For
f(x) = 3

x
and
g(x) = x4 + 2,
find the following.
(a)
(f ∘ g)(x)

(b)
(g ∘ f)(x)

(c)
f(f(x))

(d)
f 2(x) = (f · f)(x)

Answer:

Hhhhhhhhhhhhhhhhhh : x=-2

The equation of the lines are:

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

6. y - 3 = 2(x + 4)

7. y - 6 = -4/3(x - 1)

8. y - 8 = -12/9(x + 2)

9. y = -5x + 1

10. y + 1 = -2(x - 2)

11. y - 1 = 2/3(x - 3)

For any given line, the equation that represents the line can be written as:

5. Substitute m = -3, and (a, b) = (1, 5) into y - b = m(x - a):

y - 5 = -3(x - 1) [equation in point-slope form]

6. Substitute m = 2, and (a, b) = (-4, 3) into y - b = m(x - a):

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

y - 3 = 2(x + 4) [equation in point-slope form]

7. Given the points, (4, 2) and (1, 6)

Find the slope (m):

Slope (m) = change in y/change in x = (6 - 2)/(1 - 4)

Slope (m) = -4/3

Substitute m = -4/3, and (a, b) = (1, 6) into y - b = m(x - a):

y - 6 = -4/3(x - 1) [equation in point-slope form]

8. Given the points, (-2, 8) and (7, -4)

Find the slope (m):

Slope (m) = change in y/change in x = (-4 - 8)/(7 -(-2))

Slope (m) = -12/9

Substitute m = -12/9, and (a, b) = (-2, 8) into y - b = m(x - a):

y - 8 = -12/9(x - (-2))

y - 8 = -12/9(x + 2) [equation in point-slope form]

9. y - 6 = -5(x + 1)

y - 6 = -5x - 5

y - 6 + 6 = -5x - 5 + 6 [addition property of equality]

y = -5x + 1 [equation in slope-intercept form]

10. Find the slope (m):

Slope of the line (m) = rise/run = -2/1

Slope (m) = -2

Substitute m = -2, and (a, b) = (2, -1) into y - b = m(x - a):

y - (-1) = -2(x - 2)

y + 1 = -2(x - 2) [equation in point-slope form]

11. Find the slope (m):

Slope of the line (m) = rise/run = 2/3

Slope (m) = 2/3

Substitute m = 2/3, and (a, b) = (3, 1) into y - b = m(x - a):

y - 1 = 2/3(x - 3) [equation in point-slope form]

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The unknown variables and angles are as follows:

The sum of angles on a straight line is 180 degrees.

Therefore, the sum of angles on line STA is 180 degrees.

CT bisect STE

Angle STE Is a right angle.

Therefore,

5x + y + 3 + 3x + 12 = 90

5x + 3x + y + 12 + 3 = 90

8x + y + 15 = 90

8x + y = 90 - 15

8x + y = 75

Ty bisect ETA

Angle ETA Is a right angle.

Therefore,

y + 41 + 5x + 4 = 90

5x + y + 45 = 90

5x + y = 90 - 45

5x + y = 45

Combine the equation

8x + y = 75

5x + y = 45

subtract equation(ii) from equation(i)

3x = 30

x = 30 / 3

x = 10

y = 75 - 80

y = -5

Therefore,

m∠YTE = y + 41 = -5 + 41 = 36°

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The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.

A customer has 40 gallons of a cleaning solution that contains 20% soap.

The company sells a cleaning solution that contains 50% soap.

The customer wishes to create a 40% solution.

Solution:

By mixture and allegation method,

1 gallon                              1 gallon

  50%                                   20%

                         40%

  20                                       10

To create a 40%Soap solution, one must mix 20 gallons of 50%  soap solution and 10 gallons of  20% Soap solution.

Therefore, the ratio is 20 : 10 = 2:1

The customer has 40gallons of a cleaning solution that contains 20% soap, therefore in a 2:1 ratio, 1 part is 40 gallons.

Then for 2 parts = 2*40 = 80 gallons.

The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.

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Answer:

(1) y = 8.45x

(2) Total cost: $42.25

Step-by-step explanation:

Let's see by constructing a first-hand example of the information we have.

$101.40 = 12x

Divide 12 on both sides.

When we divide 12 from both sides, we get the simplified answer of:

x = 8.45

This means that each pizza will be $8.45 each, therefore this will be out=r equation

y = 8.45x

(where x is the number of pizzas and y is the total amount cost.

To find the cost of 5large pepperoni pizzas, we use our equation above (y = 8.45x) and input a 5 in x;

y = 8.45(5)

y = 42.25

The total cost for the 5 pizzas will be $42.25.

-1000 represents Jenny's change in elevation.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.

Given Data

Jenny ended a hike at an elevation of 3, 000 feet above sea level.

She had started at an elevation of 2, 000 feet above sea level.

Hike remaining = 3000 - 2000

Hike remaining = 1000

-1000 represents Jenny's change in elevation.

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The resulting complex number is -10 - 10i.

             z₁ - z₂ = (a + ib) - (c + id)

                       =  (a - c) + i(b - d)

Given complex number: -4-(1+i)-(5+9i)

-4-(1+i)-(5+9i)

Remove the parentheses and combine the real and the imaginary parts respectively.

(- 4 -1 -5) - i(1 + 9)

-10 - 10i

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[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pmt=\textit{periodic payments}\dotfill &100\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each months, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]

[tex]A=100 \left[ \cfrac{\left( 1+\frac{0.06}{12} \right)^{12 \cdot 20}-1}{\frac{0.06}{12}} \right] \\\\\\ A=100 \left[ \cfrac{\left( 1.005 \right)^{240}-1}{0.005} \right]\implies A \approx 46204.09[/tex]

It depicts horizontal linear equation, as the slope is 0.

The slope of horizontal lines is zero. Consequently, m = 0 in the slope-intercept equation y = mx + b. Y = b, where b is the y-coordinate of the y-intercept, results in the equation.

The y-coordinate of every point on a horizontal line is the same. The line's equation is y=b if two points share the same y coordinate, b. The point (0,b) is the y-intercept of the horizontal line y=b. Horizontal lines don't have an x -intercept other than the line y=0.

A horizontal line is a line that is perpendicular to the x-axis. Because the value of x never changes, the graph of a relation of the form x = 5 is a line parallel to the y-axis.

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The formulas that will appear in D2, E2, and F2, respectively are

B$2, C$2, D$2. Option A

This is further explained below.

Generally, A mathematical formula or a chemical formula, for example, are both examples of formulas, which are condensed ways of expressing information via the use of symbols.

When used informally within the realm of science, the word "formula" refers to the overall construction of a connection between a set of determinable variables.

Because of the formula =A$2, row 2 is considered to be anchored.

At this point, D2 is located to the right of C2, but still in the same row.

And the cell that is direct to the right of A2 is labeled B2.

As a result, the formula for D2 will equal B times 2.

In the same manner, the formula in E2 will be C$2, and the formula in F2 will be D$2.

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The number of shoes that have to be purchased until both companies earn the same amount is 21.

Based on the information, the profit rates for Nike and Adidas are illustrated as:

Nike -2 (x - 2)

Adidas -17 + x

In this case, x represents the number of shoes purchased,

The number of shoes that have to be purchased until both companies earn the same amount will. be:

2(x - 2) = 17 + x.

2x - 4 = 17 + x

2x - x = 17 + 4

x = 21

The number of shoes will be 21.

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Answer:

02987329619

Step-by-step explanation:

02987329619

Answer:

kk

Step-by-step explanation:

The function for profit given the conditions for  revenue and expense is P = $20a - $1,600.

The first claim is incorrect because profit is $400

The first claim is incorrect because profit is $4,400.

Profit is revenue less total cost. Total cost consists of fixed cost and variable cost. Fixed cost is the cost that does not change with the level of output. Variable cost is the cost that changes with output. It increases as the level of output increases. Revenue is output multiplied by price per unit.

Profit = revenue - total cost cost

Profit = (price x output) - fixed cost - variable cost

P = ($45 x a)  - $1,600 - ($25 x a)

P = $45a - $1,600 - $25a

P = $20a - $1,600

Where:

P = profit

a = output

Profit when 100 units is sold:

P = (20 x 100) - $1,600

$2,000 - $1,600 = $400

Profit when 300 units are sold

P = (300 x 20) - $1600

$6,000 - $1,600 = $4,400

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Answer: g=-16.3

Step-by-step explanation:

ya welcome

Given

9h-27

Answer

Greatest common factor = 9

The probability that the life span of the monitor will be more than 15,240 hours = 0.055

Given,

Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a variance σ^2 = 1,960,000 of  and a mean life span of μ = 13,000 hours.

Here, σ = [tex]\sqrt{1,960,000}[/tex] = 1,400

Let x represents  the life span of a monitor.

Then , the probability that the life span of the monitor will be more than 15,240 hours will be :-

= P(x > 15,240) = P[(x - μ)/σ >  (15,240 - 13,000)/ 1,400 ]

= P (z > 1.6) =  1 - P(z ≤ 1.6)  [∵ P(Z > z ) = 1 - P(Z ≤ z) ]

= 1 - 0.9452  = 0.0548 ~ 0.055

Hence, the probability that the life span of the monitor will be more than 15,240 hours = 0.055

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The true statement  is that both √15 and √0.001 are irrational , the correct option is (c).

Rational Numbers can be defined as the  numbers that can be expressed in the form of p/q , where p and q are integers and q not equal to 0 .

For Example : 2/3 , 2, 8/3 are all Rational Numbers.

Irrational Numbers can be defined as the  numbers that cannot be expressed in the form of p/q where , p and q are integers and q not equal to 0 .

For Example : √2 , √37 are irrational as they cannot be expressed in the form of p/q.

In the question ,

two numbers √15 and √0.001 are given .

the first number √15 is not a perfect square , hence not an integer ,

So, √15 is an irrational number .

the second number

√0.001 = √(1/1000) = 1/√1000 = [tex]\frac{1}{10\sqrt{10} }[/tex]

we see that √10 is not an integer , hence √0.001 is an irrational number .

Therefore , the true statement  is that both √15 and √0.001 are irrational , the correct option is (c).

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f(2) = 3

f⁻¹(2) = 1

f⁻¹(0) = -1

(f⁻¹o f)(1) = 1

The graph of f(x) is given. Here, f(x) = y and f⁻¹(y) = x.

That is, f(x) are y values corresponding to the given x-values and f⁻¹(y) is the x-value corresponding to the given y-value.

From the graph, f(2) is the y value when x = 2.

So, f(2) = 3

Now f⁻¹(2) is the x-value when y = 2.

So, f⁻¹(2) = 1

Also f⁻¹(0) =-1

Since f(1) = 2,

(f⁻¹o f)(1) = f⁻¹(f(1)) = f⁻¹(2) = 1

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A point that lies in the middle of a line and is equally spaced from its ends is the line's midway. The formula for the line's midpoint is [(x)1 + (x)2]/2, [(y)1 + (y)2]/2 if the line's endpoints are (x)1, (y)1, and (x), (y), respectively.

Using the equations [(x)1 + (x)2]/2, [(y)1 + (y)2]/2, one may get the midway. Here, the coordinates of two points are (x), (y), (x)2, (y)2, and the midway is a location that is equally spaced from both of these positions.

The exact middle number between two numbers is referred to as the midway. The midpoint calculation is the same as the two-number average calculation. Therefore, by adding any two numbers together and dividing by two, you may find the halfway between any two integers.

The distance formula, which is derived from the Pythagorean Theorem, is employed to determine the separation between two points in the plane. The Pythagorean Theorem is based on a right triangle where the angles are a and b.

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For the given functions, we have that:

a) The numeric value of the division function at x = 4 is of (h/g)(4) = 81/21 = 3.86.

b) The value that is not in the domain of the division function is of x = -1.25.

In this problem, the functions that we are given are defined as follows:

To find the quotient function of h(x) and g(x), we just divide the function h(x) by the function g(x), that is:

h(x)/g(x) = [(x + 5)(x + 5)]/(4x + 5).

At x = 4, the numeric value is found replacing each instante of x by 4, hence:

(h/g)(4) = [(4 + 5)(4 + 5)]/(4(4) + 5)) = 81/21 = 3.86.

The denominator of a fraction cannot be zero, as division by zero does not exist, hence the value of x that is not on the domain of the division function is found as follows:

4x + 5 = 0.

4x = -5.

x = -5/4

x = -1.25.

The complete problem is given by the image at the end of the answer. There are lots of instances of this problem, just with different functions, so we use the functions given in this problem and not on the image.

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Answer:

6.3071, 6.408, 6.47, 6.7

Step-by-step explanation:

6.3071, 6.408, 6.47, 6.7, hope this helped!

Answer:

In bold below.

Step-by-step explanation:

6.3071, 6.7 6.408, 6.47

= 6.3071, 6.408, 6.47, 6.7

The attached figure shows the location of P' and R' in the figure, after the dilation

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The figure that completes the question is added as an attachment

From the figure, we have the following parameters

The image of dilation using the above parameters is the scaled factor of the given figure

As a general rule, the following are the properties of a scaled copy of another figure

The above means that

New lengths = Old lengths * Scale factor

So, we have

P'R' = PR * Scale factor

C'R' = CR * Scale factor

This gives

P'R' = 5 * 3

P'R' = 15

C'R' = 2.6 * 3

C'R' = 7.8

Using the above as a guide, the location of P' and R' are identifies in the figure

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Answer:

$48

Step-by-step explanation:

Simple interest (I) = PRT/100

Where P = principal

R= rate

T = time

.: Simple Interest = 120 × 8 × 5

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

100

S. I = $48

.: the approximate value of the investment at the end of 5 years will be = $48

Answer:

$2

Step-by-step explanation:

To find the unit cost, divide the entire price of all the songs (22), by how many songs you bought (11)

22 Dollars / 11 Songs   =    2 Dollars / Song   (2 Dollars per Song)

Answer:

In point-slope form: y + 4 = -2(x + 1)

In slope-intercept form: y = -2x - 6

In standard form: 2x + y = -6

Step-by-step explanation:

y + 4 = -2(x + 1)

y + 4 = -2x - 2

y = -2x -6

2x + y = -6

Cans of paint (k) = Birdhouses painted

x= cans of paint

y= Birdhouses painted

y= kx

Where k is the constant of proportionality.

Replace with a set of points and solve for k

(x,y) = (3,15)

15= k 3

15/3 = k

k=5

Answer:

12

Step-by-step explanation:

(8+11+14+13+14+9+15)/7 = 12

Answer:

Total obs. = 7

Average = (n + 1 )/2

Average = 7 + 1 /2

= 8/2 = 4th obs.

= Sum of obs./ Total obs.

= 8,11,14,13,14,9,15/7

= 84/7

Answer:

f(-2) = 18

Step-by-step explanation:

In order to calculate a function of x, we replace x
For example
f(x) = x
f(-2) = -2

In this specific scenario

f(x) = 3 * (4 - x)
f(-2) = 3 * (4 - -2)

- -2 turns positive
f(-2) = 3 * (4 + 2)

Now we use PAMDAS (parentheses, exponents, multiplication, division, addition) as an operation order, so we first solve the parantheses
f(-2) = 3 * 6

f(-2) = 18

Betty spent $90 and Nan spent $ 30

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

Given that :While shopping, Betty spent three times as much as Nan. And they spent a total of $120,

Let the Betty spent total $x and Nan spent total $Y

then,

x = 3y ....(i)

x +y =120 .....(ii)

put value of c from i equation to equation ii

4y = 120

y = 30

x = 90

Hence Betty spent $90 and Nan spent $ 30

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