a function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists. show that each of the following functions has a horizontal asymptote by calculating the given limit.

For the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

As given in the question,

On a tour of a gold mine,

Ounce of gold contained by nuggets found in the mine = 0.82 ounce

Worth of gold per ounce = $1323.80 per ounce

Worth of nuggets containing 0.82 ounce of gold

Worth of 1 ounce of gold = $1323.80

⇒ Worth of nuggets containing 0.82 ounce of gold =$( 1323.80 ×0.82 )

                                                                                      = $1085.516

Therefore, for the gold worth $1323.80 per ounce ,the nugget containing 0.82 ounce of gold is worth of $1085.516.

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Answer: y=7

Step-by-step explanation:

We need to combine like factors in this term by adding up all the exponents and copying the base.

No exponent implies the value of 1.

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Answer:

y =7

Step-by-step explanation:

a)I WILL USE THE THEOREM OF PYTHAGORAS IN TRIANGLE BCD

[tex] {y}^{2} = {(5.3)}^{2} - {(4.4)}^{2} \\ {y}^{2} = 28.9 - 19.36 \\ {y}^{2} = 9.54 \\ y = \sqrt{9.54} \\ y = 3.09[/tex]

y=3.90cm

b)

[tex] \sin(x) = \frac{cb}{ac} \\ \sin(x) = \frac{5.3}{8.2} \\ x = sin^{ - 1} ( \frac{5.3}{8.2} ) \\ x =40.27[/tex]

x=40,27 cm

GOODLUCK.

1. Based on the proportional relationship table created, 4.8 gallons of water will be in the fish tank after 3 mins.

2. 25 minutes.

3. The Constant of proportionality is: 1.6.

In a proportional relationship between variables x and y, the Constant of proportionality, k, is determined using any pair of values from the table as:

k = y/x.

The relationship is modelled as y = kx.

Constant of proportionality = k = y/x = 0.8/0.5

Constant of proportionality = k = 1.6

The equation for the relationship would be: y = 1.6x. Use the equation to complete the table:

For x = 1:

y = 1.6(1) = 1

For x = 3:

y = 1.6(3) = 4.8

For y = 40:

40 = 1.6x

40/1.6 = x

x = 25

The complete table is:

x             y              

0.5        0.8

1            1.6

3           4.8

25        40

1. Using the proportional relationship table, we can conclude that, 4.8 gallons of water will be in the fish tank after 3 mins.

2. Using the proportional relationship table, the time it would take to fill the tank with 40 gallons of water is: 25 mins.

3. Constant of proportionality = k = 1.6.

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The most appropriate choice for matrix and multiplicative inverse of matrix will be given by

B is the multiplicative inverse of A

What is a matrix and multiplicative inverse of matrix?

Matrix is a rectangular representation of numbers or symbols arranged in the form of rows and column. Matrix is a very important tool in mathematics.

To learn about multiplicative inverse, it is important to know about identity matrix

[tex]\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}[/tex] is a 2 x 2 identity matrix denoted by I.

Let A and B be two matrices

A is said to be a multiplicative inverse of B if AB = BA = I

Here,

A=   [tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex] B = [tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

AB =

[tex]\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 2\times 1 + 1 \times -1& 2 \times -1 + 1\times 2\\1 \times 1+1\times-1 & 1 \times -1 + 1 \times 2\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

BA =

[tex]\begin{bmatrix} 1& -1\\-1 & 2\end{bmatrix}\begin{bmatrix} 2& 1\\1 & 1\end{bmatrix}[/tex]

[tex]\begin{bmatrix} 1\times 2 + -1 \times 1& 1 \times 1 + -1\times 1\\-1 \times 2+2\times 1 & -1 \times 1+ 2 \times 1\end{bmatrix}\\\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

AB = BA = [tex]\begin{bmatrix} 1& 0\\0&1\end{bmatrix}\\[/tex]

So B is the multiplicative inverse of A

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If the university invest in a one year CD at 5.12% interest compounded continuously, the interest it will earn is determined by calculating as: Interest = Future value – Present value which would be $2.54 million

Continuously compounded interest means that a principal amount is constantly earning interest with infinite compounding periods for a certain time period. There are no increment compounding periods as with monthly or annually compounding.

The continuously compounding formula:

FV = PV* e^rt

Where FV is the future amount, PV is the initial amount, e is a mathematical constant (2.7183), r is the rate and t is the time period.

Hence,

FV = 49* 2.7183^(0.0512*1) =51.57

Interest earned= 51.57-49=2.54

Hence, the university will earn an interest of $2.54 million.

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Value of x for equation -3x + 1 + 10x = x + 4 is 1÷2.

Given equation,

-3x + 1 + 10x = x + 4

Shifting the variables to the left-hand side and constant to the right-hand side,

-3x - x + 10x = 4 - 1

Simplifying the equation,

10x - 4x = 3

6x = 3

x = 1÷2

When x from the right side shifts to the left side, its sign changes, and similarly, when 1 from the left side shifts to the right side, its sign changes.

x = 0.5

Therefore, value of x = 1÷2 that is 0.5

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The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both sets

Therefore the answer is B.

Answer: x^2-9x+20

Step-by-step explanation: you have to distribute (x-5) (x-4)

which would be x^2-4x -5x +20 when you simplify that you get x^2-9x+20

Answer:

3(c) + 25

Step-by-step explanation:

Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?

2(25) + c

25c + 3

3(c) + 25

3(c + 25)

Answer:

108.333 km/hour

Step-by-step explanation:

See attached worksheet.

Each person will get a 5/24 portion of the available cake with Paige

Cake available with Paige = 5/6

Number of people = 4 people

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Fraction of cake each person gets:

Cake available with Paige/Number of people with whom the cake is to share equally

= (5/6)/(4)

= (5/6)*(1/4)

= 5/24

The fraction of cake each person will get is 5/24

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Answer:

QPR SAS

Step-by-step explanation:

As you can see. Hope it can help

Answer:

119º and 61º

Step-by-step explanation:

2x-15 and 3x+5 are supplementary because the angles corresponding to 2x-15 is supplementary with 3x+5

2x-15+3x+5=180

5x-10=180

5x=190

x=38

fill in x

2(38)-15

=76-15

=61

angle is 61

fill in x for angle 2

3(38)+5

=114+5

=119

angle 2 is 119

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

Given,

The equation; [tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

We have to solve this equation to get the value of x.

That is,

[tex]\sqrt{3x-4} =2\sqrt{x-5}[/tex]

Square both sides to remove square root.

[tex]\sqrt{3x-4} ^{2} = (2\sqrt{x-5} )^{2}[/tex]

We get,

3x - 4 = 4 (x - 5)

That is,

3x - 4 = 4x - 20

Here,

20 - 4 = 4x - 3x

Then,

x = 16

That is,

The solution of x for the equation [tex]\sqrt{3x - 4} = 2\sqrt{x-5}[/tex] is x = 16.

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Answer:

First, 24 divided by 8 equals 3. this means you divide 12 by 3. you get 4. 4 cups of sugar will be used when 8 cups of flour are used.

area of triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is

(x1 (y2 - y3 ) + x2 ( y3 - y1 )+ x3 ( y1 - y2))/2

hence, substituting the points (x1, y1)= (-2, 1);

( x2, y2)= (0,3) ; and (x3, y3)= (4,-4) in the area formula ,we get

area of triangle =

( -2(3-(-4)) + 0( -4 - 1) + 4(1-3))/2

(-14+0-8)\2

22\2

11 sq unit

89 squares will be present.

Given that the rectangle has the following dimensions: length = 96 cm, breadth = 84 cm, and

its total area is 8064 square centimeters, we may deduce that the maximum square area

[tex]\sqrt[2]{8064}[/tex]

that can be removed from the rectangle with its total area of 8064 square centimeters is equal to 89.8 square centimeters.

In order to determine the total number of squares, divide 8064 by 89.8 to arrive at 89.

Taking an integer's square root is the opposite of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root value is obtained by finding a number that, when squared, produces the original value of the number.

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Answer: x = 22

Step-by-step explanation:

       We will use the exterior angle theorem to solve. First, we will write an equation, then we will solve by combing like terms are using inverse operations.

(6x - 7) = (2x) + (103 - x)

6x - 7 = 2x + 103 - x

6x - 7 = x + 103

5x = 110

x = 22

Answer:

15

Step-by-step explanation:

16c+4(-5)=220

16c-20=220

16c=240

C=15

For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12

Given :

[tex]f(x) = x^{3} -9x^{2} +20x -12 \\[/tex]

One of the factors of f(x) is (x-6)

Dividing f(x) by (x-6), we get :
[tex]\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2[/tex]

Now expanding, [tex]x^{2} -3x +2[/tex]

[tex]x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)[/tex]

Hence, [tex]x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)[/tex]

For x-intercept, f(x) = 0 . Then

(x-6)(x-1)(x-2) =0

x = 1,2 and 6

For y-intercept, x=0 in f(x)

f(0) = -12

Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.

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7/3 in notation one can be written as 7 : 3 and 7/3 in notation two can be written as 0.7 and 0.3.

The ratio is a comparison between two similar quantities in the simplest fraction form. We can write ratios in fractions and in decimals also.

We know we can write a : b as a/b in fraction form and a/(a+b) and b/(a+b) in decimal form.

∴ 7/3 in decimal form can be written as 7 : 3 and 7/3 can also be written as 7/(7+3) = 7/10 = 0.7 and 3/(7+3) = 3/10 = 0.3.

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Using BODMAS we can conclude, Yes, both will give same result.

The rule used to solve mathematical expressions is known as the BODMAS rule. The order of operations for mathematical formulas requiring several operations is known as BODMAS. B. Brackets, O. Order of powers, D. Division, M. Multiplication, A. Addition, and S. Subtraction make up the acronym.

−9×(−9)−9

⇒ - 9 × 81

⇒ -729

⇒ [−9×(−9)]−9​

⇒ [81] -9

⇒ -729

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Using a linear function, it is found that her taxi ride was of 5 miles.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the cost function, we have that:

Thus the cost for a ride of x miles is of:

C(x) = 3.75x + 1.10.

Her total fee was of $19.85, hence the mileage is found as follows:

19.85 = 3.75x + 1.10

x = (19.85 - 1.10)/3.75

x = 5 miles.

Which was the length of her taxi ride.

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Answer:

D

Step-by-step explanation:

Answer:

h = 6.36619772 cm

Step-by-step explanation:

h = (3 * v) / (πr2)

Answer:

h = 20 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( where r is the radius )

given r = 9 and V = 540π , then

[tex]\frac{1}{3}[/tex] π × 9² × h = 540π

[tex]\frac{1}{3}[/tex] × π × 81h = 540π

27πh = 540π ( divide both sides by 27π )

h = [tex]\frac{540\pi }{27\pi }[/tex] = 20 cm