Consider the function represented by with x as the independent variable. How can this function be written using function notation?

The cardinality of a set refers to the number of elements in the set. It is found by counting  the elements in the set.

The cardinality of a set refers to the number of elements in the set. To obtain the cardinality, we have to count the elements in the set.

a) There are 6 elements in this set hence the cardinality is 6.

b) There is only one element in the set hence its cardinality is 1.

c) There are two elements in the set hence the cardinality is 2.

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The total cost when 881 minutes is used is $477.50.

a + 480b = 277 equation 1

a + 990b = 532 equation 2

Where:

Subtract equation 1 from equation 2

510b = 255

b = 255 / 510

b = $0.50

In order to determine the flat fee, substitute for b in equation 1

a + 480(0.5) = 277

a + 240 = 277

a = 277 - 240

a = $37

Total cost = flat fee + (variable cost x number of minutes spoken)

$37 + (881 x 0.5) = $477.50

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Convert to polar coordinates with

[tex]x = r \cos(\theta)[/tex]

[tex]y = r \sin(\theta)[/tex]

so that [tex]x^2 + y^2 = r^2[/tex], and the Jacobian determinant for this change of variables is

[tex]dx\,dy = r \, dr \, d\theta[/tex]

D is the disk centered at the origin with radius 2; in polar coordinates, this is the set

[tex]D = \left\{(r, \theta) \mid 0\le\theta\le2\pi \text{ and } 0 \le r \le 2\right\}[/tex]

Then the integral is

[tex]\displaystyle \iint_D (x + y + 10) \, dx \, dy = \int_0^{2\pi} \int_0^2 (r \cos(\theta) + r \sin(\theta) + 10) r \, dr \, d\theta[/tex]

[tex]\displaystyle = \int_0^{2\pi} \int_0^2 (r^2 \cos(\theta) + r^2 \sin(\theta) + 10r) \, dr \, d\theta[/tex]

[tex]\displaystyle = \int_0^{2\pi} \left(\frac83 (\cos(\theta) + \sin(\theta)) + 20\right) \, d\theta[/tex]

[tex]\displaystyle = 20 \int_0^{2\pi} d\theta = \boxed{40\pi}[/tex]

(since cos and sin are 2π-periodic)

Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.

The two given numbers are -84 and 17.

We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).

If we multiply 21 and -4, we get the product as -84.

That is, 21×(-4)=-84

If we add 21 and -4, we get the sum as -17.

That is, 21+(-4)=21-4=17

Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

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Considering it's vertical asymptotes, the rational function graphed below is given by:

B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

In this problem, the vertical asymptotes are at [tex]x = \pm 1[/tex], hence the function is given by:

B. [tex]F(x) = \frac{1}{(x - 1)(x + 1)[/tex]

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Answer:

750

Step-by-step explanation:

FORMULA FOR VOLUME

L×W×H

L:5

W:25

G:H

5x25x6=750

Answer:

-1

Step-by-step explanation:

Rise/Run equates it to be -1/1 wich is -1

Heya User !

Your Answer is in the attachment, do check out.

MᎥssAbhᎥ ☁

Answer:

Step-by-step explanation:

1) 5a² - 15

5a²  = 5 * a²

15    = 5 * 3

GCF = 5

5a² - 15 = 5*a² - 5*3

            = 5a(a - 3)

5) 36x²y - 48xy²  

36x²y =  2 * 2 * 3 * 3 * x² * y

48xy² = 2 * 2 * 2 * 2 * 3 * x * y²

GCF = 2 * 2 * 3*x*y  = 12xy

36x²y - 48xy²  = (12xy * 3x)  - (12xy*4y)

                        = 12xy*(3x - 4y)

6)75b²c³ + 60bc⁶  

75b²c³ =  3 * 5 * 5 * b² * c³

60bc⁶  = 2 * 2 * 3 * 5 * b * c⁶

GCF = 3*5*b*c³ = 15bc³

75b²c³ + 60bc⁶ = [15bc³* 5b]  + [15bc³ * 4bc³]

                          = 15bc³ * (5b + 4bc³)

The value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given:

sinx = -5/13

and cosx > 0

We know,

cos2x = 1 - 2sin²x

sinx = -5/13

Squaring on both sides:

sin²x = 25/169

Multiply by 2 on both the sides:

2sin²x = 2(25/169)

Add -1 on both sides:

-1 + 2sin²x = -1 + 2(25/169)

or

1 - 2sin²x = 1 - 2(25/169)

cos2x = 1 - 50/169

cos2x = 119/169    (as the cosx > 0)

Thus, the value of cos 2x is 119/169 after applying the trigonometric identity cos2x = 1 - 2sin²x option second is correct.

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Answer:

The guy above me is correct

Step-by-step explanation:

Look at the screen shot I got it correct

Answer:

107 degree

Step-by-step explanation:

interior angle sum of a hexagon is 720,

using S = (n - 2)*180

which is S =(4)*180

720-118-111-124-115-145=107

The central angle measure of the sector is 4.19 rad.

You need apply the formula: [tex]A= r^2*\frac{\alpha}{2}[/tex]  for finding the area of the sector, in radians. In this formula, the variables are:

r= radius

[tex]\alpha[/tex]= central angle

The question gives:

A=54[tex]\pi[/tex] cm²

r= radius= 9cm

Thus, the central angle will be:

[tex]A= r^2*\frac{\alpha}{2}\\ \\ 54\pi =81*\frac{\alpha }{2} \\ \\ 1.33333\pi =\alpha[/tex]

For [tex]\pi[/tex]=3.14159..., you have :

[tex]\alpha=4.19\; rad[/tex]

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Answer:

4pi/3

Step-by-step explanation:

Answer:

slope = -5/4

Step-by-step explanation:

Because you have been given two points, you can use point-slope formula to find the slope. In the equation, "m" is the slope.

1st Point: (1,3)

2nd Point: (5, -2)

y₁ - y₂ = m(x₁ - x₂)                    <----- Point-Slope Equation

3 - (-2) = m(1 - 5)                       <----- Plug "x" and "y" values into equation

5 = m(-4)                                   <----- Combine like terms

-5/4 = m                                    <----- Divide both sides by -4

Step-by-step explanation:

please mark me as brainlest

THE ANSWER IS B I THINK IF ITS WRONG IM SORRY

Step-by-step explanation:

the answer is 94206584 kk

Answer: Hope this helps

y = 3/5x + 100

Slope: 3/5

Y-int: 100

Step-by-step explanation:

y = mx + b

replace b with y-int

y = mx + 100

replace m with the slope which is 3/5

y = 3/5x + 100

How do you get slope?

Well I did rise/run with two points so I saw it ran 5 squares and rose only 3.

How do you get the y-int?

Well the y-int is the point where x is 0. So using the point (0,100), since x is 0, the y-int is 100.

Answer:  Cara takes longer

Step-by-step explanation:

cara takes 14 minutes

irena takes 11

Answer:

cara takes longer by 14 minutes than Irena who takes 11 minutes

Answer:

See the attachment photo!

Answer:

y= -6

Step-by-step explanation:

-4x and 4x are canceled out. -2y+8y= 6y. -12-24=-36

You are left with 6y=-36 . Divide from both sides and -36/6 is -6. So, y=-6.

Hope this helped.

The average rate of change for f(x) and g(x) are respectively 2.25 and -2 and so we can say that f(x) is moving more quickly.

Formula for the average rate of change is;

f'(x) = (f(b) - f(a))/(b - a)

Thus;

1)  Average rate of change of f(x) over the interval from x = 2 to x = 6 is;

f'(x) = (f(6) - f(2))/(6 - 2)

We are given;

f(6) = 10 and f(2) = 1

Thus; f'(x) = (10 - 1)/4 = 2.25

2)  Average rate of change of g(x) over the interval from x = 0 to x = 4 is;

g'(x) = (g(4) - g(0))/(4 - 0)

We are given;

g(4) = 0 and g(0) = 8

Thus; g'(x) = (0 - 8)/4 = -2

3) From the average rate of change of both functions, we see that f(x) is positive and has a higher rate of change and so we can say that f(x) is moving more quickly.

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Answer:

Q3 = $5743.49117291326

Q4 = $10955.6157151671

Step-by-step explanation:

General formula for amount in Compound Interest

Amount [A] = [tex]P(1+r)^{t}[/tex]

Here, P = principal

r = rate of interest in decimal form

t = time in years

Q3

----

Substitute current values in question with formula to give you

$5743.49117291326

Q4

----

Substitute current values in question with formula to give you

$10955.6157151671

Answer:

Irrational.

Step by step explanation:

[tex]\sqrt 6 + \dfrac{2}{3}\\\\\\=\dfrac{3\sqrt 6 +2}{3}\\\\\text{The sum of the these two numbers cannot be expressed as the the ratio of two integers,}\\\\\text{So the sum is not rational.}[/tex]

Answer:

I think it's 2275 square feet

Answer:

it is1125

Step-by-step explanation:

first 45x50=2250

next divide 2250 by 2 equals 1125

Answer:

Step-by-step explanation:

the cost of each ticket is 7 dollars.  Peter brought 2 tickets.  7 x 2 = 14

Peter spent $14 dollars on two movie tickets.

Answer:

The approximate population of bacteria in the culture after 10 hours is 93,738.  

Step-by-step explanation:

BPEMDAS Order of Operations:

We are given the following Exponential Growth Function (Doubling Time Model), [tex]\displaystyle\mathsf{P_{(t)}\:=\:P_0\cdot2^{(t/d)}}[/tex] where:

Step 1: Identify the given values.

Step 2: Find value.

1. Substitute the values into the given exponential function.

  [tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow P_{(10)} = 9300\cdot2^{(10/3)}}[/tex]

2. Evaluate using the BPEMDAS order of operations.

  [tex]\displaystyle\mathsf{P_{(10)} = 9300\cdot2^{(10/3)}\quad \Longrightarrow BPEMDAS:\:(Parenthesis\:\:and\:\:Division).}[/tex]

  [tex]\displaystyle\sf P_{(10)} = 9300\cdot2^{(3.333333)}\quad\Longrightarrow BPEMDAS:\:(Exponent).}[/tex]

  [tex]\displaystyle\sf P_{(10)} = 9300\cdot(10.079368399)\quad \Longrightarrow BPEMDAS:(Multiplication).}[/tex]

 [tex]\boxed{\displaystyle\mathsf{P_{(10)} \approx 93,738.13\:\:\:or\:\:93,738}}[/tex]

Hence, the population of bacteria in the culture after 10 hours is approximately 93,738.  

We can solve for the amount of time (t ) it takes for the population of bacteria to increase to 93,738.

1. Identify given:

2. Substitute the values into the given exponential function.

  [tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 93,378 = 9,300\cdot2^{(t/3)}}[/tex]

3. Divide both sides by 9,300:

  [tex]\displaystyle\mathsf{\longrightarrow \frac{93,378}{9,300} = \frac{9,300\cdot2^{(t/3)}}{9,300}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = 2^{(t/3)}}[/tex]

4. Transform the right-hand side of the equation into logarithmic form.

  [tex]\boxed{\displaystyle\mathsf{\underbrace{ x = a^y}_{Exponential\:Form} \longrightarrow \underbrace{y = log_a x}_{Logarithmic\:Form}}}[/tex]    

  [tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]  

5. Take the log of both sides of the equation (without rounding off any digits).  

  [tex]\displaystyle\mathsf{log(10.07936840) = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 1.003433319 = \bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996)}[/tex]

6. Divide both sides by (0.301029996).

  [tex]\displaystyle\mathsf{\frac{1.003433319}{0.301029996} = \frac{\bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996) }{0.301029996}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 3.3333333 = \frac{t}{3}}[/tex]

7. Multiply both sides of the equation by 3 to isolate "t."

  [tex]\displaystyle\mathsf{(3)\cdot(3.3333333) = \bigg[\:\frac{t}{3}\:\bigg]\cdot(3)}[/tex]

  [tex]\boxed{\displaystyle\mathsf{t\approx10}}[/tex]

Hence, it will take about 10 hours for the population of bacteria to increase to 93,378.    

__________________________________

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Answer:

A = $28,338.18 after 10 yrs

Step-by-step explanation:

hope this helps

hope you can understand

Answer:

False

Step-by-step explanation:

The answer is in its name. Its a property of equality meaning it makes sure that both sides are equal to each other

Answer:

4x²y² and 16x⁴y⁶

Step-by-step explanation: