+y2/2) plug in the values of y and x to get -11+9/2+0-1/2. simplify to get the solution of (-1,-0.5)

factorise 12x²+15xy. ​

Answers

Answer:

3x(4x+5y)

Step-by-step explanation:

to factorise this equation you have to remove the common terms,or the common factors in this case the common factor for both sides is 3 and the common letter is x

12x²+15xy

3x(4x+5y)

I hope this helps

Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Ariana will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Ariana's songs were played. Define the variables that you use to write the system.

Answers

40c+ 110m =500
c + m =9
c is variable for commercial; m is variable for movies

The sporting goods store sells 6 different brands of tennis rackets and 4 different brands of tennis balls. If Amanda buys one brand of tennis racket and one brand of tennis balls, how many different combinations of brands can she buy ?

10
12
16
24

Answers

Answer:

24

Step-by-step explanation:

There are 6 different types of rackets and 4 different types of balls.

To determine the number of different combinations

6 rackets * 4 balls

24 combinations

Answer:

24

Step-by-step explanation:

Using the box-and-whisker plot shown, find the maximum, minimum, and median values.

Answers

Hi, I'm happy to help!

for a box an whisker plot, maximum and minimum values on the edge of the lines. The maximum shown here is 8, because the line ends there. The minimum is -8 because the line ends there.

The median value is shown by the middle line, which is 4.

To sum it up: Maximum: 8, Minimum: -8, Median: 4\

I hope this was helpful, keep learning! :D

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