he table shows the relationship between the values of x and y. Which of the following equations describes the relationship for the values in the table

The relative maxima.

To find the relative maxima and minima of the function f(x) = x + 9/x + 5, we need to first find the derivative of the function.

The derivative of f(x) is f'(x) = 1 - 9/x^2.

Next, we need to set the derivative equal to zero and solve for x to find the critical points.

1 - 9/x^2 = 0

9/x^2 = 1

x^2 = 9

x = ±3

So, the critical points are x = 3 and x = -3.

To determine if these are relative maxima or minima, we need to use the second derivative test.

The second derivative of f(x) is f''(x) = 18/x^3.

Plugging in x = 3, we get f''(3) = 18/27 = 2/3, which is positive. This means that x = 3 is a relative minima.

Plugging in x = -3, we get f''(-3) = 18/-27 = -2/3, which is negative. This means that x = -3 is a relative maxima.

Therefore, the relative maxima is at x = -3 and the relative minima is at x = 3.

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As you have two side lengths but no angle measures, the Pythagorean Theorem should be used to obtain the value of x.

Then the value of x is given as follows:

x = 36.3.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The parameters for this problem are given as follows:

Hence the value of x is obtained as follows:

x² + 19² = 41²

x = sqrt(41² - 19²)

x = 36.3.

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Answer:

4:3

Step-by-step explanation:

16:12=8:6=4:3, that is simplest ratio

Since the two hexagons are similar, their corresponding sides are in the same ratio as the scale factor.

Let x be the length of a side of the smaller hexagon, then the corresponding length of a side of the larger hexagon can be expressed as (3/7)x.

The area of a hexagon can be calculated using the formula: A = (3√3/2)s², where s is the length of a side.

Since the area of the smaller hexagon is 18 m², we can solve for x as follows:

18 = (3√3/2)x²

x² = 12/√3

x = 2√3

Now we can calculate the area of the larger hexagon:

Area of the larger hexagon = (3√3/2)(3/7x)² = (3√3/2)(3/7(2√3))² = 54/49 m²

Finally, we can calculate the volume of the larger hexagon, assuming it is a regular hexagonal prism:

Volume of the larger hexagon = Area of hexagon x Height

The height of the hexagonal prism is the same as the length of the side of the larger hexagon, which is (3/7)x:

Volume of the larger hexagon = (54/49) x (3/7)x = 54/343 x² ≈ 0.212 x²

Substituting the value of x, we get:

Volume of the larger hexagon ≈ 0.212 x (2√3)² = 1.272 m³

Therefore, the volume of the larger hexagon is approximately 1.272 m³.

Well, I'm not sure if it's correct but I got 42.

I got this by doing something along the lines of:

1) 18/x = 3/7

2) Cross multiply

3) 3x = 126

4) Divide both sides by 3

5) x = 42

The required with the help of trig ratios we have,
1. x = 30.69
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
1.

Apply the sine rule,
Sin21 = perpendicular/hypotenus
sin21 = 11 / x
x = 11/sin21
x = 30.69

Similarly,
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

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The maximum number of days she can drive the car is approximately 4 days.

A rental car company charges $61.79 per day to rent a car and $0.13 for every mile driven.

She plans to drive 50 miles. She has at most $230 to spend.

Therefore, the maximum number of days that Tallulah can rent the car while staying within her budget can be computed as follows:

Using equations,

y = 0.13a + 61.79b

where

Therefore, she has a budget of 230 dollars and she wants to ride for 50 miles.

230 = 0.13(50) + 61.79b

230 - 6.5 = 61.79b

223.5 = 61.79b

b = 223.5  / 61.79

b = 3.61709014404

Therefore,

b = 4 days

Hence, she can ride maximum of 4 days.

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An expression that shows the total area of five rooms is (3 × 13²) + (2 × 15²)

The correct answer is an option (A)

Let 'a' represents the side length of the square rooms measuring 13 ft each and 'b' represents the side length of the square rooms measuring 15 ft each.

We know that the formula for the area of a square  is A = s²

where 's' is the side of a square.

Sides of three square rooms measure 13 feet each.

So, the area of the three rooms would be:

A₁ = 3 × a²

A₁ = 3 × 13²

And sides of two square rooms measure 15 feet each.,

So, the area of the two rooms would be:

A₂ = 2 × b²

A₂ = 2 × 15²

Total area of the five rooms A =  A₁ + A₂  

So, we get an expression:

A = 3 × 13²  + 2 × 15²

A = 3 × 169 + 2 × 225

A = 957 ft²

Therefore the total area of the five rooms be 957 ft².

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The complete question is:

Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of these five rooms?

a.(3 × 13^2) + (2 × 15^2)

b.(2 × 13^3) + (2 × 15^2)

c.(3 × 15^2) + (2 × 13^2)

d.(3 × 13^2) × (2 × 15^2)

We have proven that in given triangle ∠BACB is congruent to ∠DECD, as required.

Similarity of triangles refers to the property of having the same shape but not necessarily the same size. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

To prove: ∠BACB = ∠DECD

We know that, BD ∥ AE and C is the midpoint of AE.

Therefore, triangle ACE and triangle BCD are similar by the Converse of the Corresponding Angles Postulate. Hence, we have:

∠CAB = ∠CBD .... (1) (corresponding angles)

∠CAE = ∠CDB .... (2) (corresponding angles)

Also, we know that in triangle ACE, angles 3 and 4 are alternate interior angles formed by a transversal. Therefore, angles 3 and 4 are congruent. Similarly, in triangle BCD, angles 1 and 2 are congruent.

Therefore, we can write:

∠ACB = ∠BCD .... (3) (angles of similar triangles)

Adding equations (1) and (3), we get:

∠BACB = ∠DECD

Hence, we have proven that ∠BACB is congruent to ∠DECD, as required.

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Answer:

B. y=7x

Step-by-step explanation:

A direct proportion is where the ratio is constant. The ratio will stay the same. Therefore, y = 7x, this ratio will stay constant making it a direct proportion.

Hope this helps : )

The function with the largest rate of change is function a.

The rate of change defines how fast the function grows.

So, the most "vertical" or the one that grows the fastest is the function with the largest rate of change.

By looking at the graph, we can see that the fastest growing (the steepest) one is function a, so that is the correct option.

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The situations that best represent the scenario shown in the graph of the quadratic functions, y = x² and y = x² + 3 include the following:

B. "From x = -2 to x = 0, the average rate of change for both functions is negative."

C. "For the quadratic function, y = x² + 3, the coordinate (2, 7) is a solution to the equation of the function."

D. "The quadratic function, y = x², has an x-intercept at the origin."

In Mathematics, the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).

In this context, we can logically deduce that the x-intercepts of the graph of the given equation y = x² is at the origin:

x = (0, 0)

For the the coordinate (2, 7), we would evaluate the quadratic function, y = x² + 3 as follows;

7 = 2² + 3

7 = 4 + 3

7 = 7 (True).

By critically observing the graph of both functions, we can logically deduce that their average rate of change is negative from x = -2 to x = 0.

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The three-dimensional figure this net will make is a triangular prism and is denoted as option B.

This is defined as a solid figure or an object or shape that has three dimensions such as length, width, and height.

An example is the triangular prism is a polyhedron made up of two triangular bases and three rectangular sides and from the net given above we can deduce that the triangular prism can be formed from it due to the shape and vertices.

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A horizontal change of 96ft, there will be a vertical change of 3072ft.

The slope of a line is the ratio of the vertical change to the horizontal change between two points on the line. In other words, the slope is the rise over the run.

If the slope of a line is 32, that means that for every 1 unit of horizontal change, there is a 32 unit vertical change.

So, if the horizontal change is 96ft, we can use the slope formula to find the vertical change:

Vertical change = slope × horizontal change

Vertical change = 32 × 96

Vertical change = 3072

Therefore, for a horizontal change of 96ft, there will be a vertical change of 3072ft.

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Answer:

$2.50

Step-by-step explanation:

The fraction of candies left behind is 3/7.

To find the fraction of candies left behind, we need to divide the total number of candies by the number of candies in each pack and find the remainder. This remainder will be the numerator of the fraction and the number of candies in each pack will be the denominator.

Step 1: Divide the total number of candies by the number of candies in each pack: 3242 ÷ 7 = 463 with a remainder of 3

Step 2: The remainder, 3, is the numerator of the fraction and the number of candies in each pack, 7, is the denominator. So the fraction of candies left behind is 3/7.

The fraction of candies left behind is 3/7.

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The height οf the clοset is x ft = 8 ft.

The vοlume οf a rectangular prism is the amοunt οf space οccupied by the three-dimensiοnal οbject. It is calculated by multiplying the length, width, and height οf the prism.

In this prοblem, we are given that the clοset has a vοlume οf 220 ft^3 and its dimensiοns are x+3 ft. wide, x-5.5 ft. deep, and x ft. high. Sο, we can write the equatiοn:

V = (x+3)(x-5.5)(x)

where V is the vοlume οf the clοset.

Tο sοlve fοr x, we can simplify the equatiοn by multiplying the factοrs:

[tex]V = (x^2 - 2.5x - 16.5)(x) = x^3 - 2.5x^2 - 16.5x[/tex]

Nοw, we can substitute the given value οf V and sοlve fοr x:

[tex]220 = x^3 - 2.5x^2 - 16.5x[/tex]

We can rearrange this equatiοn tο get:

[tex]x^3 - 2.5x^2 - 16.5x - 220 = 0[/tex]

This is a cubic equatiοn that can be sοlved by factοring οr using numerical methοds. By using numerical methοds, we can find that οne sοlutiοn οf this equatiοn is x = 8.

Therefore, the height of the closet is x ft = 8 ft.

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Health club A costs $18 more than health club B charges.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x - 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, The equation y = 35x + 40 represents health club B charges.

And the equation for health club A is, 35x + 58.

Now, To obtain how much more health club A charges we have to take the difference which is,

= (35x + 58) - (35x + 40).

= 35x - 35x + 58 - 40.

= $18 more.

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Answer:

G

Step-by-step explanation:

Since these triangles are similar, side lengths in one must be proportional to the other.  Segment AB is similar to DE, AC similar to DF, and BC similar to EF. With that in mind, G is the only possible answer because DE/AG correspond to one another, just as DF/AC correspond to one another.

Answer:

Step-by-step explanation:

Answer:Price of the table yesterday is x.

Price of the table today is $513.

$513 is 76% of yesterday's price x. 76% can be also written down as 76 divided by 100 (percentage) or 76/100 = 0.76.

Formula we can set up now is: x= 513 / 0.76 (To get the price of yersterday's table we need to divide the price of today's table with percentage in decimal form).

x= 675

The price of yesterday's table was $675 since 76% of that price (675 times 0.76) equals 513 dollars.

Step-by-step explanation:

Answer:

We do not have enough information to find the exact value of f(2.5) without additional assumptions about the nature of the exponential function. However, we can make an estimate using the given data and the properties of exponential functions.

First, we can write the general form of an exponential function as:

f(x) = a * b^x

where a is the initial value or y-intercept, and b is the base or growth factor. We can use the two given data points to set up a system of equations and solve for a and b:

f(-1) = a * b^(-1) = 18

f(5) = a * b^5 = 75

Dividing the second equation by the first equation, we get:

f(5) / f(-1) = (a * b^5) / (a * b^(-1)) = b^6 = 75 / 18 = 25 / 6

Taking the sixth root of both sides, we get:

b = (25 / 6)^(1/6) ≈ 1.472

Substituting this value of b into the first equation, we get:

a = f(-1) / b^(-1) = 18 / 1.472 ≈ 12.223

Therefore, we have the exponential function:

f(x) ≈ 12.223 * 1.472^x

Using this function, we can estimate the value of f(2.5) as:

f(2.5) ≈ 12.223 * 1.472^(2.5) ≈ 34.311

Note that this is only an estimate, and the exact value of f(2.5) may be different depending on the specific nature of the exponential function.

The variation constant is 22 and the equation of variation where y varies inversely as x is y = 22/x.

When two variables, y and x, are inversely proportional, it means that as one variable increases, the other variable decreases proportionally, and vice versa. Mathematically, this can be expressed as:

y = k/x

where k is the variation constant. To find k, we can use the given information that "y = 11 when x = 2". Substituting these values into the inverse variation equation above, we get:

11 = k/2

Multiplying both sides by 2, we get:

k = 22

So, the variation constant is 22.

Now, we can write the equation of variation as:

y = 22/x

This means that as x increases, y decreases proportionally. For example, if x doubles to 4, y would be halved to 5.5, keeping the product (xy) constant.

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Answer:

55%

Step-by-step explanation:

When you have a question that asks you about a percentage and it gives you a fraction, most of the time you just have to divide the numbers. In this case you will do 11/20=0.55 and you will change the decimal to a percentage. Which will be 55%.

The standard form for the quadratic equation written in vertex form y = 2(x - 2)² + 5 is y = 2x² - 8x + 13.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

To change the equation y = 2(x - 2)² + 5 from vertex form to standard form, we need to expand the squared term and simplify the expression.

Here are the steps -

Start with the vertex form: y = 2(x - 2)² + 5.

Expand the squared term using the formula (a - b)² = a² - 2ab + b².

In this case, a = x and b = 2, so we have -

y = 2(x - 2)(x - 2) + 5

y = 2(x² - 4x + 4) + 5

Multiply the coefficient 2 by each term inside the parentheses -

y = 2x² - 8x + 8 + 5

Combine the constant terms -

y = 2x² - 8x + 13

This is the standard form of the quadratic equation.

In standard form, the quadratic equation is written as y = ax² + bx + c, where a, b, and c are constants.

In this case, a = 2, b = -8, and c = 13.

Therefore, the standard form is y = 2x² - 8x + 13.

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Answer: I believe its A.

Step-by-step explanation:

All of the functions have a constant rate of change since they are linear functions with a slope (rate of change) that is equal to the coefficient of the independent variable. Therefore, all functions have a constant rate of change of their slope.

Option A: y = 6(2) = 12 has a slope of 6, which means it increases by 6 for every unit increase in x.

Option B: y = 2(3) = 6 has a slope of 2, which means it increases by 2 for every unit increase in x.

Option C: y = 3(4) = 12 has a slope of 3, which means it increases by 3 for every unit increase in x.

Option D: y = 4(2) = 8 has a slope of 4, which means it increases by 4 for every unit increase in x.

Therefore, option A has the most rapid rate of change with a slope of 6.

Answer:

the ans the last person gave is very correct

Answer:

1/6

Step-by-step explanation:

Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

The expected value of the game in which you have a (1/20) chance of winning  is $1.50.  The probability of a student scoring between 75 and 89 is 0.5536. The probability of a student scoring above 85 is 0.4562.

1. To find the expected value of the game, we need to multiply the probability of each outcome by the value of that outcome and then add them together.

E(X) = (1/20)($300 + $15) + (19/20)(-$15)

E(X) = $315/20 - $285/20

E(X) = $30/20

E(X) = $1.50

So the expected value of the game is $1.50.

2. To find the probability of a student scoring between 75 and 89, we need to use the z-score formula:

z = (x - μ)/σ

For x = 75, z = (75 - 84)/9 = -1

For x = 89, z = (89 - 84)/9 = 0.56

Using a z-table, we can find the probability of a student scoring between these two z-scores:

P(-1 < z < 0.56) = P(z < 0.56) - P(z < -1)

P(-1 < z < 0.56) = 0.7123 - 0.1587

P(-1 < z < 0.56) = 0.5536

So the probability of a student scoring between 75 and 89 is 0.5536.

3. To find the probability of a student scoring above 85, we need to use the z-score formula:

z = (x - μ)/σ

For x = 85, z = (85 - 84)/9 = 0.11

Using a z-table, we can find the probability of a student scoring above this z-score:

P(z > 0.11) = 1 - P(z < 0.11)

P(z > 0.11) = 1 - 0.5438

P(z > 0.11) = 0.4562

So the probability of a student scoring above 85 is 0.4562.

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The three consecutive integers whose sum is 360 are 119, 120, and 121.

To find three consecutive integers whose sum is 360, we can use algebra to set up an equation and solve for the first integer. Let x be the first integer, then the next two consecutive integers will be x+1 and x+2. The sum of these three integers is 360, so we can write the equation:

x + (x+1) + (x+2) = 360

Simplifying the equation gives us:

3x + 3 = 360

Subtracting 3 from both sides gives us:

3x = 357

Dividing both sides by 3 gives us:

x = 119

So the first integer is 119. The next two consecutive integers are 120 and 121. Therefore, the three consecutive integers whose sum is 360 are 119, 120, and 121.

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(a) (i) The function f(x) - g(x) is  √(1-x).

    (ii) The function f(x) - g(x) is -x -1   The domain for f-g is all real numbers.
(b) (i) The function  (f-g)(1) = -2

    (ii) The function (f-g)(2) = √(-1). Therefore, (1/2)g(f(2)) is undefined.

(a)

(i) The function f(x) is already given as f(x) = √(1-x). The domain of f is all real numbers for which 1-x is non-negative. Therefore, the domain of f is x ≤ 1.

(ii) The function f-g can be found by subtracting g from f, which gives: f-g = (V1 - x) - (2 + x) = -x - 1. The domain of f-g is the same as the domain of f, which is x ≤ 1.

(b)

(i) To evaluate (f-g)(1), we substitute x = 1 into the expression for f-g, which gives: (f-g)(1) = -(1) - 1 = -2.

(ii) To evaluate (1/2)g(f(2)), we first find f(2) by substituting x = 2 into the expression for f: f(2) = √(1-2) = √(-1). Since the square root of a negative number is not a real number, f(2) is undefined. Therefore, (1/2)g(f(2)) is also undefined.

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