Graph the function y equals 12 times the quantity 1 over 3 end quantity to the x power. Does the function represent growth or decay? What is the equation of the asymptote?

points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.

points of discontinuity:

In rational functions, points of discontinuity are defined as fractions with undefined or zero as their denominator. When the denominator of a fraction is 0, the fraction is no longer defined and shows up as a hole or break in the graph.

points of discontinuity removable:

A point on the graph that is removable discontinuity is one that may be filled in with a single value despite not existing.If an is zero for a factor in the denominator that shares a factor with a factor in the numerator, a removable discontinuity at x=a in the graph of a rational function occurs.

points of discontinuity non removable:

A function's break that cannot be repaired with a single point is referred to as a non-removable discontinuity. It cannot be filled in with a single point, a vertical asymptote (a vertical line that the graph approaches but never crosses because the function is undefined at that x-value) is non removable.

given that

[tex]y = \frac{ {x}^{2} + 2x}{ {x}^{2} - 7x - 18 } [/tex]

now take the denominator and find the factors of it.

[tex] {x}^{2} - 7x - 18 = 0[/tex]

[tex] {x}^{2} - 9x + 2x - 18 = 0[/tex]

x (x -9) + 2 (x - 9) = 0

(x - 9) (x + 2) = 0

[tex]y = \frac{ {x}^{2} + 2x}{(x - 9)(x + 2)} [/tex]

now, take common on numerator

[tex]y = \frac{2(x + 2)}{(x - 9)(x + 2)} [/tex]

cancel the common factor in both numerator and denominator

[tex]y = \frac{x}{x - 9} [/tex]

now find the points of discontinuity.

x-9=0 , x+2=0

x = +9 , x = -2

now, x = +9 and x = -2

Hence the points of discontinuity of rational function y= x²+2 x / x²-7 x-18 is x = 9 & x = -2.

Learn more about rational functions from here:

https://brainly.com/question/1851758

#SPJ4

Answer: -9,0

Step-by-step explanation:

The 5th term in the sequence is 1/9

The sequence is defined by

g subscript n equals 9 times open parentheses 1 third close parentheses to the power of n minus 1 end exponent.

Rewrite properly as

g(n) = 9 * (1/3)^n - 1

For the 5th term, the value of n is 5

So, we have

g(5) = 9 * (1/3)^5- 1

Evaluate the difference

g(5) = 9 * (1/3)^4

Evaluate the exponent

g(5) = 9 * 1/81

Evaluate the product

g(5) = 1/9

Hence, the 5th term in the sequence is 1/9

Read more about sequence at

https://brainly.com/question/7882626

#SPJ1

Yes, ln 5+ log₂10 can be written as a single logarithm.

Single logarithm expression for ln 5+ log₂10 is 2.60943791243.

  ln 5+ log₂10

=1.60943791243 +1

= 2.60943791243

The logarithm is exponentiation's opposite function in mathematics.

The power to which a number must be increased in order to obtain another number is known as a logarithm. This shows that the logarithm of a fixed integer base b represents the exponent to which that number must be raised in order to reach a specific number x.

The logarithm with a base of 10 is the common logarithm, commonly referred to as the value of log base 10. The common logarithm of 10 has a value of 1, or 1.

To learn more about logarithm from the given link:

brainly.com/question/28346542

#SPJ4

The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)

Transformation is the movement of a plane figure from one point to another. Transformation may also be an increase / decrease in the size of the figure. Examples of transformation are reflection, rotation, translation and dilation.

Dilation is the increase or decrease in size of a figure by a scale factor.

The function rule for a quadrilateral that is rotated 180 degrees, translated four units to the left, and then reflected across the y axis is (x, y) ⇒ (x + 4, -y)

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

Answer:

The answer is 34.2L

Step-by-step explanation:

5buc x 1.8gal = 9gal

9gal x 3.8L = 34.2L

Answer:

at least one mile for sure

Answer:

-1/5

Step-by-step explanation:

First:

Calculate the rise:

On this graph we go down 1 meaning our rise will be -1.

Second:

Calculate the run:

On the graph we go right 5 so the run would be 5.

Third:

We put the rise and run together to get the slope.

Hence, the answer is -1/5

Notes:

Rise means how many units you move up or down from point to point.

Run means how far left or right you move from point to point.

Up and Right= + outcome

Down and Left= - outcome

Also if your rise over run is the same number but two negative number the slope would turn into a positive.

Example:

-5/-5=1

Answer:

u≤25

Step-by-step explanation:

63 ≥ 3u-12

-3u    -3u

-3u+63 ≥ -12

 -63        -63

-3u ≥ -75

/-3    /-3

u≤25

The average speed of car is 14.4 m/s.

We can see that from Photo 1 to Photo 2, the car covers 9 times the 0.8 meter distance. So, calculating the total distance traveled between the time span second photo was clicked.

Total distance traveled = 0.8×9

Performing multiplication

Total distance traveled = 7.2 meters

Now, the time is given as 0.5 seconds.

Finding the average speed using formula -

Average speed = total distance traveled ÷ total time taken

Keep the given values in formula to find the average speed.

Average speed = 7.2 ÷ 0.5

Performing division

Average speed = 14.4 m/s

Hence, the average speed of the car is 14.4 m/s

Learn more about calculations on speed -

brainly.com/question/24739297

#SPJ4

The complete question is attached in figure.

Answer:

24

Step-by-step explanation:

24 - 19 = 5

5 * -3 = -15

Answer:

answer is 5

Step-by-step explanation:

[tex] - 3(x - 19) = - 15[/tex]

cancel out both sides by -3, therefore -15 will become positive

[tex] \frac{ - 3(x - 19)}{ - 3} = \frac{ - 15}{ - 3} [/tex]

then add 19 to both sides

[tex]x - 19 +19= 5 + 19[/tex]

then X will add up to 24

Answer:

the answer is 49

Step-by-step explanation:

The value of k that makes the equation 0.000342891 = 3.42891 × [tex]10^k[/tex]  true when k = -4.

Scientific notation is a form of writing large numbers with a base that is greater than or equal to 1 and less than 10 and multiplying this base with powers of 10 in the way we can write large numbers in compact form.

Here in the given question, the actual value is 0.000342891 and we need to write it n the form of scientific notation.

We know in scientific notation base should be greater than or equal to 1 and less than 10.

∴  0.000342891 in scientific notation can be written as 3.42891×10⁻⁴ as we have moved the decimal 4 digits to the right of the actual value.

learn more about scientific form here :

https://brainly.com/question/18073768

#SPJ1

The translated figure, 1 unit left and 6 units up, is given at the end of the answer.

The original figure is missing, and is given at the end of the answer.

A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

The rule for a shift of 1 unit left and 6 units up is given as follows:

(x,y) -> (x - 1, y + 6).

The coordinates of the vertices of the original figure are given by:

(-7, -3), (-2,-4), (-7,-9), (-1,-9).

Hence the coordinates of the vertices of the translated figure are given by:

(-8, 3), (-3,2), (-8,-3), (0,-3).

The translated figure, 1 unit left and 6 units up, is given by the second graph at the end of the answer.

More can be learned about transformations at https://brainly.com/question/4521517

#SPJ1

Answer: x2 . f(x) - 2x . f (x) + 6 . f(x)

Step-by-step explanation:

The mass of the sun is 4 x 10³¹ times the mass of a golf ball.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The mass of the sun = 2 x 10³⁰ kilograms.

The mass of golf ball = 0.05 kilogram = 5 x 10⁻² kilograms

Now, Calculate the mass of the sun about the mass of the golf ball as;

The mass of the sun/the mass of a golf ball = 2 x 10³⁰/ 5 x 10⁻²

                                                                   =  4 x 10³¹

So, The mass of the sun is 4 x 10³¹ times the mass of a golf ball.

Learn more about the division method visit:

https://brainly.com/question/1679793

#SPJ1

Step-by-step explanation:

4×10^1= 40

4×10^2=400

4×10^3=4000

4×10^4=40000

Answer:

"㏑ 4-14, find each product."

Step-by-step explanation:

[tex]4 \times 10^1(10 \times 1) = 40\\4 \times 10^2(10 \times 10) = 400\\4 \times 10^3(10 \times 10 \times 10) = 4,000\\4 \times 10^4(10 \times 10 \times 10 \times 10) = 40,000[/tex]

When the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set.

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

From the number line in the question, we can see that:

As a general rule, open circles implies that the number at that endpoint is not included part of the solution set.

Hence, the complete statement is "when the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set."

Read more about number lines at

https://brainly.com/question/24644930

#SPJ1

To be the solution of all real numbers the left side expression must be the same as the right side so option (D) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

Given the equation,

3x+6=2x+10+x-4

3x + 6 = 2x + x + 10 - 4

3x + 6 = 3x + 6

For every real number will satisfy the equation.

But the left-hand side is equal to the right-hand side.

Now,

Let's consider an equation,

2x + 3 + 4x = 6x + 2 + 4

2x + 4x + 3 = 6x + 6

6x + 3 = 6x + 6

3 = 6 since it is false it means it will not have any real solution.

Hence "To be the solution of all real numbers the left side expression must be the same as the right side".

For more about the equation,

brainly.com/question/10413253

#SPJ1

The height of the rectangular prism is 3 units.

A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges.

Given:

Length(L)= 4 units

width(w)= 3 units

Diagonal(D) = [tex]\sqrt{34}[/tex] units

According to given question we have

The formula for rectangular prism  is

[tex]L^{2} +w^{2} + h^{2} = D^{2} \\\\4^{2} +3^{2} +h^{2} =(\sqrt{34} )^{2} \\\\16+9+h^{2}=34\\\\25+h^{2}=34\\\\h^{2}=34-25\\\\h=\sqrt{9} \\\\h=3 units[/tex]

Therefore, the height of the rectangular prism is 3 units.

Learn more details about rectangular prism here:

https://brainly.com/question/27812749

#SPJ1

The distance between points A and B is 9.22units, approximately.

This is further explained below.

Generally, In the image attached, you can observe a representation of the problem.

We have to find the distance between points A and B, which have coordinates (7,0) and (0,6), respectively.

The definition of distance between two given points is

[tex]d=\sqrt{\left(y_2-y_1\right)^2+\left(x_2-x_1\right)^2}[/tex]

Using points A and B, the distance between us

[tex]&d_{A B}=\sqrt{(7-0)^2+(0-6)^2}\\\\d_{A B}=\sqrt{49+36}\\\\\ d_{A B}=\sqrt{85} \\\\&d_{A B} \approx 9.22[/tex]

In conclusion, the distance between points A and Ais 9.22 units, approximately.

Read more about distance

https://brainly.com/question/13034462

#SPJ1

The number of bowling games played for $34 is 8

The  mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by linear equation y = 3.50x + 6.00

We are given that total money spent is $34

The number of bowling  games played is assumed to be x

Now, we have substitute the value of y in the linear equation to get number of bowling  games played

34 = 3.50x +6.00

34 - 6 = 3.50 x

28 = 3.5x

x = 28/ 3.5

x = 8

So, the number of bowling games played for $34 is 8

To know more about Linear equation - https://brainly.com/question/13738061

#SPJ1

The function represents an exponential growth and the y-intercept is (0,0.2)

How can you tell whether an exponential function is growing or deteriorating?

Given - y=0.2(3.8) x

For a. function, [tex]y = ab^{x}[/tex]

the function represents exponential growth if a > 0  and b > 1 .

the function represents exponential decay if a > 0 and 0> b > 1.

In either case, the y-intercept is (0,a).

From the given, a = 0.2 and b = 3.8 because 2> 0 and  b > 1 .

then the function represents an exponential growth and the y-intercept is (0,0.2)

Learn more about exponential function

brainly.com/question/11487261

#SPJ4

Answer:

E) None of the above

Step-by-step explanation:

If Larry drives to work in the morning, he will hit traffic. Therefore:

A) If Larry hits traffic, it must be morning.

B) If Larry drives to work in the afternoon, he will not hit traffic.

C) If Larry doesn't hit traffic, it must not be morning.

D) If Larry drives to work in the afternoon, he will hit traffic.

E) None of the above.

The sum of all exterior angles in any n-sided polygon is 360 degrees, so:

[tex]72 + 63 + 75 + x + 34 + 74 = 360 \\ x + 318 = 360 \\ x = 360 - 318 \\ x = 42[/tex]

Correct answer is B. We can rewrite the expression in the form of 39 - 80i

Any function that goes from complex numbers to complex numbers is said to as complex. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain. A nonempty open subset of the complex plane is typically found in the domain of complex functions.

Using (a-b)²= a²-2ab+b²

(8-5i)² = 8²-2(8)(5i)+(5i)²

= 64 - 80i + 25i²

We know that i²=-1

So

= 64 - 80i + 25(-1)

=64 - 25 - 80i

= 39 - 80i

To learn more about complex function from given link

https://brainly.com/question/27551059

#SPJ4

Express 7 and 21 as a product of their prime factors and write in index form.

The power rule states (a^m)^n = a^mn

7= 7^1

21 = 7x7x7 = 7^3 = 7^2 x7^1

(7^1)1/2 x (7^2x7^1)^1/2 = 7^1/2 x 7^2/2x7^1/2

7^1/2 x 7x7^1/2 = 7 x (7^1/2)^2

7x7 = 49

Find out more on indices at: brainly.com/question/28595100

#SPJ4