The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 40 + 0.008p3 and that its demand function is D(p) = 200 - 0.16p2, where p is the price. Determine the price for which the supply equals the demand.

Part A.

The given equation is:

y = x^2 + 6x + 7

By completing the square:

y = (x^2 + 6x + 9) + 7 – 9

y = (x + 3)^2 – 2

y + 2 = (x + 3)^2

Part B.

The vertex form of a parabola is in the form:

y – k = 4p (x – h)^2

Where (h, k) is the vertex (x, y) of the parabola.

Therefore the vertex: (-3, -2)

Since 4p = 1, a positive number, therefore the parabola opens up which makes the vertex (-3, -2) the minima of the graph.

Part C.

The Axis of Symmetry is the x - coordinate of the vertex which is x = - 3

17 x PI = 53.40707511

divided by 4 = 13.35176878

 rounded to nearest thousandth = 13.352

Answer:

A

Step-by-step explanation:

The sum of measures of all the exterior angles of ANY POLYGON is 360°.

The measure of each exterior angle of ANY POLYGON is [tex]\frac{360}{n}[/tex]

where [tex]n[/tex] is the number of sides of the polygon

A hexagon has 6 sides, thus the measure of each exterior angle of a hexagon is:

[tex]\frac{360}{6}=60[/tex] degrees

Answer choice A is correct.

a. The required equation is x² - 16x + 48 = 0

b. I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

a.

The required equation is x² - 16x + 48 = 0

Since the quadratic function y = -10x² + 160x - 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. Since we require a profit of $50, then y = 50.

So, y = -10x² + 160x - 430

-10x² + 160x - 430 = 50

-10x² + 160x - 430 - 50 = 0

-10x² + 160x - 480 = 0

Dividing through by -10, we have

x² - 16x + 48 = 0

So, the required equation is x² - 16x + 48 = 0

b.

I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

To determine the method you would use to solve the equation, you would need to determine the value of the discriminant.

For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² - 4ac

Since x² - 16x + 48 = 0 and its discriminant D = (-16)² - 4 × 48

= 256 - 192

= 48

= 64 > 0 and is a perfect square, so it is factorizable. The equation would have real and distinct roots,

So, x² - 16x + 48 = 0

x² - 4x - 12x + 48 = 0

x(x - 4) - 12(x - 4) = 0

(x - 4)(x - 12) = 0

x - 4 = 0 or x - 12 = 0

x = 4 or x = 12

I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

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Answer:

x2-2 domain an range are 0, -2

Step-by-step explanation:

Answer:

D.  [tex](x-7)^3[/tex]

Step-by-step explanation:

Given functions are,

[tex]f(x) = x-7-----(1)[/tex]

[tex]g(x)=x^3-----(2)[/tex]

Now,

[tex]g(f(x))=g(x-7)[/tex]     ( From equation (1) ),

[tex]=(x-7)^3[/tex]            ( From equation (2) ),

[tex]\implies g(f(x)) = (x-7)^3[/tex]

Hence, Option D is correct.

The number of words Jean will type when she completes 60 minutes of typing is  3,000, This is further explained below Option C is correct

Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.

In conclusion, The graph and table show the relationship between y and x

And the graph shows 3000 at "the number of words Jean has typed for her essay" axis denoted by y, for what she completes 60 minutes.

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Answer:

the answer is the first option : A

Step-by-step explanation:

Final answer:

To convert the temperature of Savannah's liquid from Celsius to Fahrenheit, use the equation °F = (°C × 9/5) + 32. Savannah's temperature in Celsius is 50°, so her temperature in Fahrenheit is 122°F.

Explanation:

To convert the temperature from Celsius to Fahrenheit, you can use the equation:
°F = (°C × 9/5) + 32.
In this case, Savannah's temperature in Celsius is 50°. Using the equation, we can calculate her temperature in Fahrenheit as:
°F = (50 × 9/5) + 32 = 122°F.
Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.

Savannah's liquid, initially measured at 50°C, converts to 122°F using the formula F = C x (9/5) + 32.

To convert the temperature from degrees Celsius to degrees Fahrenheit, we use the conversion formula: F = \( C \times \frac{9}{5} + 32 \), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.

In Savannah's case, she measured the temperature as 50°C. Applying the conversion formula:

Therefore, the temperature of Savannah's liquid to the nearest degree Fahrenheit is 122°F.

The solution would be like this for this specific problem:

f(x) = x^2 + sin(x) 

f '(x) = 2x + cos(x) 

The minimum value is at f '(x) = 0, 

So, let g(x) = 2x + cos(x) 

Thus, g '(x) = 2 - sin(x) 

x(new) = x - g(x) / g '(x) 
or 
x(new) = x - [2x + cos(x)] / [2 - sin(x)] 

Calculation 

x1 = -0.5 - [2 * -0.5 + cos(-0.5)] / [2 - sin(-0.5)] 
= -0.4506266931 
x2 = -0.4501836476 
x3 = -0.4501836113 
x4 = -0.4501836113 

This value for x, f(x) = -0.2324655752. 

After converting to 6 decimal places: the minimum point is (-0.450184, -0.232466).

Final answer:

To find the absolute minimum value of f(x)=x^2+sin(x), use Newton's method with Newton-Raphson iteration x_{n+1} = x_n - f(x_n)/f'(x_n). Start with an initial guess and iterate until the result converges to six decimal places, ensuring the second derivative at the critical point is positive.

Explanation:

To find the absolute minimum value of the function f(x)=x^2+sin(x) correct to six decimal places, we can use Newton's method. Newton's method helps to find successively better approximations to the roots (or zeroes) of a real-valued function. First, we need to find the derivative of the function, which gives us f'(x) = 2x + cos(x). We are looking for a critical point where the derivative is zero because this could indicate a potential minimum (or maximum).

Starting with an initial guess, we can apply the Newton iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find a better approximation. In this case, let's choose an initial guess close to the root of f'(x). Since we do not have the specific initial guess, we would theoretically pick a value near the expected minimum and iterate until the difference between consecutive approximations is less than the desired tolerance, which is the change in six decimal places.

The Newton-Raphson iteration would be applied repeatedly until convergence is seen at six decimal places. Note that in practice, one must also check the second derivative f''(x) at the found critical point to confirm it is a minimum (it should be positive).

Answer:

[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]

Step-by-step explanation:

Here the "X" Values are given, thus the corresponding "Y" values will be

[tex]Y = log (3 X)\\a) X = \frac{1}{1} , Y =  log (3 * \frac{1}{3} ) = log (1) = 0\\b) X = 1, Y = log (3*1) = log (3) = 0.477\\c) X = 3, Y = log (3*3) = log (9) = 0.954\\d) X = 9, Y = log (3*9) = log (27) = 1.43\\e) X = 27, Y = log (3* 27) = log (81) = 1.90\\f) X = 81, Y = log (3 * 81) = log (243) = 2.385\\[/tex]

So the pattern would be

[tex]{(1/3, 0) , ( 1, 0.477), (3, 0.954), (9, 1.43), (27, 1.90), (81, 2.385)}\\[/tex]

Answer:

Answer: Reference angle is π/3 Radians

Step-by-step explanation:

The answer would be an option (D) 17 > 2 or 6 < 9 because 17 is greater than 2 and 6 is less than 9 is always true.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

I. -(-6) = 6 and -(-4) > -4

Here -(-4) > -4 is incorrect

-(-4) = 4 is correct

These statements are not true

III. 5 + 6 = 11 or 9 - 2 = 11

Here 9 - 2 = 11 is incorrect

So 9 - 2 = 7  is correct

These statements are not true

II. -(-4) < 4 or -10 > 10 - 10

Here -(-4) < 4 is incorrect

So -(-4) = 4 is correct

These statements are not true

IV. 17 > 2 or 6 < 9

Here 17 is greater than 2 and 6 is less than 9 is always true.

Hence, the correct answer would be an option (D)

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Final answer:

The mean test score for the group is calculated by summing the products of each unique score and the number of students who received it, then dividing by the total number of students. In this case, the mean test score is 77.

Explanation:

To calculate the mean test score for the group, you multiply each score by the number of students who received it, then sum all those products, and finally divide by the total number of students. Four students scoring 90 would contribute 4 x 90 = 360 to the total sum. Three students scoring 70 contribute 3 x 70 = 210. Two students scoring 60 contribute 2 x 60 = 120. One student scoring 80 adds 80 to the sum. The total sum of all scores is 360 + 210 + 120 + 80 = 770. Since there are a total of 10 students (4 + 3 + 2 + 1), the mean score is calculated as 770 ÷ 10 = 77. Therefore, the mean test score in this group is 77.

Answer:

A is the answer