For the following, find f(2.1) and f(4).

Answers:

Domain as an inequality:  [tex]\boldsymbol{-\infty < \text{x} < \infty}[/tex]

Domain in interval notation:  [tex]\boldsymbol{(-\infty , \infty)}[/tex]

Range as an inequality:  [tex]\boldsymbol{-3 \le \text{y} \le 3}[/tex]

Range in interval notation:  [-3, 3]

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Explanation:

The domain is the set of allowed x inputs. This graph goes on forever in both directions, so we can plug in any real number for x. There are no restrictions to worry about.

As an inequality, we write [tex]-\infty < \text{x} < \infty[/tex] to basically say "x is between negative infinity and infinity". In other words, x is anything on the real number line.

That inequality condenses into the interval notation of [tex](-\infty , \infty)[/tex]

Always use curved parenthesis for either infinity, because we can't ever reach infinity. It's not a number on the number line but rather a concept.

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

Now onto the range.

Recall the range is the set of possible y outputs. We look at the lowest and highest points (aka min and max) to determine the boundaries for the range.

In this case, the smallest y can get is y = -3

The largest it can get is y = 3

The range is any value of y such that [tex]-3 \le \text{y} \le 3[/tex] which in word form is "any value between -3 and 3, inclusive of both endpoints".

That inequality condenses to the interval notation [-3, 3]

We use square brackets to include the endpoints as part of the range.

Answer:

[tex]\textsf{Domain}: \quad (-\infty, \infty) \quad -\infty < x < \infty[/tex]

[tex]\textsf{Range}: \quad [-3,3] \quad -3\leq y\leq 3[/tex]

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Interval notation

Inequality notation

From inspection of the given graph, the function is continuous and so the domain is not restricted.

Therefore, the domain of the function is:

From inspection of the given graph, the minimum value of y is -3 and the maximum value of y is 3.  Both values are included in the range.

Therefore, the range of the function is:

The number of guests that were at the party is 16.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2. 1 is the numerator and 2 is the denominator.

The equation that would be formed from the available information in this question is:

[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]

Where x represents the number of guests that are in the party.

[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]

Add the fractions:

[tex]\frac{3x + 4x + 6x}{12}[/tex] = 17

[tex]\frac{13x}{12}[/tex] = 17

Multiply both sides of the equation by 12

13x = 12 x 17

13x = 204

Divide both sides of the equation by 13

x = 204 / 13

x  = 15.7 ≈ 16

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Answer:

  7/3

Step-by-step explanation:

You want the ratio 3.50 : 1.50 written as a fraction.

A ratio can be written 3 ways. Any of them can be reduced to a ratio of mutually prime integers:

  3.50 : 1.50 = 3.50/1.50 = 3.50 to 1.50

Here, the fraction can be made to be a ratio of integers by multiplying both numerator and denominator by 2:

  3.50/1.50 = (2·3.50)/(2·1.50) = 7/3

The ratio 3.50:1.50 is equivalent to the fraction 7/3.

a)36 is 75 % of 48

b)18 is 25% of 72

Explanation

when we have the percentage and the number , the easiest way to find the value is by applying this formula:

hence

Step 1

a)

what percet of 72 is 18?

let

100 % = 72, ( the number)

x %, = 18

so

replace

therefeore,

18 is 25% of 72

Step 2

b) 36 is 75 % of what,so

let

100%= x=original value

75%=36

so

therefore, 36 is 75 % of 48

I hope this helps you

Thirty thousandths in decimal is written as ;

Note that numbers after the decimal point begin from tenths, hundredths, thousandths, tens of thousandths, and so on.

Thirty-thousandths therefore is four digits after the decimal point, starting from the digit 3.

Given that 3x+2=17

3x=17-2

3x=15

x=15/3

x=5

so,the numbers we end up using are 17,3,15,5,2

we have that

the answer is the option First

perpendicular bisector

because, is perpendicular to the segment at its midpoint

Answer:

Step-by-step explanation:

eq. of any line with slope -1/2 and through (-1,-5) is

y+5=-1/2(x+1)

2y+10=-x-1

2y=-x-11

x+2y=-11

y=0

x=-11

point is (-11,0)

draw a line through (-11,0) and (-1,-5)

Answer: you can get the full fraction by multiplying 6x3 which is 18 so then you add 18 and 2 and you get 20 so now the fraction is 20/3

and you need 11/3 for a batch so now you have 1 whole batch and 9/3 so you just make the 11 a percentage which is 81%

so the answer is 1 whole batch and 81% of another

or 1 9/3

The personal trainer took 11 plan A and 7 plan B classes.

Let the number of sessions of plan A be x. So, the number of sessions of plan B be (18 - x). Now forming the equation as per the mentioned information.

25×x + 50 (18 - x) = 625

Performing multiplication on Left Hand Side of the equation

25x + 900 - 50x = 625

Rearranging the equation

900 - 625 = 50x - 25x

Performing subtraction on both the sides of the equation

275 = 25x

Shifting 25 to other side of equation

x = 275/25

Performing division to find the value of x

x = 11

Number of plan A classes = 11

Number of plan B classes = 18 - 11

Number of plan B classes = 7

Thus, the number of plan A classes is 11 and plan B classes is 7.

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The price of gasoline before the 15% increase is $4.75/gallon.

What is gasoline?
Petroleum-derived clear flammable liquid known as gasoline or petrol is the primary fuel for the majority of spark-ignited internal combustion engines (also known as petrol engines). It mostly comprises of organic compounds made from petroleum fractional distillation that have been improved with various additions. In the United States, refineries typically create 19 to 20 gallons of gasoline, 11 to 13 gallons of distillate fuel, the majority of which is sold as diesel fuel, and 3 to 4 gallons of jet fuel from a barrel of crude oil. The crude oil test and oil refinery processing determine the product ratio. 42 US gallons, or around 159 litres or 35 imperial gallons, is the standard measurement for the volume of an oil barrel.

How can we calculate the price before the 15% increase?

Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon.

15÷100+x = $4.90/gallon

0.15+x = $4.90/gallon

Therefore, x = $4.90/ gallon - 15÷100

 x = $4.90/gallon - 0.15

x = $4.75/gallon.

Hence , the price of gasoline before the 15% increase is $4.75/gallon.
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The x intercept is (-7.5,0).

The y intercept is (0,5.5).

Answer: 1050 is the answer trust me i took the quiz and it was correct pls give me brainliest and friend request me ur welcome :)

Step-by-step explanation:

Total utility of movies and cds will be $160

What is Budget?

A spending plan based on income and costs is called a budget. In other words, it's a projection of your income and expenses for a specific time frame, like a month or a year. (Or, if you're keeping track of the money coming in and going out of your home as a whole, that's a family budget.)

The cost of 1 movie = $5

The cost of 1 CDS    = $10

The marginal utility from fifth movie = 30

The marginal utility from fifth CDS = 70

Total cost spent in month for movies = 5+5+5+5+30

                                                             = $50

Total cost spent in month for CDS = 10+10+10+10+70

                                                         = $110

The total monthly entertainment budget will be

                                               = 50 + 110

                                               = $160

Hence, The total monthly entertainment budget is $160

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Answer:

the answer is C

Step-by-step explanation:

25% of 150 is 37.5 so 150-37.5 is 112.5

Answer: [tex]4x^{5} y^{6} \sqrt{7y}[/tex]

Step-by-step explanation:

1) Separate the radicals

sqrt(112x^10y^13) = sqrt(112)*sqrt(x^10)*sqrt(y^13)

2) For sqrt(112), rewrite it as the product of a perfect square and some other number.

sqrt(112) = sqrt(16) * sqrt(7)

= 4*sqrt(7)

3) For sqrt(x^10), rewrite it in terms of it being raised to a fraction

[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]

n = 2, so x^(10/2), and when simplified you have x^5

4) For sqrt(y^13), do the same thing.

y^(13/2) = sqrt(y)*(y^6)

5)Combine everything

4x^5y^6sqrt(7y)

The total dollar amount of her commission last year equals to $19,200.

This refers to the percentage of the value of a sale that a sales associate or representative may earn.

To start, we must analyze the data we have. Given that Alexandria's total sales were $ 480000, and the commission received is 1/25 of that sales.

The commission earned from the sales:

= 1/25 * $480000

= $19,200

Therefore, the total dollar amount of her commission last year equals to $19,200.

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Answer:

To find the perimeter of the rectangle, simply add all sides of the rectangle together to get the answer. For finding the area, you have to multiply the length and width together.

Step-by-step explanation:

math.

Answer:

Area = 4πr²

Step-by-step explanation:

- We know that a moon revolves around its orbit as per Keplar. The moon is not a perfect sphere, so we shall take an assumption;

Assume the moon is a perfect and regular sphere

[tex]{ \tt{volume \: of \: moon = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \boxed{ \tt{ \: v = \frac{4}{3} \pi {r}^{3} }}}[/tex]

- From engineering mathematics (rates of change), we know that volume is first order integral of area and area is the first order derivative of volume;

[tex]{ \tt{area = \frac{d(volume)}{dr} }} \\ \\ { \tt{volume = \int area \: dr}}[/tex]

- So, from our formular;

[tex]{ \tt{area = \frac{dv}{dr} = \frac{4}{3}\pi ( \frac{d ({r}^{3} )}{dr} ) }} \\ \\ { \tt{area = \frac{4}{3}\pi(3 {r}^{2}) }} \\ \\ { \boxed{ \rm{area = 4\pi {r}^{2} }}}[/tex]

[tex]{ \boxed{ \mathfrak{DC}}}{ \underline{ \mathfrak{ \: delta \: \delta \: creed}}} \\ [/tex]

We know that

• The dimensions of the pool are 26 meters by 12 meters.

• The uniform surrounding path has a width of ,x, meters.

To find a function of x to express the whole area, we have to define the width and length including the path.

The width would be-

The length is

The total area is

We use the distributive property to show the function in the simplest form.

Then, we reduce like terms. So, the function is

Area of rectangle = Length x Width

. = 14.3 x 13.9

. = (13.9+ 0.4) x 13.9

. = 13.9^2 + 5.56

. = 13•14 +( 1.4)•8 + 5.56

. =198.77 cm2

The solution for the given equation is x = -5 and x = 3.

How to solve a quadratic equation by substitution?
The equation is first transformed into a more familiar form. Replace the substitutions with the original variables after factoring the problem. The difference of squares equation is used to finish the factorization and locate the answers for x.

Given, the equation for solving is: (x + 2)² - 2(x + 2) - 15 = 0 --(i)
Let in the equation, y = x + 2 --(ii)
Equating (i) and (ii), we get:
y² - 2y - 15 = 0 ⇒ y² - 5y + 3y - 15 = 0 ⇒ y(y - 5) + 3(y - 5) = 0
⇒ (y + 3)(y - 5) = 0 ⇒ y = -3, 5 (by solving the equations)
Thus, from (ii) and value of y obtained above, we get,
x + 2 = -3 ⇒ x = -3 -2 = -5 and x + 2 = 5 ⇒ x = 5 - 2 = 3
Thus, (b) x = -5 and x = 3 is the correct answer.

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The value of the length of the segment SR is; 12 units.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

According to the diagram at point it makes the angle of 90° with both triangles, thus;

SR = SQ

2x + 8 = 8x - 4

And to find the value of x, we will find the value of  line segment SR

8x -2x = 8+4

6x = 12

x = 12/6

x = 2

Then we will put the value of x in SR ;

SR = 2x + 8 = 2(2) + 8 = 4 + 8 = 12

SR = 12

Hence, The value of the length of the segment SR is; 12 units.

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The probability of selecting the integer 361 from the random generator is 0.

It should be noted that probability simply has to do with the likelihood that a particular thing will take place.

In this case, a random number generator is used to select an integer from 1 to 50 .

The probability of selecting the integer 361 from the random generator will be 0. This is because the numbers given are from 1 to 50.

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1. Store A's unit price = $4 per pound

2. Store B's unit price = $2 per pound.

3. Store C's unit price = $3 per pound.

4. Store B's unit price is the lowest.

The unit rate of the relationship between variables x and y, is given as:

Unit rate, m = y/x.

In a given equation, y = mx, the value of m represents the unit rate of the relationship.

In the scenario given, y represents cost in dollars while x represents the  number of pounds of apples.

1. The unit rate = unit price of apples. For store A, we are given 3 pounds of apples will cost $12, therefore:

Unit price = y/x = 12/3

Unit price = $4 per pound

2. For store B, the "2" in the equation, y = 2x, represents the unit price.

Unit price for store B = $2 per pound.

3. Using one point on the graph for Store C, say, (2, 6):

Unit price = y/x = 6/2

Unit price = $3 per pound.

4. The lowest unit price is $2 per pound, therefore, Store B has the lowest unit price for apples.

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If a bicycle has a listed price of $522.95  before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47

The listed price of bicycle = $522.95

The sales tax percentage = 7.75%

We know

C = p(t×p)

Where C is the total cost

p is the listed price

t is the sales tax percentage

Substitute the values in the equation

C = 522.95+((7.75/100)×522.95)
= 522.95+40.53

= $563.47

Hence, if a bicycle has a listed price of $522.95  before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47

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[tex] = 2(4)^{2} - (10 \div 2) \\ = 2(16) - 5 \\ = 32 - 5 \\ = 27[/tex]

THE ANSWER IS OPTION 2. 27

HOPE THIS HELPS

Answer:

Answer is 27                  

    ♬      

⚫    

ANSWER

EXPLANATION

To find the two numbers that are located 5/8 of a unit from 1/6 on the number line, we have to first understand that for a number on a number line, there are numbers both ahead and behind the number.

So, the numbers that are 5/8 from 1/6 on the number line will be:

=> one number that is +5/8 from 1/6

=> one number that is -5/8 from 1/6

Therefore, the two numbers are:

Those are the two numbers.

Answer: Infinite Solution

Step-by-step explanation:

3x+12-4=2x+8+x

3x+8=3x+8

Answer:

All real numbers

The answer to this equation is 0=0

Step-by-step explanation:

3(x+4)-4= 2(x+4)+x

3x+12-4= 2x+8+x    

3x+8=3x+8              

3x-3x=8-8

0=0 Answer

We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given Data

We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). Pre-image and image are always congruent with one another.

Series of transformation Matt can perform:

Reflection (Flip)

Because the equivalent points from the pre-image to the image remain at the same distance from the line of reflection, a reflection maintains its original shape.

Rotations as a Transformation of Congruence

A rotation is when a figure turns. Although the figure is the same size and shape, it appears to have fallen over. A clock is a fantastic example of a rotation in the real world. Every hour or every day, the connecting arms of a clock revolve around its central point. The degree of rotation is used to characterize a rotation; popular rotations include 90 degrees, 180 degrees, and 270 degrees. The figure returns to its original position after a full 360-degree spin. A rotation must additionally include the direction, either clockwise or counterclockwise. A rotation's degree amount and direction can be computed using this information.

Congruence transformation through translation

When we move an object or shape from one location to another without changing its size, shape, or orientation, we call that movement a translation. A translation, often known as a slide, involves moving each point on an object or shape by the same amount and in the same direction.

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