Cos (pi/11)+cos (3pi/11)+cos (5pi/11)+cos (7pi/11)+cos(9pi/11)

Answer:

1. Dividing the expressions [tex]ax^2+bx+c[/tex] by a is a different step.

2. Yes, both of these factorization are correct. They are not complete because they can be factored further.

3. The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.

Step-by-step explanation:

1.

To factorize the quadratic expressions [tex]ax^2+bx+c[/tex] first we divide it by a. Then we factorize it same as [tex]x^2+bx+c[/tex].

It means all the steps of factoring a quadratic expressions [tex]ax^2+bx+c[/tex] and [tex]x^2+bx+c[/tex] are same except the first step, i.e., divide the expressions [tex]ax^2+bx+c[/tex] by a.

2.

The given quadratic expression is

[tex]P(x)=2x^2+6x-20[/tex]

[tex](2x-4)(x+5)=2x(x+5)-4(x+5)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)[/tex]

[tex](x-2)(2x+10)=x(2x+10)-2(2x+10)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)[/tex]

The product of factors is equal to the given expression. It means both of these factorization are correct.

They are not complete because they can be factored further.

[tex](2x-4)(x+5)=2(x-2)(x+5)[/tex]

[tex](x-2)(2x+10)=(x-2)2(x+5)[/tex]

3.

If the factored form of a quadratic expression is defined as

[tex](x-a)(x-b)[/tex]

Then the related quadratic equation is

[tex](x-a)(x-b)=0[/tex]

[tex]x=a,b[/tex]

The roots of the quadratic equation are a and b.

The related function is

[tex]f(x)=(x-a)(x-b)[/tex]

The x-intercepts of the function are a and b because at x=a and x=b the value of function is 0.

The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.

It should be noted that in order to factorize the quadratic expression, one will have to divide it by a.

The factorization of the quadratic expression ax² + bx + c is different from factoring x² + bx + c as one has to first divide it by a.

Secondly, the factorization by the students isn't complete because they can be factored further.

Lastly, the relationship between the factors of a quadratic expression, the roots of the related quadratic equation is that the roots are the x-intercept of the related function.

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2 men for every 1 woman

24/3 =8

8*2 = 16

there are 16 men and 8 women

In this problem, it is TRUE that the instructor would need to use a t distribution with 10 degrees of freedom to be able to test whether any improved occurred.

In order to check for its correctness, we need to measure the absolute difference between the mean value in two groups in a clinical trial by using the mean difference. Next, we check for the degrees of freedom. The degrees of freedom are the number of independent pieces of information that went into calculating the estimate.

You have to subtract 1 from the number of items to be able to get the df for the estimate. Let’s check this scenario:

Let’s say you need to find the mean weight loss for a low carbohydrate diet. You can use 4 people and giving 3 degrees of freedom (4 -1 = 3), in turn, you can also use 100 people with a df of = 99.

See the attached graph

The comparison operator includes "or equal to" in each case, so the graph of the boundary line is solid. Each bounary line can be graphed in the usual way. Considering the y-intercept and slope is often easiest when the equations are presented in this form:

Since the solution space includes y-values less than those in the first line, the graph is shaded below that line.

Since the solution space includes y-values greater than those in the second line, the graph is shaded above that line.

Where the graph is doubly-shaded is the solution space for the system of equations.

4% = 0.04

 divide 6 by 0.04 = 150

6 is 4% of 150

double check 150*0.04 = 6

1/5 = 0.20

25% = 0.25

 therefore 1/5 is not the same as 25%

Answer:

[tex]f(x)= 2x[/tex]

Step-by-step explanation:

For which function is f(x) not equal to f^-1(x)

LEts check with each function, we find out inverse for each option

[tex]f(x)= 2-x[/tex]

Replace f(x) by y, then switch the variables and solve for y

[tex]y= 2-x[/tex]

[tex]x= 2-y[/tex], Add y on both sides

[tex]x+y= 2[/tex], Subtract x from both sides

[tex]y= 2-x[/tex], Inverse is equal to f(x)

[tex]-f(x)= \frac{2}{x}[/tex]

Replace f(x) by y, then switch the variables and solve for y

[tex]-y= \frac{2}{x}[/tex]

[tex]-x= \frac{2}{y}[/tex],  cross multiply it

[tex]-xy = 2[/tex], divide by x on both sides

[tex]-y= \frac{2}{x}[/tex], Inverse is equal to f(x)

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

Replace f(x) by y, then switch the variables and solve for y

[tex]y= -x[/tex]

[tex]x=-y[/tex], Add y on both sides

[tex]x+y= 0[/tex], Subtract x from both sides

[tex]y=-x[/tex], Inverse is equal to f(x)

[tex]f(x)= 2x[/tex]

Replace f(x) by y, then switch the variables and solve for y

[tex]y= 2x[/tex]

[tex]x= 2y[/tex], divide by 2 on both sides

[tex]\frac{x}{2}=y[/tex],  Inverse is not equal to f(x)

multiply 35 by tan(42)

 this equals 31.5141

rounded to 31.51

The value of trigonometric function sec A is,

⇒ sec A = 25/24

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC angle c is a right angle.

And, c = 25, a = 7

Now, We can draw the tringle ABC.

And, Find the value of side b by using Pythagoras theorem as;

⇒ c² = a² + b²

⇒ 25² = 7² + b²

⇒ 625 = 49 + b²

⇒ b² = 625 - 49

⇒ b = 24

We know that;

⇒ sec A = Hypotenuse / adjacent

Hence, We get;

⇒ sec A = Hypotenuse / adjacent

⇒ sec A = 25 / 24

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Try graphing y=x^3.  It crosses the x-axis at (0,0), and this point represents the one and only real root.

Every form of a cubic function has a graph that crosses the x-axis in 1 or 3 places. 

Thus, the correct answers to this particular problem are B and C.

Additionally, certain cubic function forms have graphs that cross the x-axis in one unique place, but which touch (but do not cross) the x-axis.  Here you have one unique real root plus one repeated (duplicated) real root, for a total of 3 roots.

Using these facts, decide which of the four given answers are correct.

Answer:

A = 114°, B = C = 33°

Step-by-step explanation:

The triangle relationships let you write two equations:

A+B+C = 180

B=C

Substituting the expressions for A, B, and C, you have ...

(x+7y+41) +(2y+13) +(6x+15) = 180

7x +9y +69 = 180

7x +9y = 111

And the second equation gives ...

(2y+13) = (6x+15)

6x -2y =-2

3x -y = -1

Now, we can add 9 times this second equation to the first to eliminate the y-variable.

(7x +9y) +9(3x -y) = (111) +9(-1)

34x = 102

x = 3

Then the angle measures are ..

B = C = 6·3+15 = 33

A = 180 -2·33 = 114

The angles in the triangle are (A, B, C) = (114°, 33°, 33°).

The width of the rectangle is 5 feet, and the length is 7 feet.

To find the dimensions of the rectangle, set up the equation (3W - 8)W = 35, where W is the width and solve for W. You'll find that the width is 5 feet, and the length, which is 8 less than three times the width, is therefore 7 feet.

To find the dimensions of the rectangle with an area of 35 feet2 where the length is 8 feet less than three times the width, let's denote the width as W and the length as L. The problem gives us two equations:

Now, replace L in the first equation with 3W - 8, so we have:

(3W - 8)W = 35

Expanding the equation, we get:

3W2 - 8W = 35

Solve this quadratic equation to find the width W, and then substitute W back into L = 3W - 8 to find the length L. Let's solve the quadratic equation:

3W2 - 8W - 35 = 0

By factoring or using the quadratic formula, we can find that W=5 and L=7 are the solutions that makes sense for the dimensions of the rectangle.

So, the width of the rectangle is 5 feet, and the length is 7 feet.

First floor:

paint department 1,575 square feet

space engine department 2,925 square feet

Total = 4,500 square feet

Second floor:

space window department 1,845 square feet

electrical department 765 square feet

accessory department 1,890 square feet

Total = 4,500 square feet

Since 70% is allocated to the 1st floor, therefore the floor is receiving:

First floor expense = $110,000 * 0.70 = $77,000

Second floor expense = $110,000 - $77,000 = $33,000

The expense for each department is the proportion on the total expense per floor.

First floor:

paint department = (1575/4500) * 77,000 = $26,950

space engine department = 77,000 – 26,950 = $50,050

Second floor:

space window department = (1845/4500) * 33,000 = $13,530

electrical department = (765/4500) * 33,000 = $5,610

accessory department = 33,000 – 13530 – 5610 = $13,860

divide 18 by 0.5

18/0.5 = 36

36 jugs are needed

thy get 55/75 and you want to know x/300

55/75 x X/300

 cross multiply 55 x 300 = 16500

 divide that by 75

16500/75 = 220

 x = 220

 they will get $220

The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the left three units and up two units.

To vertically compress the parent function f(x) = 5x by a factor of one-half, we multiply the function by the compression factor, which is 1/2. So the compressed function is f(x) = (1/2)(5x) = 2.5x.

To shift the function to the left three units, we subtract the shift amount from the x-variable. So the shifted function is f(x + 3) = 2.5(x + 3) = 2.5x + 7.5.

To shift the function up two units, we add the shift amount to the y-variable. So the final transformed function is f(x + 3) + 2 = 2.5x + 7.5 + 2 = 2.5x + 9.5.