Explain why f(x) = x^2-x-6/x^2-9 is not continuous at x = 3.

Answer: the answer is b(5)

Step-by-step explanation:

To find the third term work backwards and plug it in. That was when you plug the solution of b(n-1) everything fits.

Answer:

b(3)=-16

Step-by-step explanation:

We have to figure out the second term

b(2)=b(1)-7

b(2)=-2-7

b(2)=-9

and now the third one

b(3)=b(2)-7

b(3)=-9-7

b(3)=-16

Answer:

The parts are 24 and 16

Step-by-step explanation:

Let's call the two parts x and y. We can write the following system:

x + y = 40 -- Equation 1

1/4x = 3/8y -- Equation 2

2x = 3y -- Equation 3 (Multiply Equation 2 by 8 to get rid of denominators)

2x + 2y = 80 -- Equation 4 (Multiply Equation 1 by 2)

3y + 2y = 80 -- (Substitute 2x = 3y into Equation 4)

5y = 80 -- (3y + 2y = 5y)

y = 16 -- (Divide by 5)

x + 16 = 40 -- (Substitute y = 16 into Equation 1)

x = 24 -- (Subtract 16)

Answer:

C. 3

Step-by-step explanation:

C&D, A&F, K&J

The pairs of points are reflections across the x-axis will be 3. The correct option is C.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the given graph number of points is given in all four quadrants. The reflections of the points across the x-axis will be of the points C and D, A and F, K and J.

Therefore, the pairs of points that are reflections across the x-axis will be 3.

To know more about Coordinate geometry follow

brainly.com/question/18269861

#SPJ2

Answer:

The information given are;

[tex]r(V)=\sqrt[3]{\dfrac{V}{6\cdot \pi ^{2}}}[/tex]

Where;

r(V) = The radius of the doughnut (cm)

V = The volume of the doughnut (cm³)

The data are;

V,          r(V)

-30,     -0.8

-20,     -0.7

-10,      -0.55

0,          0

10,         0.55

20,        0.7

30,        0.8

From the table of values, the identified key features are;

a) There is a direct relationship between the radius and the volume of the doughnut

b) The correlation between the data increases to direct proportionality from the volume of 20 cm³ and above

c) The data values are symmetric and continuous about the y and x-axis

2) There is a direct linear relationship between radius, r and the volume V at end ends of the data between r and  V where V = -30 and-20 at one end and 20 and 30 at the other end

b) The x and y-intercept are

The x -intercept = (0, 0)

The x -intercept = (0, 0)

c) The pivot point is the point about which change occurs, therefore, the pivot point is the (10, 0.55)

d) The domain is a member of the set of real numbers, R while the range is also a member of the set of real numbers, R

Step-by-step explanation:

Answer:

y = -2/3x - 2

Step-by-step explanation:

Step 1: Find slope m of perpendicular line

Simply take the negative reciprocal of the given line

m = -2/3

y = -2/3x + b

Step 2: Find b

6 = -2/3(-12) + b

6 = 8 + b

b = -2

Step 3: Rewrite perpendicular equation

y = -2/3x - 2

Answer: D

Step-by-step explanation:

In synthetic division, if the divisor is an expression like x+3, you should always switch it to if x+3 were equal to 0.

[tex]x+3=0\\x=-3[/tex]

So, you should use -3. The only options with -3 are B and D.

The coefficients for the dividend are 7, -2, and 4, so D is the correct answer.

Hope this helps! If you still have questions, please ask.

Answer:

25.52791653032955454422437424679625318128649677442393276098...

Step-by-step explanation:

You can just paste this into wolframalpha.

Answer: 970.72312

Step-by-step explanation:

Straightforward operation.

Answer:

x = -5

Step-by-step explanation:

-7(x + 2) = 21​

Divide each side by -7

-7/-7(x + 2) = 21​/-7

x+2 = -3

Subtract 2 from each side

x+2-2 = -3-2

x = -5

Answer:

x = -5

Step-by-step explanation:

distribute: -7x-14 = 21

add 14 to both sides

divide by -7

x = -5

Answer:

work is shown and pictured

Answer:

[tex]n^6[/tex].

Step-by-step explanation:

[tex]n^4 * \frac{n^7}{n^5}[/tex]

= [tex]n^4 * n^{7 - 5}[/tex]

= [tex]n^4 * n^2[/tex]

= [tex]n^{4 + 2}[/tex]

= [tex]n^6[/tex].

Hope this helps!

a) The population is all of the flights belonging to the particular airline. It's not all flights in general because the airline does not have control over a rival company's flight schedule.

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

b) The sample is the 5 airlines the company selected. Ideally the sample should represent the population as much as possible. The larger the sample, the more representative the sample is.

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

c) No, the sample is likely not representative because one day of flight does not represent the entire lifetime of all flights done so far for that company. This particular day could have been a very good day with good weather, which may explain why the 5 flights were all on time.

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

d) It would be better for the company to select the days at random and sample all of the flights for those particular days chosen. This is a cluster sample. Each cluster is a day. Also, I think more flights should be sampled. Five flights does not seem like enough.

Answer:

A. (-8, 20)

Step-by-step explanation:

The formula for dilations is

[tex]\left(x_{1}\cdot t_{1},\ y_{1}\cdot t_{1}\right)[/tex] Where t is the scale factor

The first step is to plug in the numbers appropriately

[tex](-2*4,5*4)[/tex]

Then, multiply -2 by 4 and 5 by 4 to get

[tex](-8, 20)[/tex]

So your answer is (-8, 20)

Hope this helps

Have a great day! :)

Answer:

41/99

Step-by-step explanation:

There are two types of non terminating decimals. These are: Simple and Mixed

The one that you wrote up here is Simple, Since 41 is the only number that goes on repeating itself.

And mixed non terminating decimal is like 0.352 whereas 52 keeps repeating itself.

So when you change a non terminating decimal the denominator is always 9. But it depends on the decimal whether it is simple or mixed.

Since the decimal you wrote is simple and 2 digits keep on repeating themselves the denominator will be 99.

And the numerator will be the decimal number that keeps repeating itself without the repeating bar.

Therefore, the answer is 41/99.

Hope it helps ;) ❤❤❤

Answer:

0.2

Step-by-step explanation:

it works out to be 0.2 as a decimal and 20% as a percentage.

Answer:

.2

Step-by-step explanation:

Answer:

a) More.

b) Less.

c) More.

Step-by-step explanation:

a) If you invest $10 with an interest rate of 50% (that's very high I know XD), you would earn 10 / 2 = $5 in interest. If you invest $100 with an interest rate of 50%, you would earn 100 / 2 = $50 in interest. So, the more principal invested, the more interest earned.

b) Let's say you are investing $100. If there is an interest rate of 50%, as stated before, you would earn $50 in interest. If the interest rate were lowered to 25%, you would earn 100 / 4 = $25 in interest. So, the lower the interest rate, the less the interest.

c) The same exact thing as part a.

Hope this helps!

This question is incomplete. Please find attached to this solved question, the diagram required to solve this question.

Answer:

11 units

Step-by-step explanation:

The shaded portion of the rectangle forms the shape of a trapezium

The area of a trapezium = 1/2(a + b)h

From the diagram, we can see than x = b

a = 7 units

b = 7 units

Area of the trapezium = Area of the shaded portion = 63 square units

A = 1/2(a + b)h

63 = 1/2(7 + b)7

63 = 1/2(49 + 7b)

63 × 2 = 49 + 7b

126 - 49 = 7b

7b = 77

b = 77/7

b = 11 units

Since x = b, x = 11 units

The value of x is 11

Start by calculating the area (A) of the trapezoid using

[tex]A= 0.5 * (a + b)h[/tex]

Using the parameters from the complete question, we have:

[tex]63 = 0.5 * (7 + x) * 7[/tex]

Multiply both sides by 2

[tex]126 = (7 + x) * 7[/tex]

Divide both sides by 7

[tex]18 = 7 + x[/tex]

Subtract 7 from both sides

[tex]x = 11[/tex]

Hence, the value of x is 11

Read more about shaded areas at:

https://brainly.com/question/24579466

Answer:

Length of first leg = 1.4feet

Hypotenuse = 4.2feet

Explanation:

Since we are dealing with a right angled triangle, we will apply the Pythagoras theorem to solve the question. According to Pythagoras theorem, the square of the hypotenuse is equal to the sum if the square of the other two legs.

Mathematically, a² = b²+c² where a is the hypotenuse and b, c are the other two legs.

From the question, since hypotenuse of a right triangle is three times the length of its first leg, then a = 3b.

Also the other leg is four feet i.e c= 4

Substituting this values into the Pythagoras formula;

a²=b²+c²

(3b)² = b²+4²

9b² = b²+16

9b²-b² = 16

8b² = 16

b² = 16/8

b² = 2

b = √2

b = 1.4

Since a = 3b

a = 3(1.4)

a = 4.2

Hence, the length of the first leg is 1.4feet and that of the hypotenuse is 4.2feet both to the nearest tenth.

Answer:

The total revenue will decrease.

Step-by-step explanation:

The price elasticity of demand is 1.30 that shows that change in the quantity of tomatoes is greater than the change in the price of tomatoes. The hail storm will decrease the quantity (supply) of tomatoes. However, this decrease in supply will increase the price but the ratio of change in quantity will be more than the ratio of change in price. Thus, total revenue from tomatoes will also fall.

[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]

Answer:

Step-by-step explanation:

P (m) = a (m + 1) + b (m + 1) - c (m + 1)

P (m) = (a + b - c) (m + 1)

There are 2 prime factors

Answer:

Shaded area: 70cm^2

Step-by-step explanation:

Whole=120cm^2

White Square=

10-2.5-2.5=5

12-1-1=10

5✖️10=50cm^2

Whole-white=70cm^2

======================================================

Work Shown:

f ''' (x) = cos(x) .... third derivative

f '' (x) = sin(x)+C ... integrate both sides to get second derivative. Don't forget the +C at the end

We are given f '' (0) = 9, so we'll make use of this to find C

f '' (x) = sin(x)+C

f '' (0) = sin(0)+C

9 = sin(0) + C

9 = 0 + C

9 = C

C = 9

Therefore, f '' (x) = sin(x)+C turns into f '' (x) = sin(x)+9

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

Integrate both sides of the second derivative to get the first derivative function

f '' (x) = sin(x)+9

f ' (x) = -cos(x)+9x+D ... D is some constant

Make use of f ' (0) = 4 to find D

f ' (x) = -cos(x)+9x+D

f ' (0) = -cos(0)+9(0)+D

4 = -1 + 0 + D

D = 5

So we have f ' (x) = -cos(x)+9x+D turn into f ' (x) = -cos(x)+9x+5

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

Lastly, apply another round of integrals and substitutions to find the f(x) function. We'll use f(0) = 8.

f ' (x) = -cos(x)+9x+5

f(x) = -sin(x) + (9/2)x^2 + 5x + E .... E is some constant

f(0) = -sin(0) + (9/2)(0)^2 + 5(0) + E

8 = 0 + 0 + 0 = E

E = 8

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

We have

f(x) = -sin(x) + (9/2)x^2 + 5x + E

turn into

f(x) = -sin(x) + (9/2)x^2 + 5x + 8

Answer: C

1/4

Step-by-step explanation:

Given a graph for the transformation of f(x) in the format g(x) = f(kx),

This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.

Therefore, the value of k will be 1/4.

Answer:

k=4

Step-by-step explanation:

Answer:

$6.8

Step-by-step explanation:

Let x be the amount of money in Molly's amount

according to question,

4x-25=2.20

4x=2.20+25

4x=27.20

x=27.20/4

x=6.8

So,the amount of money in Molly's amont is $6.8

Answer: $6.80

Step-by-step explanation:

We will represent the amount of money that Molly has with a m. So it tells us the relationship between Kevin's amount and Molly's amount. It is says Kevin has 2.20 less that 4 times Molly's amount so we could represent it by the equation.

25 = 4m -2.20   solve for m.

+2.20     +2.20

27.20 = 4m

m= 6.8

4(6.8) = 27.20 - 25 = 2.20

Answer:

30 mph

Step-by-step explanation:

let s represent speed and h represent rebound.

Given that s is proportional to h then the equation relating them is

s = kh ← k is the constant of proportion

To find k use the condition s = 20, h = 10, then

20 = 10k ( divide both sides by 10 )

2 = k

s = 2h ← equation of proportionality

When h = 15 , then

s = 2 × 15 = 30 mph

Answer:

9 and 23

Step-by-step explanation:

Let x be smaller length in inches.

x+3x-4=32

4x=36

x=9

9*3-4=23

So they're 9 and 23 inches long.

The lengths of the two parts of the pipe are 9 and 23 inches long.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Let x be the smaller length in inches.

x + 3x - 4 = 32

4x = 36

x  =9

Now substitute;

9*3 - 4 = 23

Hence, the lengths of the two parts of the pipe are 9 and 23 inches long.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

A) 22°

∡DBG = (360° - BD - BG)/2

= (360° - 170° - 146°)/2

= 44°/2

= 22°

Answer:

For sample size n = 39 ; P(X < 31.6) = 0.9756

For sample size n = 76 ; P(X < 31.6) = 0.9970

Step-by-step explanation:

Given that:

population mean μ = 31

standard deviation σ = 1.9

sample mean  [tex]\overline X[/tex] = 31.6

Sample size n                 Probability

39

76

The probabilities that the sample mean is less than 31.6 for both sample size can be computed as  follows:

For sample size n = 39

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{39}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{6.245}})[/tex]

[tex]P(X < 31.6) = P(Z< 1.972)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9756

For sample size n = 76

[tex]P(X < 31.6) = P(\dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}})[/tex]

[tex]P(X < 31.6) = P(\dfrac{31.6 - \mu}{\dfrac{\sigma }{\sqrt{n}}}< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{31.6 - 31}{\dfrac{1.9 }{\sqrt{76}}})[/tex]

[tex]P(X < 31.6) = P(Z< \dfrac{0.6}{\dfrac{1.9 }{8.718}})[/tex]

[tex]P(X < 31.6) = P(Z< 2.75)[/tex]

From standard normal  tables

P(X < 31.6) = 0.9970

Answer:

1. 2.997

2. 29.93

Step-by-step explanation:

1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.

2. Same thing, gotta multiply all given values

Answer:

q = 108-n

Step-by-step explanation:

Given: 108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

The solution is : q = 108-n, is the value could replace q on the chart.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Given:

108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

The solution is : q = 108-n, is the value could replace q on the chart.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ7