Example 2:

If f(x) = 2x+5, find each value. Show all work.

a) f(-2)

b) f(1)+5

c) f(x+3)

The relation that is not a function, but whose inverse is a function are:

for every x in the domain of f, f -1[f(x)] = x, and

for every x in the domain of f -1, f[f -1(x)] = x

An inverse function is a characteristic that undoes the movement of another characteristic. A feature g is the inverse of a characteristic f if whenever y=f(x) then x=g(y). In different words, applying f and then g is the equal aspect as doing not anything. we are able to write this in terms of the composition of f and g as g(f(x))=x.

A few capabilities do not have inverse functions. for instance, remember f(x) = x2. There are numbers that f takes to four, f(2) = 4 and f(-2) = four. If f had an inverse, then the fact that f(2) = 4 might mean that the inverse of f takes four again to 2.

To discover the inverse function of an algebraic relation in terms of x and y, simply interchange the variables x and y, and resolve the equation for y. as an example, to discover the inverse of a relation y = x3, interchange x, and y after which clear up it for y. Then we get x = y3 ⇒ y = x1/3.

An inverse version can be represented by means of the equation xy=k or y=kx. this is, y varies inversely as x if there are a few nonzero steady k such that, xy=k or y=kx in which x≠0,y≠0 . assume y varies inversely as x such that xy=3 or y=3x.

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The solution of expression rounded to nearest tenth is -1.1

Rewriting the equation first -

-1.2x = 11.3x + 13.75

Now, shifting 11.3x to other side of the equation and rewriting the equation -

- 1.2x - 11.3x = 13.75

Rewriting the equation according to sign on Left Hand Side

-(1.2x + 11.3x) = 13.75

Performing addition of similar values on Right Hand Side of the equation

-12.5x = 13.75

Solving for the value of x from above mentioned equation -

x = 13.75 ÷ (-12.5)

Performing division to find the value of x

x = - 1.1

The number 1.1 rounded to nearest tenth will be 1.1.

So, the solution of expression rounded to nearest tenth is -1.1

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All the angles of the given triangle are;

∠1 = 41°

∠2 = 85°

∠3 = 95°

∠4 = 85°

∠5 = 36°

∠6 = 49°

∠7 = 106°

We are given different angles. Thus;

∠3 will be equal to 95° because of the definition of vertically opposite angles.

∠4 = 180° - 95° because sum of angles on a straight line is equal to 180°. Thus;

∠4 = 85°

∠2 = ∠4 = 85° because they are both vertically opposite angles.

∠5 = 180° - 144° because sum of angles on a straight line is equal to 180°.  Thus; ∠5 = 36°

∠7 = 180° - (38° + 36°) because sum of angles in a triangle is equal to 180°. Thus; ∠7 = 106°

Sum of angles in a quadrilateral is 360°. Thus;

∠1 = 360 - (90 + 144 + 85)

∠1 = 41°

∠6 = 180 - (90 + 41)

∠6 = 49°

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The given expression contains a fractional exponent and would be simplified through solving for it.

The reciprocal of power associated with the base is the degree of the radical signs.

For example: ∜7=7^1/4

In the given expression, there are two considerations. The number 243 has a power of 1/5, and the negative sign or say -1 also has a power of 1/5.

As a general rule, if the denominator of the fractional exponent is an odd number, as 5 in this case, the negative sign is extracted from the radical. Another way to look at it is -1 raised to any odd power would be -1.

Hence, (-243)^¹/₅ =-(243)^¹/₅

Factorizing the term,

243=3*3*3*3*3

Which can be expressed as 3^5

Hence,

-(243)^1/5=-(35)^1/5

As we know that (a^b)^c=a^bc, thus,

-(3^5^)1/5=-(3^5*1/5)= -(3^1)=-3

(-243)^¹/₅is simplified to -3

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After solving the given equation 7x-2=252, the value of x = 36.9.

So,

Then,

7x-2=252

Therefore, after solving the given equation 7x-2=252, the value of x = 36.9.

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Answer:

The Distributive Law

Step-by-step explanation:

The given question represents the commutative property of addition.

Given, (8 + 3) + 11 = 8 + (3 + 11)

According to the commutative property of addition, no matter how the numbers are arranged, the total of two or more numbers remains the same.

The commutative property of addition states that no matter how the numbers are organized, the result of adding or summing two or more numbers will always be the same. The representation of the bracket placement and arrangement in the provided addition problem is referred to as grouping in this context.

The addends can be grouped in several ways without affecting the result, according to the associative feature of addition. Rearranging the addends won't affect the result, according to the commutative property of addition.

Hence the given expression represents the commutative property of addition.

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The model equation to find the number of hours she should work to earn $728 per week is given as 16a +56b = 728

It is given that,

Elena is earning as a swimming instructor = $16.00 an hour

Also, she is earning as an intern in a genetics = $56.00 per hour

The condition which is given is that, Elena needs to earn at least $728

per week in order par her college fees

We need to find the, equation which can resolve this situation to find the number of hours she should work to earn $728 per week

Let the number of hours she works teaching swimming = a

And, let number of hours she works as an intern in genetics = b

Then, the equation can be made as = 16a +56b = 728

Hence, the model equation to find the number of hours she should work to earn $728 per week is given as 16a +56b = 728  

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The average number of miles she would have to meet her goal will be 2.62 miles each day.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Keilantra plans to pedal her bike 28.8 kilometers each week. She has already written a great deal. assuming she rides for another four days.

Let n be the number of days required more. Then the equation is given as,

⇒ 28.8 / (7 + n)

⇒ 28.8 / 11

⇒ 2.62 km each day

The average number of miles she would have to meet her goal will be 2.62 km each day.

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Answer:

z=120

Step-by-step explanation:

z/12 = 10

multiply both sides by

12 12z/z =

10 x 12

z= 120

Answer:

z=12x10=120

Step-by-step explanation:

hope this helps ˙˚ʚ(´◡`)ɞ˚˙

A uniform distribution has the data values evenly distributed throughout the range of the data. A bimodal distribution has two very common data values seen in a dot plot or histogram as distinct peaks.

A Dot Plot, also called a dot chart or strip plot, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete bins (categories). A dot plot is similar to a bar graph because the height of each “bar” of dots is equal to the number of items in a particular category.

A dot plot is a graphical display of data using dots: Dot Plot is a graph for displaying the distribution of quantitative variable where each dot represents a value. For whole numbers, if a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value.

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After expanding logarithm equation is : [tex]\frac{5.log_4(\sqrt{x} )y^7}{zu^4}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_4((\sqrt{x})^5 )y^7}{zu^4} \\[/tex]

apply formulas log a^x = x log a

[tex]log_4\sqrt{x}^5 = 5 log_4\sqrt{x}[/tex]

=> [tex]\frac{5.log_4(\sqrt{x} )y^7}{zu^4}[/tex]

Thus, after expanding the logarithm equation is : [tex]\frac{5.log_4(\sqrt{x} )y^7}{zu^4}[/tex]

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The side length of each face of a cube is equal to 2 feet.

We know, Total surface area of a cube = 6a², where a is the side length of the cube.

Here, a = 2 feet

∴ Total surface area of the given cube is equal to

⇒ 6(2)²

⇒ 6(4)

⇒ 24 sq. ft.

∴ Total surface area of the given cube is 24 sq. ft.

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The measure of angles 1, 2 and 3 for fig in 11. are 100°, 80° and 100°. And for part 12. are 80°, 80° and 100° respectively.

For 11. part:

Considering two parallel lines l and m cut by a transversal p,

If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.

m∠1 + 80° = 180°

m∠1 = 180° - 80°

m∠1 = 100°

Similarly, m∠1 + m∠2 = 180°

⇒ 100° + m∠2 = 180°

⇒m∠2 = 180° - 100°

⇒m∠2 = 80°

and also, m∠2 + m∠3 = 180°

⇒ 80° + m∠3 = 180°

⇒m∠3 = 180° - 80°

⇒m∠3 = 100°

Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.

For 13. part:

m∠3 = 100° (vertically opposite angle)

Now, let us suppose the angle adjacent to ∠3 be x then, m∠x will be simply equal to

m∠3 + m ∠x = 180° (Linear pair property.)

100° + m ∠x = 180°

m ∠x = 180° - 100°

m ∠x = 80°

Now, from the figure we can clearly see that,

m∠1 = m∠2 = m ∠x  = 80°(Corresponding angles are equal.)

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The common factors of the numbers 18 and 30 is 6

The numbers are given as

18 and 30

Express 18 and 30 as a product of its factors

So, we have

18 = 2 * 3 * 3

30 = 2 * 3 * 5

Multiply the common factors in the above expression

Common factors = 2 * 3

Evaluate the product

So, we have

Common factors = 6

Hence, the common factors of the numbers 18 and 30 is 6

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The best option including the commissions is the Hight tech job.

He was offered a job at high tech and Job at the best computers.

The options are as follows:

The offer that will be best option can be determined as follows:

High tech:

total salary per week = 500 + 5% of 500

total salary per week = 500 + 5 / 100 × 500

total salary per week = 500 + 25

total salary per week = $525

Best Computer:

total salary per week = 400 + 7.5% of 400

total salary per week = 400 + 7.5 / 100 of 400

total salary per week = 400 + 30

total salary per week = $430

Therefore, the best option including the commissions is the Hight tech job.

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Answer:

The answer is D. 20,000

Step-by-step explanation:

Hope this helps!!!

Sorry if I'm wrong

Answer:

21.875%.

Step-by-step explanation:

This is a Binomial Probability Distribution.

Prob (exactly 5 heads) = 8C5(0.5)^5(0.5)^3

= 56 * 3.90625 * 10^-3

= 0.21875

= 21.875%.

The value of the product expression 67 x 5 is 335

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

67 x 5

The above expression is a product expression

So, we have

67 x 5

Express 67 as 60 + 7

So, we have

67 x 5 = (60 + 7) x 5

Evaluate the products

So, we have

67 x 5 = 300 + 35

Evaluate the sum

So, we have

67 x 5 = 335

Hence, the value of the product expression 67 x 5 is 335

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The surface area of a rectangular cuboid cake which covered by a cookie crumble is approximately 35.1 m²

The cake can be depicted as in the attached picture with

length (l) = 4.45 meters

wide (w) = 4.06 meters

height (h) = 1 meter

It is a rectangular cuboid, or a right rectangular prism, which has 6 rectangular faces. Since all surfaces were covered by a cookie crumble except the bottom, hence, the surface areas are:

top face = l x w = 4.45 x 4.06 = 18.067 m²

left/right faces = 2 x w x h = 2 x 4.06 x 1 = 8.12 m²

front/back faces = 2 x l x h = 2 x 4.45 x 1 = 8.90 m²

Therefore, total surface area covered by the sprinkle is:

Total surface = 18.067 + 8.12 + 8.90  ≈ 35.1 m² ( to the nearest tenth)

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When a function is plotted, the domain and the range of the function are the x-coordinate and the y-coordinate respectively. The domain and range of the assumed function for Melissa's garden :

x = ( 2, infinity )

p(x) = (0 , infinity )

The function is not given. So, I will give a general explanation to calculate domain and range.

The domain is all possible values the independent variables of a function can take while the range is all possible values the dependent variables of a function can take

Assume the function of Melissa's garden is:

p(x) = x. (x-2)

Start by equating the function to 0

x. (x-2) =0

Split

x=0, x-2=0

x=0 x=2

x will give p(x)  = 0

the length of the garden cannot be 0 or less.

So, the domain of the function is:

x = ( 2, infinity )

p(x) = (0 , infinity )

This means that the domain starts from a value greater than 2 (e.g. 3) and ends at infinity

To calculate the range, we substitute x = ( 2, infinity )  in the function

x=2

p(x) = 2.2-2 =0

So, the range of the function is:

p(x) = (0 , infinity )

This means that the domain starts from a value greater than 0 (e.g. 1) and ends at infinity

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[tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{x}{y} } }[/tex] is the correct form.

We need to find the error in the statement [tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{xy}{y} } }[/tex]

Starting from LHS of the statement, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}}[/tex],

we can cancel the like terms ∛y from the numerator and denominator.

So we get, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}[/tex]

Since both of the numerator and denominator has the cubic root, we can combine it.

That is, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}[/tex]  = ∛(x/y) is the right answer.

So in this expression  [tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{xy}{y} } }[/tex], y on the numerator is the error.

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The equation 18/6 = 3 shows that 6 is a factor of the number 18.

An equation is an expression that shows the relationship between two or more numbers and variables.

A factor is a number that divides the given number without having any remainder.

Given that 6 is a factor of 18, hence:

18/6 = 3

The equation 18/6 = 3 shows that 6 is a factor of the number 18.

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Answer: I just did the ones that did not already have an answer

Section A:

7. 1.5 hours

9. 480 meters

10. 10 km

Section B:

1. 40 mph

2. 160 miles

3. 168 miles

4. 5.2 mph

5. 26.25 km/h

Answer: $1875

Step-by-step explanation:Take x as the amount of money you have. 30%=30/100. So, 30/100*x=15. x= 2500. So, 75% of x is 75/100 * 2500 = 1875$

Answer:

4v^2 + 6v + 3

Step-by-step explanation:

When calculating time zone differences, you should always add and subtract an hour for each time zone to the west.

A time zone is a region that adheres to a common standard time for social, commercial, and legal activities. Because it is easy for locations in frequent communication to preserve the same time, time zones typically follow the boundaries between countries and their subdivisions rather than rigidly following longitude.

The definition of every time zone is an offset from Coordinated Universal Time. For nearly half of the year, certain regions at higher latitudes observe daylight saving time, which is commonly accomplished by adding an hour to local time in the spring and summer.

It should be noted that the Time Zone gives an overview of current local times around the world. It should be noted that calculating time zones is simple and involves adding or subtracting an hour for every 15 degrees of longitude.

Therefore, when calculating time zone differences, you should always add and subtract an hour for each time zone to the west.

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Inverse of the give function F(x) = √2 x + 1 is F⁻¹(x) = ( x - 1 ) / √2

Given is a function of x, F(x) = √2 x + 1

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = √2 x + 1 becomes y = √2 x + 1

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = √2 x + 1, we get

x = √2 y + 1

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x = √2 y + 1

=> x - 1 = √2 y

=> √2 y = x - 1

=> y = ( x - 1 ) / √2

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = ( x - 1 ) / √2 becomes F⁻¹(x) = ( x - 1 ) / √2

Therefore, we get the inverse of the given function F(x) = √2 x + 1 as F⁻¹(x) = ( x - 1 ) / √2.

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Answer:

2/3

Step-by-step explanation:

btw was it -11/3 or -1 & 1/3 cuz I did -2/3 - (-1 &1/3)​