graphing piece wise functions

We will plot the graph for a LN function by keeping in mind that the domain must be greater than 0.

LN means natural logarithm. LN function denotes natural logarithm function. It has also another name, logarithm of base e.

It is expressed as

y = ㏑x that is the inverse of                            

the natural base exponential function

y = ex

If we have a logarithm function, f(x) = y = ln x

while plotting with the above function, ln x can be found for only the positive value of x and there is no value of ln x for negative values.

The properties of the graph of the LN function are following.

The domain of the LN function is only the real numbers that means x > 0.

The ranges of the LN function are all real number.

The coordinate of x intercept of the LN function is (1, 0).

The graph of LN function will be such that it will never touch the Y axis although it always approaches to it.

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Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). The total, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more objects in a logical order.

given

Δ DOG AND ΔCAT

According to Chanel, the series of transformations that maps triangle ABC onto triangle DEF is as follows:

Reflect it across the x-axis, then translate it up 6 units and left 1 unit before reflecting it across the y-axis.

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Answer:

Step-by-step explanation:

f(x) is quadratic function and g(x) is linear (since AP in the right column).

Find the equation of the function f(x), use the points on the graph:

The function is:

Find the equation of g(x)

Find the slope of g(x):

Use (-4, 7) to find its equation:

The y-intercepts:

Values at x = 3:

Average rate of change in the interval [2,5]:

Max of function in the interval [-5, 5];

Answer:

Step-by-step explanation:

What grade are you in bc I did this

Answer:

x=12

Step-by-step explanation:

10x-18+6x+6=180

16x-12=180

16x=180+12

16x=192

x=192/16

x=12

plz mark as brainliest

r = (sin theta + C)^(-1) where C is an arbitrary constant of integration.

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y.

r = (cos(theta) - d/d(theta) of sec(theta)) / sec(theta)

The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. Be a function with the form: y=f(x), where x is an independent variable, f is an unknown function.

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The slope of a logarithmic graph depends on the type of logarithm used.

For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.

For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.

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Answer:

dont click on the link its no the answer

Step-by-step explanation:

Answer:

139⁰

Step-by-step explanation:

since g and h are parallel

then n= 139⁰ (corresponding angles)

The amount of eroded rock in cubic kilometres is 1 km3.

To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.

In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:

20 m / 1000 = 0.02 km

Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:

10 km * 5 km * 0.02 km = 1 km3

So the amount of eroded rock in cubic kilometres is 1 km3.

Complete Question:

The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?

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Answer:

27.3%

Step-by-step explanation:

300/1100 = 0.2727

to get percentage we multiply ^^ by 100

so = 27.27% or rounded to nearest tenth = 27.3

When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.

To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b

This is only possible when the other term has 14,

Lets solve

 2a + 7b = - 5

- 4a + 14b = -10

-2a -7b = 5

Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

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The solution of the equations are x = √1 = ± 1

Now, According to the question:

The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]

Using the substitution rule we put [tex]x^{2}[/tex] = u .

The given equation now changes to

[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)

Equation(1) is a simple quadratic equation which can be solved by factorization as follows:

[tex]9u^2 - 2u - 7 = 0[/tex]

(9u + 7)(u - 1) = 0

Therefore

9u + 7 = 0 → u = -7/9

u -1 = 0→ u = 1

Since u = [tex]x^{2}[/tex] implies

x = √-7/9 = ± i√7/9

x = √1 = ± 1

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The complete question is this:

What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.

The coefficient of x⁸y⁹ is 81662929920.

A binomial is a two-term algebraic expression. Examples of binomials include a + b, x - y, and more.

The binomial expansion formulae are used to find the powers of the binomials that cannot be extended using the algebraic identities. 

Given expansion (3x + 2y)¹⁷

to find the coefficient of x⁸y⁹

this is found by binomial expansion,

(x + y)ⁿ = ∑ₙˣ⁻⁰ ⁿCₓxⁿ⁻ˣyˣ

here n = 17 and x = 9

(3x + 2y)¹⁷ = ¹⁷C₉ (3x)¹⁷⁻⁹ (2y)⁹

¹⁷C₉ = 24310

(3x + 2y)¹⁷ = 24310 (6561) (x)⁸ (512) (y⁹)

(3x + 2y)¹⁷ = 81662929920x⁸y⁹

Hence the coefficient is 81662929920.

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Answer:

D: 21.23 sq in

Step-by-step explanation:

A tennis ball is a sphere, so we're going to use the surface area of a sphere formula. (4πr²)

Remember that radius is HALF of the diameter, which in this case is 2.6. This means the radius is 1.3.

π represents 3.14

Once you plug the values into the above equation, you should receive the above answer.

Answer:

7 : 1 or 7/1

.........................

Answer:

-2 and -7

Step-by-step explanation:

This problem is about using the Factoring X.

Two numbers will multiply to the number placed at the top. These same two numbers will add to the value placed on the bottom.

Let's look at the factors of 14.

1 • 14 = 14

2 • 7 = 14

Now let's look at their sums.

1 + 14 = 15

2 + 7 = 9

We can see that 2 and 7 multiply to 14 and add to 9.

However, we need them to add to -9.

Note that two negative numbers multiplied will become positive.

-2 • - 7 = 14

Now let's look at their sum.

-2 + (-7)

Simplify the negative.

-2 - 7 = -9

We can see that -2 and -7 multiply to 14 and add to -9.

Hope this helps!

Answer:

The correct answer is 0 or choice A on edge

Step-by-step explanation:

right on edge

Therefore, value of r(x) as x approaches Infinity : zero

[tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]

"A function is a special relationship where for each input and their is single outputs."

"Limit is defined as the value that a function approaches for the given input value."

For given situation,

We have been given a function,

r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction

We can rewrite it as,

[tex]r(x)= \frac{ax^b+8}{cx^d}[/tex] , where a, b, c, and d are positive integers and b < d.

We need to find the value of r(x) approach as x approaches Infinity.

This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]

Now, we find the value of limit for given function.

[tex]\lim_{x \to \infty} r(x)[/tex]

=  [tex]\lim_{x \to \infty} \frac{ax^b+8}{cx^d}[/tex]

= [tex]\lim_{x \to \infty} (\frac{ax^b}{cx^d} + \frac{8}{cx^d})[/tex]

= [tex]\lim_{x \to \infty} \frac{a}{cx^(d-b)} + \lim_{x \to \infty} \frac{8}{cx^d}[/tex]                          ...............(since d > b)

= [tex]0 + 0[/tex]

= [tex]0[/tex]

Therefore, [tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]

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In simplest radical form as A = 22 = 4 cm2

The formula for the volume of a cube is V = a3, where a is the length of each of the cube's sides. In this case, we know that the volume of the cube is 8 cm3, so a3 = 8. When we take the cube root of 8, we get that a = 2 cm.

Therefore, the area of the rectangle formed by the intersection of the plane and cube is A = 2*2 = 4 cm2. This can also be expressed in simplest radical form as A = 22 = 4 cm2.

To calculate this step by step, we first use the formula V = a3 to find the length of each side of the cube. We plug in 8 cm3 for V and solve for a.

V = a3

8 cm3 = a3

Taking the cube root of both sides gives us:

a = ∛8

a = 2 cm

Next, we use the formula for the area of a rectangle, A = l*w, where l is the length and w is the width. We know that the length and width of our rectangle are both equal to 2 cm.

A = l*w

A = 2*2

A = 4 cm2

This can also be expressed in simplest radical form as A = 22 = 4 cm2.

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The expressions that represent this week's price of gasoline per gallon =g+0.05g.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Here, we have,

the price of a gallon of gasoline was `g` dollars.

the price of gasoline per gallon increased by `5%`.

So, the expressions that represent this week's price of gasoline per gallon

=g + g*5%

=g+0.05g

Hence, the expressions that represent this week's price of gasoline per gallon =g+0.05g.

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Answer:

7:13

Step-by-step explanation:

Answer:

if im thinking correctly ratios can be written in 3 ways

Step-by-step explanation:

so it could be 7/13, 7 to 13, or 7:13

Answer:

27 L

Step-by-step explanation:

To find 12.5% of 24, move the decimal all the way to the left and multiply 24 by 0.125. You get 3, which is how much was added to the original volume.

24 + 3 = 27, which is the new volume.

The percentage increase in the population from 1965 to 2015 is 35 %.

To calculate the population growth rate (PG), take the difference (subtraction) between the original population and the population at time point 1, divide by the original population, and multiply by 100. The population growth rate (PGR) for that period (10 years) was 12%.

Given:

In the year 1965, the population of country A was 2714000.

In the year 2015, the population of country A was 3663900.

Percentage increase in population 50 years

                         = [tex]\frac{(3663900-2714000)}{2714000}[/tex] × 100

                         = 35 %

Thus, the percentage increase in the population from 1965 to 2015 , i.e, 50 years is 35%.

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Answer:

4 + 9 = 13

+ +

12 - 8 = 4

= =

16 17

Took a while to solve but hope this helps!!

Answer:

top left=4, top right =9, bottom left=12, bottom right =8 -- set it up as a system of small equations.  

Step-by-step explanation:

x+y=13

x+w=16

y+z=17

w-z=4

x=16-w

y=17-z

then substitute.

(16-w)+y=13

-w+y= -3

-w+(17-z)= -3

-w-z = -20 add that to w-z=4

-2z= -16

z=8

then plug back in until you have all 4 values

w-(8)=4 --> w=12

-(12)+y= -3 --> -12+y= -3 --> y=9

x+(9)=13 --> x=4

Answer:

Supplementary angles

Step-by-step explanation:

I took the test and this was the correct answer

The equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that a line has a slope of 1/5 and passes through the point (3, 10)

We can write the slope of the line as -

m = 1/5

For the point (3, 10), we can write -

y = (1/5)x + c

10 = (1/5) x 3 + c

c = 10 - 3/5

c =  47/5

Therefore, the equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).

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For example, if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 6}, then x=6>5=y, but if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 7}, then x=6=y. not sufficient.

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Complete question is: If the ranges of values = 40 and the number of sets = 10 , then what will be the length of set ?

Answer:

C)

hope this helped

Step-by-step explanation: