Complete the explanation of how you can use a table of values, an equation, and
a qraph to determine whether a function represents a proportional relationship.

GA = 34.2

7) m∠OAG = 40 degree

GO = 22

GA = ?

opposite = side opposite the angle = 22

hypotenuse = GA

So we would apply sine ratio (SOH):

sin 40 = opposite/hypotenuse

sin 40 = 22/GA

GA(sin 40) = 22

GA = 22/sin 40

GA = 22/0.6428

GA = 34.2

The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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Answer:

x=3

Step-by-step explanation:

Hey there!

In order to solve this equation, we must first distribute the 3

3x + 9 = -4x + 30

Now we combine like terms

7x = 21

Then we divide both sides by 7 to get x by itself

x = 21/7

x = 3

Answer: x=3

Step-by-step explanation:

To solve the given equation, it means to find the value of x. We want to use inverse properties to isolate x. The inverse properties are add/subtract and multiply/divide. Be sure to use the corresponding inverse operation.

3(x+3)=-4x+30                 [distribute]

3x+9=-4x+30                    [add both sides by 4x]

7x+9=30                            [subtract both sides by 9]

7x=21                                 [divide both sides by 7]

x=3

Therefore, we get x=3.

Class members that should be the public are: Constructors, accessors/ mutators and methods the user needs to manipulate the objects of the class. The correct answer is c. I, III, V.

All members declared in a class as well as all members (apart from constructors and finalizers) defined in all classes in its inheritance structure are considered to be members of the class. Although they are inherited, derived classes cannot access private elements of base classes.

Class members are all the members (apart from constructors and destructors) defined in the class, as well as all the classes in its inheritance structure. Members of a class may be any of the following: Constant values represented by constants. Variables represented by fields.

If you want the class to be instantiated from anywhere, you must make the constructor public. If you want a class to be inheritable and its inherited classes to be instantiated, you must make the constructor protected.

A technique used to regulate changes to a variable is known as a mutator method. They're also frequently referred to as setter methods. A getter, often referred to as an accessor, frequently follows a setter and returns the value of the private member variable.

Therefore, the correct answer is (c). I, III, V.

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writing the linear equation can be used by any any of those coordinates that are given

y - y1 = m(x - x1)

m = Gradient

m = y - y1 / x - x1

Where:

(-7, 1) = (x, y)

(-3,  9) = (x1, y1)

m = (1 - 9) /( -7 + 3)

m = -8/- 4

m = 2

Inputing this into our point slope form equation : y - y1 = m(x - x1)

We have:

y - 9 = 2(x + 3)

Therefore, Option D is the correct option

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Answer:

Step-by-step explanation:

The total angle is 180 so 180 is 95 is 75

x=75

A traingle has a total of 180

180-50-75=55

y=55

Step-by-step explanation:

yes, the step is correct.

a² = cx | multiply by c

ca² = c²x

I am just not sure how that simplified the equation.

what do you want to achieve ? what's the goal here ?

to solve the equation for x it would be to divide both sides by c, which gives

a²/c = x

Answer:

x = -4, 1, 4

Step-by-step explanation:

The function is given as:

f(x) = (x² - x -2)/[(x² - 1)(x² -16)]

We want to find the values of x where the graph will have vertical assymptote.

Vertical asymptotes are defined as vertical lines which correspond to the values of x that will make the denominator of a rational function to be zero.

Thus, to get the values of x that we will have vertical assymptotes, we have to equate the denominator to zero.

We have;

[(x² - 1)(x² -16)] = 0

Thus,

x² - 1 = 0

Or

x² - 16 = 0

So;

x² = 1

x = √1

x = 1

Or

x² = 16

x = ±√16

x = ±4

Values of x that give vertical assymptote are;

x = -4, 1, 4

The area of the composite figure is equal to 89.5 square yards

The composite figure can be observed to be made up of a large rectangle at the center with a smaller rectangle and a triangle by the sides, so we shall calculate for the area of the three shape and sum the results to get the total area of the composite figure as follows:

area of the larger rectangle = 14 yd × 5 yd = 70yd²

area of the smaller rectangle = 5 yd × 3 yd = 15 yd²

area of the triangle = 1/2 × 3 yd × 3 yd= 4.5 yd²

total area of the composite figure = 70yd² + 15 yd² + 4.5 yd²

total area of the composite figure = 89.5 yd²

Therefore, the area of the composite figure is equal to 89.5 square yards

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Answer:

degree 3

Step-by-step explanation:

Note that

(- 3)³ + 4 = - 27 + 4 = - 23

(- 2)³ + 4 = - 8 + 4 = - 4

0³ + 4 = 0 + 4 = 4

1³ + 4 = 1 + 4 = 5

2³ + 4 = 8 + 4 = 12

3³ + 4 = 27 + 4 = 31

Then

f(x) = x³ + 4 ← a polynomial of degree 3

Answer:

the value of the h is 6

Step-by-step explanation:

6 x 7 = 42

Answer:

5216.844

Step-by-step explanation:

Let x be the fourth number.

We know that the sum of the four numbers is 20500:

2341.578 + 10690 + x + 2341.578 = 20500

Simplifying and solving for x:

x = 20500 - 2341.578 - 10690 - 2341.578

x = 5216.844

To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)

The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)

The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)

Solving for\(\(x\),\) we divide both sides of the equation by 3:

\(\(x = \frac{71}{3}\).\)

Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.

The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:

\(\(x = 2\pi r\).\)

Substituting the value of x we found earlier, we have:

\(\(\frac{71}{3} = 2\pi r\).\)

Solving for r, we divide both sides of the equation by \(\(2\pi\):\)

\(\(r = \frac{71}{6\pi}\).\)

Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.

In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.

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The distance it will take to drive from Toronto to buffalo (distance between Toronto and buffalo is 154km) is 1.75 hours.

We are given that;

distance = 154 km speed = 88 km/hr

Now,

we need to use the formula:

time = distance / speed

where time is in hours, distance is in kilometers, and speed is in kilometers per hour.

Plugging these values into the formula, we get:

time = 154 / 88 time ≈ 1.75

Therefore, by speed the answer will be 1.75 hours.

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Answer:

6x = 180

x = 30

Step-by-step explanation:

Answer:

y=-1/2x+4

Step-by-step explanation:

The line is going down, which means it's negative. You then do rise over run, go up by 1 and go to the left by 2. To find the y intercept, it's 4 since the coordinate is (0,4).

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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In conclusion, none of the given statements are correct based on the information provided.

To determine the correct statement, let's analyze the given information and the regression equation:

The regression equation for estimating the number of customers on a given day is y = 1.03x + 229.4, where x represents the day number and y represents the number of customers served.

We are also given that the restaurant has been making a net profit of $5.82, on average per customer:

Now let's evaluate each statement:

A. On day 7, the owner can expect 15 more customers than she has served on day 6.

To determine the number of customers on day 7, we substitute x = 7 into the regression equation:

y = 1.03(7) + 229.4 = 7.21 + 229.4 = 236.61

So, the number of customers on day 7 is approximately 237, which is not 15 more than the number of customers served on day 6.

Therefore, statement A is incorrect.

B. If the number of customers continues to follow the current trend, the restaurant will make a net profit of $1,377 on day 7.

To calculate the net profit on day 7, we need to multiply the average net profit per customer ($5.82) by the number of customers on day 7:

Net profit on day 7 = $5.82 \(\times\) 237 ≈ $1,379.34

So, statement B is incorrect as the net profit on day 7 is not expected to be $1,377.

C. On day 12, the owner can expect a net profit of $1,300.

Since the question only provides information about the number of customers served for the first 6 days, we cannot determine the net profit on day 12.

Therefore, statement C is incorrect.

D. Net profit for days 6 and 7 combined is expected to be less than the earned net profit on day 1.

To calculate the net profit for days 6 and 7 combined, we need to calculate the number of customers on both days using the regression equation and then multiply it by the average net profit per customer.

Let's substitute x = 6 into the regression equation:

y = 1.03(6) + 229.4 = 6.18 + 229.4 ≈ 235.58

Now, let's calculate the net profit for days 6 and 7 combined:

Net profit on days 6 and 7 = ($5.82 \(\times\) 235) + ($5.82 \(\times\) 237) ≈ $2,735.2

Comparing this to the earned net profit on day 1, we cannot determine if it is less or greater without the information provided.

Therefore, statement D is incorrect.

In conclusion, none of the given statements are correct based on the information provided.

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Solution:

Given:

The fenced part of the field must add up to 2400ft.

The possible fencing of the field if the fencing along the river is not needed are shown below;

Possibility 1:

Possibility 2:

From the two possible scenarios, to get the dimensions of the field with the largest area,

Therefore, the dimension of the field with the largest area is 600ft x 1200ft

The amount of time until there are 90 grams remaining is given as follows:

7.3 minutes.

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

Hence the amount after x minutes is given as follows:

\(y = 370(0.824)^x\)

The time needed for an amount of 90 grams is given as follows:

\(y = 370(0.824)^x\)

\(90 = 370(0.824)^x\)

\((0.824)^x = \frac{9}{37}\)

\(x = \frac{\log{\frac{9}{37}}{\log{0.824}}\)

x = 7.3 minutes.

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The rate of change can be identified with the velocity of the cars.

The car which will travel the furthest in 2 hours will be the fastest car.

The 2009 Camry has the greatest rate of change, with 75 miles/hour.

Therefore, the 2009 Camry will travel the furthest in 2 hours.

Answer:

2(x+3)

Explanation:

2x+3x=2(x+3)

Answer:

a) If the spinner is fair, then each color must have the same probability, this means that the probability for each color is the number of times that the color (in this case blue) is in the spinner divided the total amount of colors in the spinner, then the theoretical probability for each color is:

Pt = 1/5 = 0.20

The experimental probability can be found by dividing the number of times that the spinner landed on a given color (in this case for blue we have 15 times) divided the total number of spins ( 50)

Pe = 15/50 = 0.30

B) As we increment the number of spins, we should see that the experimental probability gets closer to the theoretical probability.

Answer:

y = (x + 1 ) ^2

Step-by-step explanation:

y = x^2 + 2x + 1

Completing the Square

y = ( x + 1 ) ^2 + 0

The probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

Since there are 8 cameras in the box, the total number of ways to choose 2 cameras from the box is given by the combination formula:

C(8,2) = 8!/(2!×(8-2)!) = 28

So there are 28 possible ways to choose a sample of 2 cameras.

Now, let's calculate the probability of each possible value of x:

When x = 0, both cameras in the sample are non-defective. The number of ways to choose 2 non-defective cameras from the 4 non-defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 0 is:

P(x=0) = (number of ways to choose 2 non-defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

When x = 1, one camera in the sample is defective and the other is non-defective. The number of ways to choose 1 defective camera from the 4 defective cameras in the box and 1 non-defective camera from the 4 non-defective cameras in the box is given by the product of the corresponding combinations:

C(4,1) × C(4,1) = 4×4 = 16

So the probability of x = 1 is:

P(x=1) = (number of ways to choose 1 defective camera and 1 non-defective camera)/(total number of ways to choose 2 cameras)

= 16/28

= 0.571

When x = 2, both cameras in the sample are defective. The number of ways to choose 2 defective cameras from the 4 defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 2 is:

P(x=2) = (number of ways to choose 2 defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

Therefore, the probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

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Answer & Step-by-step explanation:

2. 4 times (*) f equals (=) 1/2

Equation: 4f=1/2

4 times (*) 1/8 equals (=) 1/2

f = 1/8

3. 832 divided by (/) n equals (=) 16

Equation: 832/n=16

832 divided by (/) 52 equals (=) 16

n = 52

4.  10 subtracted from (-) x equals (=) 6

Equation: 10-x=6

10 - 4 = 6

x = 4

Hope this helps ;)

Answer:

2.9%

Step-by-step explanation:

Answer:

20 inches

Step-by-step explanation:

Let x be the current height of Jada's dog in inches.

The equation to represent the problem is:

x = 5 1/2 + 14 1/2

To solve, we first need to add the mixed numbers:

5 1/2 + 14 1/2 = 20

So, the current height of Jada's dog is 20 inches.

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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Step-by-step explanation:

For a rational function, we cannot values in the domain that will make the denominator 0.

So set the denominator =0

\( {x}^{2} - 1 = 0\)

\( {x}^{2} = 1\)

\(x = 1\)

or

\(x = - 1\)

So the answer is (-1,1)