(Simplify your answer.)Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. x-8 f(x) = 4x + 8 and g(x) = 4

Answer:

There are roughly 2,488,600 more people living in Chicago.

After solving the exponential function y = 12.5ˣ, the value of y = 1.

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.

So, the exponential function:

y = 12.5ˣ

We know that x is 0.

The exponential function rule states that when the power is 0, the answer is always 1.

y = 12.5ˣ

y = 12.5⁰

y = 1

Therefore, after solving the exponential function y = 12.5ˣ, the value of y = 1.

Know more about exponential function here:

https://brainly.com/question/2456547

#SPJ1

Correct question:

For this exponential function, what is the output value (y), when the input value (x) is O?

y = 12.5ˣ

The least angle at which given figure maps onto itself is 180°. This can be understand by using magnitude of symmetry.

What is symmetry?

In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more precise definition of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Although these two interpretations of "symmetry" can occasionally be distinguished from one another, they are intricately linked and are therefore discussed jointly in this article. Aspects of mathematical symmetry can be seen in abstract objects like theoretical models, language, and music, as well as in the passage of time, as a spatial relationship, through geometric transformations, and in other types of functional transformations.

A figure in the plane has rotational symmetry if the figure can be mapped into itself by a rotation between 0° to 360° about the center of figure.

The given figure has one line of symmetry,

figure is divided into two parts that can overlap

angle will be = 360/2=180° .

So, the smallest angle is 180°.

Learn more about symmetry from the given link:
https://brainly.com/question/1002723
#SPJ1

The product of two rational numbers is always rational because (ac/bd​) is the ratio of two integers, making it a rational number.

We need to prove that the product of two rational numbers is always rational. A rational number is a number that can be stated as the quotient or fraction of two integers : a numerator and a non-zero denominator.

Let us consider two rational numbers, a/b and c/d. The variables "a", "b", "c", and "d" all represent integers. The denominators "b" and "d" are non-zero. Let the product of these two rational numbers be represented by "P".

P = (a/b)×(c/d)

P = (a×c)/(b×d)

The numerator is again an integer. The denominator is also a non-zero integer. Hence, the product is a rational number.

To learn more about rational numbers, visit :

https://brainly.com/question/24398433

#SPJ1

Answer:

b

Step-by-step explanation:

it is the answer

The next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.

What is Fabonacci type sequence ?

The first two terms are already defined in the this sequence. The nth term of a Fabonacci type sequence is given by the following expression:

[tex]F_n=F_{n-1}+F_{n-2}[/tex]

(a)

In this case 5 terms are given hence, calculate the 6th term.

[tex]F_6=F_5+F_4\\F_6=9+5\\F_6=14[/tex]

Now, calculate the 7th term.

[tex]F_7=F_6+F_5\\F_7=14+9\\F_7=23[/tex]

(b)

Calculate the 4th term.

[tex]F_4=F_3+F_2\\F_4=14+9\\F_4=23\\[/tex]

Calculate the 5th term.

[tex]F_5=F_4+F_3\\F_5=23+14\\F_5=37[/tex]

(c)

The series is 4, 6, 10, 16, ...

[tex]F_5=F_4+F_3\\F_5=16+10\\F_5=26[/tex]

[tex]F_6=F_5+F_4\\F_6=26+16\\F_6=42[/tex]

Hence, the next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.

Learn more about Fabonacci sequence from the following link:

https://brainly.com/question/11149413

#SPJ1

Using the concepts of area of rectangle, we got that  72 feet  is the the least amount of fencing he can use to create the area for his sheep.

Lets, suppose that the length of rectangle as x feet,

and width of rectangle as y feet.

So perimeter of rectangle as 2×( length + breadth)

We are given perimeter of rectangle as 72 feet

So, length of two sides of rectangle + width of rectangle=72feet.

=>2x+y=72 feet----------(eq1)

Now, we know that area of rectangle is given by =(length × breadth),or

=>(x × y)=20000

Putting values of y from eq1,we get

=>x × (72-2x)=20000

=>72x-2x²=20000

We need to find the least amount of fencing, so we find the local minima by using the differentiation

=>d(72x)/dx-d(2x²)/dx=d(20000)/dx

=>72-4x=0

=>x=18feet

Therefore, y=72-2×18=72-36=36feet

Hence, length of rectangle is 18 feet, and width is 36 feet

Therefore, length of fencing is =2x+y=2×18+36=72 feet.

Hence, if a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 square feet, then the least amount of fencing he can use to create the area for his sheep is 72 feet.

To know more about area of rectangle, visit here:

https://brainly.com/question/20693059

#SPJ4

(Complete question) is:

a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. Perimeter of rectangle is given as 72 feet. He wants the area to be 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?

Answer:

Step-by-step explanation:

24

Answer:

  11 mi/h

Step-by-step explanation:

You want the speed of the boat when it travels 12 miles upstream against a current of 5 mph in the same time it travels 32 miles downstream with the current.

The relation between time, speed, and distance is ...

  time = distance/speed

If b represents the speed of the boat, the times upstream and downstream are the same, so we have ...

  (12 mi)/(b -5) = (32 mi)/(b+5)

Multiplying by the product of the denominators gives ...

  12(b+5) = 32(b-5) . . . . . . also divided by "mi"

  12b +60 = 32b -160 . . . . multiply by (b+5)(b-5)

  220 = 20b . . . . . . . . . . . . add 160 -12b

  11 = b . . . . . . . . . . . . . . . . . divide by 20

The speed of the boat in still water is 11 miles per hour.

__

Additional comment

Each trip took 2 hours.

-4 is the absolute value of -3.5 and three fifths.

An expression is combination of variables, numbers and operators.

negative absolute value of negative three fifths.

−3.5-3/5

Three fifths means three by five

-3.5-3/5

(-5(3.5)-3)/5

Minus seventeen point five minus three divided by five

-17.5-3/5

Minus twenty point five divided by five

-20.5/5

Minus four point one

-4.1

-4

Hence -4 is the absolute value of -3.5 and three fifths.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

Answer:

75%

Step-by-step explanation:

To solve this equation, we need to turn the fraction 72/96 into a percentage.

72 ÷ 96 = 0.75

0.75 as a percentage is 75%

Therefore, 75% of the coffees were regular.

The sample size must be 543 so the sample proportion is will not differ by 5%

We are given the following in the question:

Margin of error = 5%

Confidence interval:

p ±z√(p'(1 - p')/n)

Margin of error =

p = ±z√(p'(1 - p')/n)

Since no particular proportion is given, we take

p' = 0.5

Z critical at α 0.02 is ± 2.33

Putting values, we get,

p = ±z√(p'(1 - p')/n)

2.33 x √(0.5(1 - 0.5)/n)

√n = 2.33x 0.5/0.05

n = 542.89 = 543

Thus, the sample size must be 543 so the sample proportion is will not differ by 5%

To learn more about confidence interval refer here

https://brainly.com/question/15712887

#SPJ4

Answer:

w = 6 units

Step-by-step explanation:

The perimeter is found by adding all the sides of a rectangle. The perimeter can be found using this equation:

[tex]P=2w+2l[/tex]

Where w represents width and l represents length.

To find the width, rearrange the equation so it is in terms of w:

[tex]P=2w+2l\\2w=P-2l\\w=\frac{P-2l}{2}[/tex]

Now, plug in the known values!

[tex]w=\frac{20-2(4)}{2}[/tex]

Simplify!

[tex]w=\frac{12}{2} \\w=6[/tex]

Answer:

27.5

Step-by-step explanation:

2x-6=49

2x=55

x=27.5

The two additional roots are:-0.17-7i and -2i

Given,

A polynomial function P(x) with rational coefficients has the given roots.

P(x) = 0.17+7i and 2i

we are asked to determine the two additional roots of the given P(x).

we know that a+bi is a root of P(x)=0, then a-bi is also a root of P(x)=0

we have:

0.17+7i and 2i are two roots pf P(x)

so, -0.17-7i and -2i are two additional roots of P(x).

Hence we get the required roots.

Learn more about Roots here:

brainly.com/question/25841119

#SPJ1

Relay exchanges will not take place at any of the 0.25-mile markers

The calculated relay exchanges are

The number of team members which is 9 is equal to the number of relay exchanges in the 4-mile race.

This will result to the relay exchanges occurring at  every 4/9, and repeated addition of 4/9 will give the  other points, and the list is

4/9, 8/9, 4/3, 16/9, 20/9, 8/3, 20/9, 32/9, and 4 in fraction

In decimal form this will be listed in four decimal place

0.4444

0.8889

1.3333

1.7778

2.2222

2.6667

3.1111

3.5556

4

Learn more about decimals here:

https://brainly.com/question/29401139

#SPJ1

Three betas will be in our model aside from the y-intercept.

In the given question, we have to find how many betas will be in your model aside from the y-intercept.

You operate a theme park and want to use the temperature outside and the day of the week to predict how many people will be in attendance each day.

While testing this model, you also want to see if the relationship between temperature and theme park visitors will be curvilinear.

You decide not to test for interactions.

From the given question,

We have y intercept that means our model well be

[tex]y=\beta_{0}+x_{1}\beta _{2}+x_{2}\beta _{2}+x_{1}x_{2}\beta _{12}[/tex]

where [tex]\beta _{1}[/tex] is for temperature and [tex]\beta _{2}[/tex] is day of the week.

3 betas are there aside intercept of y.

To learn more about y-intercept model link is here

brainly.com/question/12995616

#SPJ4

Answer:

scalene acute

Step-by-step explanation:

scalene = 2 sides are the same and one is different

acute = all three angles are smaller than 90

Answer: try a c and e

Step-by-step explanation:

Answer:

The is no number that I can substitue in for x to make the statement true.

Step-by-step explanation:

s + 3 = x -6  Subtract x from both sides

3 = -6  We get a false statement.

Answer:

115°

Step-by-step explanation:

They are the same angle because we know the lines are parallel.

Answer:

115°

Step-by-step explanation:

alternate exterior, they're the same

The amount of time it takes for the cannonball to strike the ground is equal to 6.516 seconds.

Based on the information provided, we can logically deduce that the height (h) in meters, of this cannonball during above the​ ground is related to time by the following function:

h(t) = - 4.9t² + 30.5t + 9.3.

Generally speaking, the height of this cannonball would be equal to zero (0) when it strikes the ground. Therefore, we would equate the height function to zero (0):

0 = - 4.9t² + 30.5t + 9.3.

4.9t² - 30.5t - 9.3 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-30.5)\; \pm \;\sqrt{(-30.5)^2 - 4(4.9)(-9.3)}}{2(4.9)}\\\\x = \frac{30.5\; \pm \;\sqrt{930.25\; + \;182.28}}{9.8}\\\\x = \frac{30.5\; \pm \;\sqrt{1112.53}}{9.8}[/tex]

Time, x = (30.5 ± 33.3546)/9.8

Time, x = (30.5 + 33.3546)/9.8

Time, x = 63.8546/9.8

Time, x = 6.516 seconds.

Read more on time here: brainly.com/question/26746473

#SPJ1

Answer:

I would say answer D is correct since it is closest to 1,760 yards.

Step-by-step explanation:

;)

The cost of one pound is $3.3 or the rate of per pound fruits is $3.3.

What is meaning of one pound?

Pound is an unit to measure mass of an object. The plural form of pound is pounds.

What is the unitary method?

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that Miranda buys 5.1 pounds of avocados at the local store. The cost of the fruits is $16.83.

Apply unitary method to calculate the cost of 1 pound:

The cost 5.1 pounds fruit is $16.83.

The cost 1 pound fruit is $16.83/5.1 = $3.3.

To learn more about rate, you can visit the below link:

https://brainly.com/question/13209775

#SPJ1

Answer:

Step-by-step explanation:

5.8, 5.8042, 5.84, 6.328

The length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.

According to the question,

We have the following information:

The perimeter of an isosceles triangle is 48 inches. Each leg is 6 inches less than two times the base.

We know that in an isosceles triangle two sides are equal.

Let's take the base of the triangle to be x inches.

Other sides = (2x-6) inches

So, we have the following expression:

2x-6+2x-6+x = 48

5x-12 = 48

5x = 48+12

5x = 60

x = 60/5

x = 12 inches

Now, the other two sides of triangle:

2*12-6

24-6

18 inches

Hence, the length of two same sides of isosceles triangle is 18 inches and the third side of the triangle is 12 inches.

To know more about isosceles triangle here

https://brainly.com/question/2456591

#SPJ1

Parking 11,000 automobiles at the venue and 4,600 in satellites will bring in total $166,500.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Given,

If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot,

Multiplying:

$7.5 x 4,600 = satellite parking

$34,500 = satellite parking

The next step is to determine how much it will cost to park in the arena lot.

$11,000 ×12 = arena lot

$32,000 = arena lot

Let's now calculate the entire revenue from parking.

Total earnings equal $132,000 + $34,500.

Amount made in total is $166,500.

In conclusion Parking 11,000 automobiles at the venue and 4,600 in total satellites will bring in $166,500.

To learn more about multiplication, visit:

https://brainly.com/question/23354835

#SPJ4

Answer:

[tex]\textsf{B.} \quad g(x)=-x^2-2[/tex]

Step-by-step explanation:

Transformations

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.[/tex]

From inspection of the given graph, we can see that g(x) is function f(x) reflected in the x-axis and translated 2 units down.

Given function f(x):

[tex]f(x)=x^2[/tex]

Reflected in the x-axis:

[tex]-f(x) \implies g(x)= -x^2[/tex]

Translated 2 units down:

[tex]-f(x)-2 \implies g(x)=-x^2-2[/tex]

Therefore:

[tex]g(x)=-x^2-2[/tex]

Note:  

If the leading coefficient of a quadratic function is positive, the parabola opens upwards.

If the leading coefficient of a quadratic function is negative, the parabola opens downwards.

Therefore, as g(x) opens downwards, the term in x² will be negative.

Answer:

4/20=1/5 or 20% or 0.2

Step-by-step explanation:

if u write 4/20 simplify it which becomes 1/5

u can write in percentage or in decimal depending on what the question wants