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If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

The function f has an inverse if and only if the result of reflecting a function's graph about the line y = x is the function's graph (passes the vertical line test).

Therefore, if and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).

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Answer:

The limit does not exist

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Constant]:                                                                                             [tex]\displaystyle \lim_{x \to c} b = b[/tex]

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Step-by-step explanation:

*Note:

In order for the limit to exist, the right-hand and left-hand limits must equal each other

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left \{ {{x + 10,\ x < 8} \atop {10 - x,\ x \geq 8}} \right.[/tex]

Step 2: Find Right-Hand Limit

Step 3: Find Left-Hand Limit

∴ since  [tex]\displaystyle \lim_{x \to 8^+} f(x) \neq \lim_{x \to 8^-} f(x)[/tex],  [tex]\displaystyle \lim_{x \to 8} f(x) = DNE[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits

Exponential equation in the form y = a(b)* that can model the value of the pizza oven, y, x years after purchase is y = 16000(0.985625)ˣ.

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.

The exponential equation is y = a(b)ˣ

The value of y = 15770, a = 16000 and x = 1

b = 0.985625

y = 16000(0.985625)ˣ

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The amount of money should you deposit now to have $10,000 5 years from now is $7407.

Theoretically, continuously compounded interest means that interest is continuously earned on an account balance as well as reinvested into the balance to increase future interest earnings.

Given that If an investment company pays 6% compounded continuously and $10,000 for 5 years.

The amount of money invested will be calculated by the formula below,

[tex]P = P_o(e)^{rt}\\10000 = P_o ( e)^{0.06\times5}\\[/tex]

P₀ = 10000 / 1.35

P₀ = 7407

The amount of money invested would be 7407.

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Answer:

Step-by-step explanation:

Answer: y ≥ −3/2x − 3

Step-by-step explanation:

Graph the inequality by finding the boundary line, then shading the appropriate area.

Hope this helps!

Step-by-step explanation:

hope this helps. n=6 or n=9 work is in the attached pic

The given expression is equivalent to 22 for x = 17 and y = 12.

Given is the expression as follows -

2x - y

For x = 17 and y = 12, we can evaluate the expression as -

2 x 17 - 12

34 - 12

22

Therefore, the given expression is equivalent to 22 for x = 17 and y = 12.

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O(-, -28] is the formula for resolving the inequality +4 = 0. Inequality is the state of having a connection between two expressions or values that is not equal to them.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

A disparity is presented to us.

[tex]y+4\leq 0[/tex]

The answer to the inequality must be discovered.

For each side of the inequality, deduct 4

y +4 - 4 ≤ 0 - 4

y ≤ -4

y ∈ ( - ∞ , - 4 ]

As a result, the solution set for the given inequality is provided by y (- , - 4].

O(-, -28] is the formula for resolving the inequality +4 = 0. Inequality is the state of having a connection between two expressions or values that is not equal to them.

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Answer:

14.46ft

Step-by-step explanation:

this would be solved using Pythagoras

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

15^2 - 4^2

225 - 16 = 209

the square root = 14.46

Answer:

( 2 , 1 ) , ( 4 , 1 ) , ( 4 , 4 ) .......

Answer:

Points of B are (-4,-1), (-2,-1) and (-4,-4)

Step-by-step explanation:

Points of A are (-4, 1), (-2, 1) and (-4,4)

Name the reflected trangle B.

If you have a point (x,y) and you reflect in the x-axis. That point becomes (x,-y).

Therefore. Points of B are (-4,-1), (-2,-1) and (-4,-4)

Answer:

5% of 120 is 6, so you would add that 6 to 120.

120 + 6 = 126.

The total cost will sales tax would be $126.00.

Step-by-step explanation:

Hope it helps! =D

The required weight of the dollar amount of Stock C is $64.96.

The Correct option is (B).

In mathematics, the operation and interpretation of a function to make it simple or easier to grasp is known as simplifying, and the process is known as simplification.

Given:

Investment Amount Invested ROR

Stock A     $1,800     1.5%

Stock B     $4,600     3.7%

Stock C     $580        11.2%

Stock D     $1,122      −2.8%

According to the question,

Weight of dollar amount of Stock C

= 580 × 11.2%

= 580 x 0.112

= $64.96

Hence, the required weight is $64.96.

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Answer:

3.9 inches

Step-by-step explanation:

area of a circle = πr²

= π 3²

= 9 π

9π = 28.3 (rounded).

area of a square = length x width

= 6 x 6

= 36 inches

36 - 28.3

= 7.7

÷2 to get the individual value

= 3.9 inches rounded

The area of the yellow region will be  [tex]3.86[/tex] squared inches.

Area is the space occupied by any shape.

Area of the square [tex]=side*side[/tex]

We have,

A square of [tex]6[/tex] inch in side, divided in two semi-circles.

Radius of semi-circle[tex]=3[/tex] inch

Now,

Area of the square [tex]=side*side=6*6=36[/tex] squared inches

Now,

Area of a semi-circle[tex]= \frac{\pi }{2}r^{2}=\frac{22 }{2*7} (3)^2=14.14[/tex] squared inches

So,

Area of two semi-circles[tex]=28.28[/tex] squared inches

Now,

Area of yellow part [tex]= \frac{36-28.28}{2}=3.86[/tex] squared inches

So, Area of yellow part is [tex]3.86[/tex] squared inches find out by dividing by two because other part is equals to yellow part.

Hence, we can say that the area of the yellow region will be  [tex]3.86[/tex] squared inches.

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The polynomial which has a degree of  7 can be known as a polynomial of class 7.

Polynomials are expressions containing of variables and constants. The variable having the highest power forms the degree of the polynomial.

The degree of a polynomial with one variable is known as the highest exponent power of that variable in the mentioned polynomial.

Finding the degree of a polynomial with more than one variable is a simple task , as adding the exponents of each variable in the supplied terms and then determining which term has the highest degree. That is the polynomial's degree.

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{13}-\underset{x_1}{1}}} \implies \cfrac{ -4 }{ 12 } \implies {\Large \begin{array}{llll} - \cfrac{1 }{ 3 } \end{array}}[/tex]

Answer:

Below.

Step-by-step explanation:

So lets go over what we know of the first question.

Jacob took 2/6th of a pound of candy.

Louis ate 7/9th of a pound of candy.

We need to find who ate more candy.

We need to find how much more candy one person ate.

To find this information, lets get a common denominator for both fractions.

Both 6 and 9 in 2/6 and 7/9 go into 18, so:

2/18 and 7/18

Now we need to fix the numerator.

To do this, we must see how many times 6 and 9 go into 18, and then multiply the numerator by that.

So:

6 goes into 18 3 times. 3x2 is 6. So our first fraction is 6/18ths.

9 goes into 18 2 times. 7x2 is 14. So our second fraction is 14/18ths.

Now, comparing our fractions:

Jacob - 6/18

Louis - 14/18

#1 part 1 - 14/18 > 6/18

#1 part 1 - So Louis ate more candy than Jacob.

Now to find how much more, lets subtract Louis's from Jacob's:

14/18 - 6/18

=

#1 part 2 - 8/18

So the difference is 8/18

Next we have question 7.

So lets go over what we know.

We need to write division problems.

A fraction itself is a division problem.

In a fraction, the numerator is divided by the denominator.

So in our first question:

1/5 can be written as: 1 divided by 5 equals 1/5, or:

#2 part 1 - 1÷5=1/5

In our second one:

4/8 can be written as: 4 divided by 8 equals 4/8, or:

#2 part 2 - 4÷8=4/8

In our third one:

9/12 can be written as: 9 divided by 12, equalling 9/12, or:

#2 part 3 - 9÷12=9/12

Im sorry I have to go ill finish answring in like 15 minutes! Hope this will help you so far! :D

Answer:

Ok, to countinue on from what I was saying.

Step-by-step explanation:

So, lets go over what we know for #3:

Becca has 3 cookies.

She needs to divide these 3 cookies into 7 pieces.

Or, we can think of this as:

She needs to divide 3 by 7.

3÷7 is equal to 3/7, so our answer is:

#3 part 1 - 3/7

#3 part 2 - I attached a image below of this.

Next lets go over what we know for #4.

Kelsey has 25 pages.

She reads 4 6/8ths of these pages.

We need to find what she has left.

We can do this by subtrating her 25 pages by 4 6/8ths:

25-4 6/8

Well, lets start by subtracting the whole number, 25-4 is 21:

21-6/8

Now lets subtract the fraction. Since we know that there is a total of 8/8ths in 1, and we are subtracting 6/8ths, we can now look at this as:

#4 part 1 - 20 2/8

Since we took 1 from 21, making it 20. Then we subtracted 6/8 from 8/8:

8/8-6/8 = 2/8

So it was 20 2/8.

Now we are on our last question.

We need to add 1/4 to 2 1/3

First off, we need to find a common denominator.

This will be 12. So:

3/12 and 2 4/12

Now lets add them together:

#5 part 1 - 2 7/12

So this is your answer.

Hope this helps! :D

Coordinate (-a , b ) belongs to second quadrant.

The axes (x-axis and y-axis) of a two-dimensional Cartesian plane system divide the plane into four infinite regions called quadrants. The horizontal line or x-axis and vertical line or y-axis intersect each other at the right angle.  The intersection of two lines is known to be the reference point. All the measurement is done by taking this point as the reference (or starting point) in the coordinate system.

"A quadrant is simply defined as the region of a cartesian plane formed when the x-axis and y-axis intersect each other."

Given, Coordinate ≡ (-a , b)

1st Quadrant: The upper right-hand corner of the graph is the first quadrant. In this quadrant the values of x and y both are positive.

2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant, the value of x is negative whereas the value of y is positive.

3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains the negative values of both x and y.

4th Quadrant: Finally, the fourth quarter is at the lower right-hand corner, which has a positive value of x and a negative value of y.

Hence, by the above observation, given coordinate (-a, b) belongs to the 2nd quadrant.

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The number of full test tubes Russel fill with water must be discrete number and not rational. 36 test tubes is the answer.

Volume of a cylinder can be known either by the use of formula (V = πr²h) or by measuring with the volume of a known liquid.

Given that Russel is doing an experiment for a science fair project. He fills a beaker with water three times. He puts 16.5 milliliters of water in each test tube. How many full test tubes can Russel fill with water?

1. Describe one way to estimate the solution to this problem.

By dividing the amount of milliliters of water in the baker by 16.5 ml

2. Russel calculates correctly and says the answer to the problem is 36.36 test tubes. Is Russel's answer reasonable?

No! The reason is based on the fact that the answer must be a whole number and not a decimal number since the question centered on number of full test tubes filled with water.

Therefore, the correct answer should be 36 test tubes.

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Answer:

C. Connor is correct because it is likely that the increased income and better benefits he will earn throughout his career will outweigh the $80,000 and four years he invests in his college education.

Step-by-step explanation:

I did 100% on edge 2021

good luck! :)

Each of the cuboidal blocks B and D has a volume of 24 cubic units. As a result, choice D is the right response.

What is the formula to find the volume of a cuboidal block?

The formula to find the volume of a cuboidal block is l×b×h.

The dimensions of cuboidal block A are length=6 units, breadth=2 units and height=1 units

Now, the volume of a cuboidal block A=6×2×1=12 cubic units.

The dimensions of cuboidal block B are length=4 units, breadth=2 units and height=3 units

Now, the volume of a cuboidal block B=4×2×3=24 cubic units.

The dimensions of cuboidal block C are length=5 units, breadth=3 units and height=3 units

Now, the volume of a cuboidal block C=5×3×3=45 cubic units.

The dimensions of cuboidal block D are length=6 units, breadth=2 units and height=2 units

Now, the volume of a cuboidal block D=6×2×2=24 cubic units.

The volume of cuboidal blocks B and D is 24 cubic units each. Therefore, option D is the correct answer.

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Answer: The answer would be C

Step-by-step explanation:

You want to divide. 15/3= 5 and then a^3 is basically being divided by 1 so your completed answer would be 5a^3

The value of x is 9.32 after solving using the Pythagoras theorem.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The diagram has 4 corners namely - A, B, C and D.

Draw a perpendicular through B.

The intersecting point at line AD is named as E.

It can be seen in figure that EDCB is a rectangle and falls under the category of parallelogram.

So, angle ADC = angle DEB = angle AEB = 90° .

Now, side BC = ED = 5.

So, side AE = 18 - 5 = 13.

Here, it can be seen that triangle ABE is a right-angled triangle.

So, to get the measurement of side BE, apply the Pythagoras theorem -

c^2 = a^2 + b^2

Where, a is perpendicular, b is base and c is hypotenuse.

So, according to the diagram -

(16)^2 = (13)^2 - (BE)^2

(BE)^2 = (16)^2 - (13)^2

(BE)^2 = 256 - 169

(BE)^2 = [tex]\sqrt{87}[/tex]

(BE)^2 = 9.32

Now, as  EDCB is a rectangle so, side BE = side CD.

Therefore, the value for side CD = x = 9.32.

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You went to the supermarket to buy 10 bananas. Each banana weighed 50 grams. If the price for bananas was $6.50 per kilogram, how much would you have to pay?

You do 10 x 50 = 500                     /                      Your bananas weigh 500g

$6.50 halved is $3.25                     /                       So $3.25 for 500g

So your answer is $3.25

Hope this helps! :)

Answer:

B

Step-by-step explanation:

hope it helped : )

Answer:

x > 64

therefore, 65 and 66 both apply

Step-by-step explanation:

[tex]\sqrt{x}[/tex] > 8

square each side to get:

x > 64

Answer:

D

Step-by-step explanation:

The area of the triangle is equal to the squareroot of 10(10-5)(10-7)(10-8), which is equal to 24.

The area of an acute triangle without height can be calculated using Heron's Formula. Heron's Formula states that the area of a triangle is equal to the squareroot of s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.

To find the area, first calculate the semi-perimeter of the triangle. The semi-perimeter is equal to one-half the sum of the three sides. For example, if the lengths of the three sides of a triangle are 5, 7, and 8, the semi-perimeter is equal to 5 + 7 + 8 divided by 2, which is equal to 10.

Next, plug the values into Heron's Formula. Using the same triangle as an example, the area of the triangle is equal to the squareroot of 10(10-5)(10-7)(10-8), which is equal to 24.

Finally, calculate the area of the triangle by taking the square root of 24, which is equal to 4.9. Therefore, the area of the triangle is 4.9 square units.

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Answer:

No Solution

Step-by-step explanation:

When we solve for the first variable in one of the equations, then substitute the result into the other equation. Which would lead to these equations having no solutions .  

I really hope this helps !

I'm terribly sorry if It didn't .

If you need me to elaborate please feel free to ask :))

I hope you have a wonderful day , stay safe!!

~Sleepy~

Answer:When we solve for the first variable in one of the equations, then substitute the result into the other equation. Which would lead to these equations having no solutions .