Stuck on homework please help

The answer is cos(B/2) = 2√5 / 5

Half angle formula of cosine: cos B/2 = ±√[(1 + cos B) / 2]

Given: The positive value of cos 1/2 B in the simplest radical form with a rational denominator, if cos B = 3/5:

Regarding applying the cosine half-angle formula:

cos²(B/2) = (1 + cos B) / 2

put value of cos B =3/5 (given)

cos²(B/2) = (1 + 3/5) / 2

on simplifying

cos²(B/2) = (8/5) / 2

cos²(B/2) = 4/5

on taking under root we get

cos(B/2) = 2/√5

use a rational denominator and the simplest radical form hence, cos(B/2) = 2√5 / 5

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Answer:

254

Step-by-step explanation:

i think it is correct

Answer:

-76.5

Step-by-step explanation:

see image attached for sol

Answer:

60

Step-by-step explanation:

1=3

2=6

3=9

The relation is Y=3X

Y20 = 3X20=60

Answer: x = −2, y= 9

Step-by-step explanation:

Solving for X

-3x+3=y

-x+3y=29

Plug the top equation into the bottom one

-x+3(-3x+3)=29

Distribute

-x - 9x + 9 = 29

combine like terms

-10x + 9 = 29

-10x = 20

Divide the x

x = -2

Solving for Y:

Plug the value x into any of the equations'

-3(-2) + 3 = y

Distribute

6 + 3 = y

y = 9

To check if that is right, plug x into the other equation

-(-2) + 3y = 29

Distribute and combine like terms

2 + 3 y = 29

3y = 27

y = 9

A. The area of the glass portion is 6x². B. Length of window and pane is 3x + 8 inches, and Width is 2x + 7 inches. C. Area of the window and pane is 6x² + 23x + 56. D. Area of the wooden pane is  23x + 56 inches².

A: The area of the glass portion can be found by multiplying the length and width of the glass.

Given that the height of the glass portion can be represented as 3x and the width can be represented as 2x, we have:

Area of glass portion = 3x × 2x = 6x²

B: To find the length and width of the window and the pane, we must add the wooden trim to the height and width of the glass portion. The wooden trim adds 7 inches to the width and 8 inches to the height, so we have:

Length of window and pane = 3x + 8 = 3x + 8 inches

Width of window and pane = 2x + 7 = 2x + 7 inches

C: Using the length and width from Part B, we can calculate the area of the window and the pane by multiplying the length and width:

Area of window and pane = (3x + 8) × (2x + 7) = 6x² + 23x + 56

D: To find the area of just the wooden pane, we subtract the area of the glass portion from the area of the window and the pane:

Area of wooden pane = Area of window and pane - Area of glass portion = 6x² + 23x + 56 - 6x² = 23x + 56 inches²

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(b)  The value of f^(-1) is g.

(c)  The value of f ◦ f ◦ f = f ◦ (f ◦ f) is f((f ◦ f)(x)) = f((x * (x-1))*((x * (x-1)) - 1)).

According to the question

(a) To prove that f is bijective, we need to show that it is both injective (one-to-one) and surjective (onto).

Injectivity: Let x, y ∈ a such that f(x) = f(y). Then, x * (x-1) = y * (y-1). Multiplying both sides by x-1, we get x = y, meaning that f is injective.

Surjectivity: Let z ∈ a. Then, z = z * (z-1) / (z-1), which means that there exists an x ∈ a such that f(x) = z. This shows that f is surjective.

Therefore, f is bijective.

(b) To find the inverse of f, we need to find a function g: a → a such that f(g(x)) = x and g(f(x)) = x for all x ∈ a.

Consider the function g: a → a defined by g(x) = x / (x-1) for all x ∈ a.

Let x ∈ a. Then, f(g(x)) = f(x / (x-1)) = (x / (x-1)) * ((x / (x-1)) - 1) = x. Similarly, g(f(x)) = g(x * (x-1)) = x * (x-1) / (x * (x-1) - 1) = x. This shows that f and g are inverses.

Therefore, f^(-1) = g.

(c) To find f ◦ f ◦ f, we first evaluate f ◦ f and then evaluate f of the result.

Let x ∈ a. Then, (f ◦ f)(x) = f(f(x)) = f(x * (x-1)) = (x * (x-1)) * ((x * (x-1)) - 1). Hence, f ◦ f ◦ f = f ◦ (f ◦ f) = f((f ◦ f)(x)) = f((x * (x-1)) * ((x * (x-1)) - 1)).

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We can use graphical or numerical methods to estimate the solutions os equations by finding the x-values at which the graph of f(x) intersects the x-axis at y = -1.

We must identify the values of x that cause f(x) to equal -1 in order to estimate the solutions to the equation f(x) = -1.

It is challenging to identify the precise solutions of the equation without knowing the precise shape of the function f. (x). However, by locating the x-values where the graph of f(x) intersects the x-axis at y = -1, we can use graphic or numerical techniques to approximate the solutions. Based on the degree, there are three primary sorts of equations. linear, cubic, and quadratic equations.

Equation Solving: A General Principle

On each side of the equation, merge like terms and remove parentheses.

You can use either addition or subtraction to separate the variable word.

Use multiplication or division to find the solution for a variable.

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Answer:

Below

Step-by-step explanation:

Her base salary (500) for the week PLUS her comission (.3 * 1575)

   totals 972.50 dollars

The possible locations of point P are  (-7, -1) and (-7, -11)

From the question, we have the following parameters that can be used in our computation:

M = (-7, -6)

Also, we have"

P = 5 units from M

And

P = same x coordinate as point m.

This means that

P = (-7, y)

5 units from (-7, -6) is calculated as

(-7, -6 + 5) and (-7, -6 - 5)

Evaluate

(-7, -1) and (-7, -11)

Hence, the possible location is (-7, -1) and (-7, -11)

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The value of y when x = 45 using the given table is; y = (6/√2) + 4

The equation that represents the table is;

y = a cos x° + b

At x = 0, y = 10. Thus;

10 = acos 0 + b

cos 0 = 1

Thus;

10 = a + b    ------(1)

At x = 60, y = 7

Thus;

7 = a cos 60° + b

cos 60 = 0.5

Thus;

7 = 0.5a + b    -----(2)

Subtract eq 2 from eq 1 to get;

3 = 0.5a

a = 3/0.5

a = 6

b = 10 - 6

b = 4

Thus, the equation is;

y = 6cos x° + 4

At x = 45. we have;

y = 6cos 45° + 4

y = (6/√2) + 4

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Here, we don't know the exact values for the speed or the lap length, so we need to use symbols in the equation  i.e., x= 8 / (5.5  / lap length × speed ).

There are a couple of ways to approach this problem, but one common method is to use the formula: distance = speed x time.

To find the time it took Andre to run each lap, we need to find the distance he covered in 8 minutes and then divide that by the number of laps. Here are the equations:

1. Distance = 5.5 laps x lap length

2. Distance = speed x 8 minutes

3.  x = (5.5 x lap length) / (speed x 8)

4.  x = 8 / (5.5 / lap length x speed)

Note that we don't know the exact values for the speed or the lap length, so we need to use symbols in the equations.

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5x = 60

Let x be the value of 12. Then, 5 times as great as 12 is 5x.

So, the equation can be written as:

5x = 60

To isolate x, we can divide both sides of the equation by 5:

x = 60/5

⬇️

x = 12

At the four corners of an equilateral triangle are three point charges.

Due to the fact that three charges do not cancel one another out with Colombian force, the system can never reach equilibrium.

A subatomic particle's electric charge causes it to experience a force when it is in an electric and magnetic field.

Electric charge is the property of matter that causes it to experience a force when subjected to an electromagnetic field. Protons and electrons most typically carry positive and negative charges, which are the two forms of electric charges. Energy is created by charge movement.

The most frequent charge carriers for positive and negative electric charges, respectively, are protons and electrons. The coulomb (C) is the standard unit of electric charge used by the International System of Units (ISO) (SI).

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Complete question -

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic force are acting

The sum of interior angle in 12-gon is 1800°, in 102-gon is 18000°, in 90-gon is 15840° and 36-gon is 6120° and measure of interior angle in 12-gon is 150°, in 102-gon is 176.5°, in 90-gon is 176° and 36-gon is 170°

A polygon is a two-dimensional geometric shape consisting of straight lines and having three or more sides. The sides of a polygon are line segments that connect its vertices, or corners, and the vertices are where the sides meet. The most common types of polyggon include triangles, squares, rectangles, and hexagons. There are also many types of irregular polygon, which have sides of different lengths or angles, as well as regular polygon, which have equal sides and equal interior angles.

The sum of the interior angles and the measure of the interior angle of a regular polygon can be found using the formula:

Sum of interior angles = (n-2) * 180°

Measure of interior angle = Sum of interior angles / n

Where n is the number of sides of the polygon.

For a 12-gon:

Sum of interior angles = (12-2) * 180° = 1800°

Measure of interior angle = 1800° / 12 = 150°

For a 102-gon:

Sum of interior angles = (102-2) * 180° = 18000°

Measure of interior angle = 18000° / 102 = 176.5°

For a 90-gon:

Sum of interior angles = (90-2) * 180° = 15840°

Measure of interior angle = 15840° / 90 = 176°

For a 36-gon:

Sum of interior angles = (36-2) * 180° = 6120°

Measure of interior angle = 6120° / 36 = 170°

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The value of the composite function f(g(-3) is -32

From the question, we have the following parameters that can be used in our computation:

f(x) = x + 4. q(x) = 12x

The above are individual functions

This means that

f(g(x)) = 12x + 4

For f(g(-3)), we have

f(g(x)) = 12 * -3 + 4

Evaluate

f(g(x)) = -32

Hence, the value of the composite function is -32

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An estimate of the real height of the lamp post is 9m.

The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm

here, we have,

Scale = length of the lamp post / height of the car

10.8 / 1.8 = 6

Now, multiply the scale by the width of the car.

The real height of the lamp post = 6 x 1.5 = 9m

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A car was worth $24,000 two years ago. The automobile is worth $23,160 this year. 3.5% of the value of the car has decreased.

24,000 - 23,160 = 840

840/24,000 = 0.035

Simplifying the above equation, we get,

0.035 = 3.5%

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The length of WY  is 4.9.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

From two triangles the proportional sides are

11.1/5.55=8/4=9.8/WY

2=2=9.8/WY

So 2=9.8/WY

WY=9.8/2

WY=4.9

Hence, the length of WY  is 4.9.

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Answer:

The boat traveling at 30 miles per hour will travel 30 * (2/3600) = 0.05 miles in 2 seconds.

Step-by-step explanation:

Here's a step-by-step explanation to find the distance traveled by the boat in 2 seconds:

Start with the speed of the boat, which is given as 30 miles per hour.

To find the distance traveled in 2 seconds, we need to convert the speed from miles per hour to miles per second.

To convert from miles per hour to miles per second, divide the speed by 3600 (since there are 3600 seconds in an hour).

30 / 3600 = 0.008333333 (miles per second)

Multiply the speed in miles per second by the time in seconds to find the distance traveled.

0.008333333 * 2 = 0.016666666 miles

So the boat will travel 0.016666666 miles in 2 seconds, or approximately 0.05 miles.

The perimeter of the triangle which has a bisector that splits a triangle into 6 sides would be = 47½

A bisector is defined as the line that divides a shape into two equal parts.

The perimeter of triangle is the sum total of all the sides of the triangle. That is;

perimeter = a1 + a2 + b1 + b2 + c1 + c2

But the value of only 3 sides which is exactly half of the perimeter where given;

= 11/3+22/3+153/12

= 44+ 88+ 153/12

= 285/12

Therefore perimeter

= 285/12 + 285/12

= 570/12

= 47½

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The values of x in the equation is x = -2.39 and x = 1.89

From the question, we have the following parameters that can be used in our computation:

2(4x + 8 - x²) = 9x + 7

Open brackets

This gives

8x + 16 - 2x² = 9x + 7

Evaluate the like terms

2x² + x - 9 = 0

Using a graphing calculator, we have the following values

x = -2.386 and x = 1.886

Approximate

x = -2.39 and x = 1.89

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Answer: probably greater than 3 1/2 inches, since bumper stickers are usually wider than they are tall

Step-by-step explanation:

The painting is worth $22,225.62 today.

Compound interest is computed on the principal as well as the interest accumulated over the preceding period. It differs from simple interest in that interest is not added to the principal when computing interest for the next month.

Compound annual growth rate (CAGR) is the average yearly growth rate of an investment over a time period greater than one year. It is one of the most reliable methods for calculating and determining returns for individual assets, investment portfolios, and anything else whose value might grow or decline over time.

The formula to calculate the increase in the value of the painting is:

value_today = value_yesterday * (1 + 0.32)^number_of_years

Plugging in the given values:

value_today = $12,430 * (1 + 0.32)^2 = $12,430 * 1.32^2

= $12,430 * 1.7984

= $22,225.62

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The value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.

The value of the test statistic in this case is the percentage of drivers under the age of 18 who still use a cell phone while driving. The test statistic is calculated using the following formula:

Test Statistic = (Number of Drivers under 18 using Cell Phone)/ (Total Number of Drivers under 18) x 100

For this case, the test statistic is calculated as follows:

Test Statistic = (150/200) x 100 = 75.00

Therefore, the value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.

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The expressions for (h - g)(x) and (h . g)(x) are -x - 8 and  (x - 5)(2x + 3)

While the function (h + g) (-1) is -5

From the question, we have the following parameters that can be used in our computation:

g (x) = 2x+3

h(x) = x - 5

This means that

(h - g)(x) = x - 5 - 2x - 3

Evaluate

(h - g)(x) = -x - 8

Also, we have

(h . g)(x) = (x - 5)(2x + 3)

Lastly, we have

(h + g)(-1) = (x - 5) + (2x + 3)

So, we have the following equation

(h + g)(-1) = ((-1) - 5) + (2(-1) + 3)

Evaluate

(h + g)(-1) = -5

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The quantities that are proportional to 8⁄12 are 24 / 36 and 2 / 3.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the fraction is 8 / 12. The equivalent expression will be calculated as:-

8 / 12 = 2 / 3

16⁄36 = 4 / 9

12⁄16 = 3 / 4

24⁄36 = 2 / 3

2⁄3 = 2 / 3

18⁄24  = 3 / 4

The equivalent expressions will be 8 / 12 = 24 / 36 = 2 / 3.

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Answer: 36.4

Step-by-step explanation:

27.3= (3/4)y

divide both sides by 3/4 to isolate the y

27.3/(3/4)= 36.4

To double-check, plug in 36.4 to y; should get you 27.3

The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.

A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.

Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.

It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.

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