Find the domain of the rational function. f(x)=x−2/x+3Enter your answer in interval notation.

Answer:

1/6

Step-by-step explanation:

Check the attachment.

Answer:

4.5 ywww

Step-by-step explanation:

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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The average rate of change of the function over the interval is 4

From the question, we have the following parameters that can be used in our computation:

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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Answer:

all of the expressions are equivalent

Step-by-step explanation:

if you simplify each expression, you get the same answer for all of them

The value of angle 1 given the value of angle 4 as 47° will be 133°

Parallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.

Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.

The value will be:

= 180° - 47°

= 133°

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Answer:

180 pages

Step-by-step explanation:

200*1/10

= 200/10

= 20 pages

total pages =200

read = 20 pages

left to read =200-20

=180 pages

The practical range of the function is D. all real numbers from 2.7 to 10.8, inclusive.

A function's range refers to all of the possible values for y. The formula for determining a function's range is y = f. (x). A function's range is the set of all its outputs. After we have substituted the domain, the range of a function is the complete set of all possible resulting values of the dependent variable (y, usually).

In this case, since the range is the value that satisfies the given function. For function f(t) = 2.7t the practical range of the function can be solved by substituting the lowest time and the highest possible time which are 1 and 4.

At t = 1 f(t) = 2.7 and at t = 4 f(t) = 10.8. so the range is all real numbers from 2.7 to 10.8, inclusive.

Therefore, the correct option is D.

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Answer:

200 17/23

Step-by-step explanation:

Mathxway.....

The evaluation of the statements with regards to the graph of a function are;

A function maps an input value to an output based on a definition or rule.

First part of the statement;

The graph of a non-vertical straight line has a range of values for the slope, m, of 0 ≤ m < ∞

The equation of a straight line function is of the form; y = m·x + c

Therefore;

The graph of a non-vertical straight line can be represented by the equation, y = m·x + c, where y has possible values of; -∞ < y < ∞, which indicates that as x increases or decreases, y increases (or decreases), such that each value of x maps unto only one value of y, which indicates that the graph is a function. The statement is therefore true.

Second part of the statement.

The graph of the quadratic function; y = a·x² + b·x + c has a shape of a parabola, therefore, the statement, the graph of a function is not always a straight line is true also.

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Answer:

Step-by-step explanation:

Answer:

18.56

Step-by-step explanation:

6.4% of 290 is 18.56

you find this by multiplying 290 by 0.064 (which is the decimal form of 6.4%)

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer: The triangles will all be the same.

Step-by-step explanation: They might be in different orientation, but they are congruent, and they can be rotated to all match up.

One proof of congruence is "sss" meaning "If the three sides of different triangles are the same, the triangles are congruent."

Answer:

It’s .1060606

With a remainder its: 0 remainder 7

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

I want to say because if you divide 8 by 2 you get 4 so then you multiply by 3. I think...

Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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Answer:

60 minutes

Step-by-step explanation:

Answer:

The Supreme Court.

Step-by-step explanation:

After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.

Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.

This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.

After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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The required trasformation is given as,
(A) Function f translated 4 units down.
(B) Function f translated 3 units left.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here.
Given function

f(x) = ∛[x + 1]

put x = -3 and y = y - 4
f(x) = ∛[x - 3 + 1]  - 4
f(x) = ∛[x - 2]  - 4

Thus, the required trasformation is given as,
(A) Function f translated 4 units down.
(B) Function f translated 2 units left.

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Answer:

9

Step-by-step explanation:

f(5) = 1+2(5-1)

f(5) = 9

I hope it helps.

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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Answer:

2.The set of all values for output of a function. 4.The values for the dependent variable. And 6.The set of all y values.

Step-by-step explanation:

Domain is the input of the function and is also the independent variable, as for the range is the output and dependent variable. Given a function f , the set x values (inputs) is the domain of f , and the set y values ( outputs ) is the range of f . The domain of a function f is all of the values for which the function is defined. For instance, 1x is not defined when x=0 . Also, √x is not defined when x is negative.

(I’m also just learning this so I apologize if I am incorrect. I try my best.)