Define the domain of the following:A. -3,-2,-1,0,1,2,3,4,5,6,7,8,B. 3,-1,2,0,-2C. -3,-1,1,3,6D. All real numbers

Given:-

To find the inverse of the function.

So now we change the value of x in the given function as y and find the value of y. so we get,

Now we find the value of y. so we get,

So the required solution is,

The flying distance between the greenhouse and the stadium = 5 units

The coordinates of the greenhouse: (-6, 0)

The coordinates of the stadium: (-2, 3)

The distance between two points of coordinates (x₁, y₁) and (x₂, y₂) is given as:

For the flying distance between the greenhouse and the stadium:

x₁ = -6, y₁ = 0, x₂ = -2, y₂ = 3

Substitute these values into the distance equation given above:

The flying distance between the greenhouse and the stadium = 5 units

It is given that

Now to find the inverse of g

Let

So

Now we know that

So

And since

So

Given the expression:

if 'p' represents the profit in dollar and 's' represents the number fo sweaters that the store sells, then we have that the store makes 26 dollars per sweater.

We can see this since the equation is the same as a linear function with rate of change m:

Given:

The objective is to explain the method of solving pi equations.

The term with pi can be solved

Similar means that the figure has the same shape, but not neccesarily the same size. It is said, also, that it is incoungruent, so it definetly doesn't have the same size. A transformation that gives you a similar but incongruent figure is a dialation, rotation and/or translation. I'll do a drawing to illustrate:

Notice that I've done the three of them. I have the same figure, smaller, in another position and rotated.

Donavan has 6x + 1/2 x total number of fishes.

Let Donovan has x number of blue fishes.

Hence the number of red fishes = 5x

The number of gray fishes = 1/2  of x = 1/2 x

Total number of fishes = red + blue + gray = 5x + x + 1/2 x = 6 + 1/2 x

For something like an equation to have any importance, the coefficient involving at least any variable must not be 0. In actuality, the following equation would either be inconsistent (for b ≠ 0) and have no solution, or full n-tuples are solutions, as was mentioned for one variable, if any variable does actually have a zero coefficient.

A regular polynomial over such a field, from which the coefficients are drawn, can also be equalized to zero to produce a linear equation. Since linear equations typically do a good job of representing non-linear systems, they are used extensively in all branches of mathematics as well as in physics and engineering.

Therefore we can infer that Donavan has 6x + 1/2 x total number of fishes.

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The economic system that  has no government involvement in the market is d. No economic system is free from government involvement.

In reality there is no government intervention because at some point the government will comes in , this could actually be mininmal, only in the free market is where there is no government intervention.

It should be noted that in this free market, there is  an unregulated system of economic exchange, where the act of  taxes collection as well as  quality controls,  has no economic interventions  which can be attributed to government .

Therefore option D is correct.

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This problem describes two points in a route of 4 hours. He went through 68 miles after the first two hours, and 132 miles after 4 hours of driving. We need to calculate the average rate of change.

The average rate of change is the division between the total distance and the time it took to travel that distance, so we have:

The average rate of change is equal to 33 miles per hour.

Answer:

Step-by-step explanation:

Expression:

y = mx + n*b

In which m is the cost per ride and b is the entrance fee.

y is the total cost, x is the number of rides and n is the number of people.

When 6 teachers went to Six Flags and rode on 20 rides total, they ended up paying $350.

This means that:

20m + 6b = 350

When 15 people went to Six Flags and rode on 47 rides they paid $900.

This means that:

47m + 15b = 900

Solving the system:

20m + 6b = 350

47m + 15b = 900

Multiplying the first equation by -5, the second by 2.

-100m - 30b = -1750

94m + 30b = 1800

-6m = 50

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

LM = 14

MN = 11

KM = ?

Step 02:

We must apply the triangle rules to find the solution.

Pythagoras Theorem

LM² = LN² + MN²

(14)² = LN² + (11)²

(14)² - (11)² = LN²

LN = 8.66

8.66 * 8.66 = 11 * KN

6.818 = KN

KM = KN + MN

KM = 6.818 + 11 = 17.818

The answer is:

The value of KM is 17.82

Given that the average payout for slots machines is 84 cents on each dollar.

We know that

The cost of return for every dollar spent is 100-84=16 cents.

The percent return on every dollar spent in playing slots is

The percent return on every dollar spent in playing slots is 16%.

Given the following functions:

f(x) = 3x

g(x) = x + 4

h(x) = x^2 - 1

Before simplifying g(f(-1)), let's first determine f(-1).

f(x) = 3x

f(-1) = 3(-1)

f(-1) = -3

g(x) = x + 4

g(f(-1)) = (-3) + 4

= -3 + 4

g(f(-1)) = 1

Therefore, the answer is 1.

To solve this equation, we can follow the next steps:

First: we can sum similar terms like 3x + 3x.

6(x - 1) = 3x + 3x + 6

6(x - 1) = 6x + 6

Then, solve 6(x-1) using the distributive property:

6x - 6 = 6x + 6

Subtract 6x from both sides of the equation:

6x - 6x - 6 = 6x - 6x + 6

0 - 6 = 6

-6 = 6

Since the result is not congruent, we can say that this equation has no solution.

Answer:

Explanation:

Given the expression:

First, the expression can be rewritten in the form below:

Next, we simplify:

The simplest form of the expression is:

You can notice that each point of both images are at the same distance of the origin of coordinates. It means that the transfromation is a reflection across the line y = x

answer: reflection across y = x

Answer:

Domain: (-∞, ∞)

Range: (-∞, ∞)

Explanation:

The parenting function of g(x) = (x + 3)³ + 5 is f(x) = x³.

The graph of f(x) = x³ is

Then, if we have a function g(x) = f(x + c), we can say that g(x) is the graph of f(x) shifted c units to the left and if we have a function g(x) = f(x) + c, we can say that g(x) is the graph of f(x) shifted c units up

In this case, g(x) = f(x + 3) + 5 because

g(x) = f(x + 3) + 5

g(x) = (x + 3)³ + 5

So, g(x) has the graph of f(x) shifted 3 units to the left and 5 units up.

Therefore, the graph of g(x) is

Now, the domain is the set of values that x can take and the range is the set of values that y can take, so the domain and range are all the real number.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Answer:

(4) -2

Explanation:

Given the system of equations:

Set x as the subject in the second equation: x=6-y

Substitute x=6-y into the first equation:

The value of y that solves the system of equations is -2.

Solution

Circle: The set of all points in a plane that lie the same distance from a single point in the plane.

Perpendicular lines: Intersecting lines that form right angles

Congruent: Having exactly the same shape and size

Angle: A figure formed by two rays that have the same endpoint

Solution

Let sin (47) = 0.7314. Enter an angle (B), in degrees,

where cos (B) = 0.7314 means

since the vaule of sin(A) = 0.7314

Hence the cos(B) = cos43 = 0.7314

The angle of B = 43°

In order to find the rate of change of the given line, use the following formula:

where (x1,y1) and (x2,y2) are two points of the line.

From the given graph you can select any pair of points, for example:

(x1,y1) = (2,400)

(x2,y2) = (4,1200)

replace the values of the previous coordinates in the formula for m:

Hence, the rate of change is 400

The expression is given to be:

Rewrite the terms so that we can factorize the common terms out:

Therefore, the expression can be rewritten to be:

Since there is a common term, 2x², we can factorize to give:

The quadratic function in the parentheses cannot be factored further.

Therefore, the answer is:

Answer: They have the same area.

Step-by-step explanation:

Here you just have to count the small squares.

In the blue shape, you can see there are 16 small squares.

And in the green shape, there is also 16 squares.

And the small squares are all equal.

So they both have the same area.

My first step is always to draw a picture

We are told the length is 4 less than twice the width

l = 2w-4

We are told the perimeter is 34

P =2(l+w)

Substitute the first equation in for l

P = 2( 2w-4 + w)

Combine like terms

34 = 2( 3w-4)

Distribute the 2

34 = 6w -8

Add 8 to each side

34+8 = 6w-8+8

42 = 6w

Divide by 6

42/6 = 6w/6

7 =w

Now we can find l

l = 2w-4 = 2(7) -4 = 14-4 = 10

The question asks for the area

A = l*w = 10 *7 = 70

The ratios are equivalent if:

For example, given a length of 20cm:

Since:

We can conclude that they are equivalent

Simplification of Algebraic Expression.

Thus, the correct answer is 11 +7i ( option D )

The first thing we have to know is that the trinomial (polynomial of three terms) is called a perfect square trinomial, the polynomial that when factorized gives us a perfect squared expression in the following way

If a point divides two other points in any ratio m : n, then the coordinate of the point dividing the given two points can be known using section formula. The coordinate of the point ZZ on the number line is (4.06, 8.46).

Section formula is used in Coordinate geometry to find the ratio between two points on a line given one another point on the line.

Given that,

The ratio XZ : XY : YZ = 5 : 75 : 7

The coordinates of XX are (1.31, 3) and of YY are (3.83, 8).

Since YY is partitions the point XX and ZZ. In order to find the the coordinates of ZZ section formula can be used as below,

x = (m₁x₂ + m₂x₁) ÷ (m₁ + m₂) and  y = (m₁y₂ + m₂y₁) ÷ (m₁ + m₂)

Here, m₁ : m₂ is equal to XY : YZ which can be known from the given ratio as,

XY : YZ = 75 : 7

=>  m₁ : m₂ = 75 : 7

=> m₁ = 75 and m₂ = 7.

Suppose the coordinates of XX, YY and ZZ are (x₁, y₁),  (x, y) and (x₂, y₂) respectively.

Substitute the respective values in the section formula to get,

3.83 = (75x₂ + 7 × 1.31) ÷ (75 + 7)

=>  (75x₂ + 7 × 1.31) = 82 × 3.83

=> 75x₂ = 82 × 3.83 - 7 × 1.31

=> x₂ = (82 × 3.83 - 7 × 1.31) ÷ 75

=>  x₂ = 4.06

And,

8 = (75y₂ + 7 × 3) ÷ (75 + 7)

=>  (75y₂ + 7 × 3) = 82 × 8

=> 75y₂ = 82 × 8 -  7 × 3

=> y₂ = (82 × 8 -  7 × 3) ÷ 75

=>  y₂ = 8.46

Thus, ( x₂,  y₂) is equal to (4.06, 8.46).

Hence, the coordinate of ZZ is given by (4.06, 8.46).

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Let's draw the scenario to understand it better:

From the figure, the information given are:

Question:

Step 1: We write a function that relates the quantities in the diagram using Pythagorean

Theorem.

Step 2: Differentiate with respect to t.

Now we wish to plug in specific numbers for every quantity in the above equation except for dD/dt. However, we notice that we don’t have a specific value for D at y = 400 ft. So first we need to find D at y = 400 ft. using the Pythagorean Theorem.

Step 3: Finish the problem by plugging in numbers for every quantity in the equation

containing dD/dt.

Conclusion: When the rocket is 300 ft. feet from the ground, the distance between the observer and the rocket is increasing at a rate of 180 ft./sec.