Solve the equation. If the equation is an identity, choose identity. If it has no solution, choose no solution.
4y + 2 =-1/3
(8-12y)

The solution to the equation 1/3|x - 8| = 10 is x = 38

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

1/3|x - 8| = 10

Multiply through by 3

So, we have

|x - 8| = 30

Remove the absolute bracket

So, we have

x - 8 = 30

Add 8 to both sides of the equation

So, we have

x = 38

Hence, the solution to the equation is x = 38

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The system of inequalities for the given situation is x+y≤11 and 2x+4y≥40.

Given that, the cost of each drink = $2 and the cost of each taco = $4.

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

x represents the number of drinks purchased and y represents the number of tacos purchased.

Juan has $40 to spend and must buy a minimum of 11 drinks and tacos altogether.

So inequalities are x+y≤11 and 2x+4y≥40

Therefore, the system of inequalities for the given situation is x+y≤11 and 2x+4y≥40.

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The expression of the mathematical statement given as "Jaun's age, x, is 4 times his age 15 years ago" is x = 4 * (x - 15)

The mathematical statement is given as

Jaun's age, x, is 4 times his age 15 years ago

From the statement, we have:

x represent Juan's current age

This means that his age 15 years ago is

15 years ago = x - 15

4 times his age 15 years ago is

4 * 15 years ago = 4 * (x - 15)

The above equation is equivalent to his current age

So, we have

x = 4 * (x - 15)

Hence, the expression of the mathematical statement given as "Jaun's age, x, is 4 times his age 15 years ago" is x = 4 * (x - 15)

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The slope of line AB with points A(4, 5) and B(9, 7) is 2/5.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

We have,

A(4, 5) and B(9, 7)

The slope of a line with points A and B is given by:

= d - b / c - a

Where A(a, b) and B(c, d) are the coordinates of the points.

We have the points:

A(4, 5) = (a, b)

B(9, 7) = (c, d)

The slope of the line AB:

= (7 - 5) / (9 - 4) = 2 / 5

Therefore the slope of line AB with points A(4, 5) and B(9, 7) is 2/5.

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Answer:

The circumference is 153.93804... or 153.94...

Step-by-step explanation:

Hope it helps! =D

Answer:

153.94 meters.

Step-by-step explanation:

The formula for finding the circumference of a circle is C = πd, where d is the diameter of the circle. With a diameter of 49m, the circumference can be calculated as C = π(49) ≈ 153.94m. Therefore, the circumference of the circle is approximately 153.94 meters.

Using prime factors the root of given variety of 777924 is 882 .

The image of prime factorization of 777924 is given below

By prime factorization of 777924 we have a tendency to follow five easy steps:

1. we have a tendency to write variety 777924 higher than a 2-column table

2. we have a tendency to divide 777924 by the tiniest attainable factor

3. we have a tendency to write down on the left facet of the table the factor and next variety to factorize on the ride facet

4. we have a tendency to still consider this fashion (we subsume odd numbers by making an attempt little prime factors)

5. we have a tendency to continue till we have a tendency to reach one on the ride facet of the table

Prime factorization of 777924 = 1×2×2×3×3×3×3×7×7×7×7

On doing square root , we get

[tex]\sqrt{777924} =\sqrt{ 1\times2\times2\times3\times3\times3\times3\times7\times7\times7\times7}[/tex]

              = 882

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A∩B = {10, 20, 50}

The given two function is

A = { 10, 20, 30, 40, 50, 60}

B = { 10, 20, 50}

We have to find the value of function of A∩B

A∩B means the number which is common in both the function,

The number common in function A and B is 10, 20, 50.

Therefore the function A∩B = {10, 20, 50}

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Answer: None of these

Step-by-step explanation:

First term

[tex]\int 12e^{12t} \text{ } dt=12 \int e^{12t} \text{ } dt=e^{12t}+C[/tex]

Second term

[tex]\int \sqrt[3]{27t} \text{ } dt=3\int t^{1/3} \text{ } dt=\frac{9}{4}\sqrt[3]{t^4}+C[/tex]

Third term

[tex]\int \frac{5}{t} \text{ } dt=5 \int \frac{1}{t} \text{ } dt=5\ln t+C[/tex]

Fourth term

[tex]\int 15 \text{ } dt=15t+C[/tex]

Adding these integrals, we get

[tex]\int g(t) \text{ } dt=e^{12t}+\frac{9}{4}\sqrt[3]{t^4}+5\ln t+15t+C[/tex]

which matches none of the options.

Answer: 6.12315 × 105

Step-by-step explanation: No worry's just here for the fun of it

The garden has a length of 37.5 yards and width of 37.5 yards as well as an opening of 12.5 yards.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width.

150 yards of fencing is available, hence:

2(x + y) = 150

x + y = 75

y = 75 - x     (1)

The area (A) of the garden is given as:

A = xy

A = x(75 - x)

A = 75x - x²

The maximum area is at A' = 0

A' = 75 - 2x

75 - 2x = 0

x = 37.5 yards

y = 75 - x = 75 - 37.5 = 37.5

Opening of the garden = 1/3 * 37.5 = 12.5 yards

The garden has a length of 37.5 yards and width of 37.5 yards as well as an opening of 12.5 yards.

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The base 10 representation of the number 142 base 5 as required to be determined in the task content is; 47.

Since, the conversion of numbers from any base to base 10 requires imaginary exponents to represent place value in such number as follows;

142₅ can therefore be written as follows; 1²4¹2⁰₅.

On this note the evaluation is carried out by summing the product of each digits and 5 to the corresponding power as follows;

1²4¹2⁰₅ = (2 × 5⁰) + (4 × 5¹) + (1 × 5²)

= (2 × 1) + (4 × 5) + (1 × 25)

= 2 + 20 + 25.

= 45.

Ultimately, the base 10 representation of the number 142 base 5 as required to be determined in the task content is; 47.

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The dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.

She wants to buy a rug for a room that is 25 ft wide and 33 ft long.

She wants  to leave a uniform strip of floor around the rug.

she can afford to buy 513 square feet of carpeting.

Cynthia room area = lw

where

Therefore,

Cynthia room area = 25 × 33

Cynthia room area = 825 ft²

She wants to leave a uniform strip of floor all around the rug and has affordability to buy 513 square feet of carpet.

Therefore, the dimension the rug should have is as follows:

(25 - 6) (33 - 6) = 513

19 × 27 = 513 ft²

Therefore, the dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.

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Answer:

The probability of rolling a 2 the next time that same die is rolled is 0.167.

Step-by-step explanation:

In this question it is given that there is rolling dice that is six sided and which is rolled for a 100 times and it was further observed that the probability of rolling a 2 was 12%.

Firstly, let us understand what is probability;

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

Now,

Let us understand the concept of impossibility and certainty of an event;

An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Further, In the above-mentioned condition, it is observed that the die has been rolled a 100 times;

The probability of getting X is only 12%.

Now,

In the condition where the die is rolled in for an extra time being a six sided, the probability of getting a 2 is 1/6.

=> 1/6

=> 0.167

Therefore, the probability of rolling a 2 the next time that same die is rolled is 0.167.

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In the differential equation

[tex]\dfrac{dy}{dx} + 12y = \cos\left(\dfrac{\pi x}{12}\right)[/tex]

multiply on both sides by the integrating factor

[tex]\mu = \exp\left(\displaystyle\int12\,dx\right) = e^{12x}[/tex]

Then the left side condenses to the derivative of a product.

[tex]e^{12x} \dfrac{dy}{dx} + 12 e^{12x} y = e^{12x} \cos\left(\dfrac{\pi x}{12}\right)[/tex]

[tex]\dfrac{d}{dx}\left[e^{12x}y\right] = e^{12x}\cos\left(\dfrac{\pi x}{12}\right)[/tex]

Integrate both sides with respect to [tex]x[/tex], and use the initial condition [tex]y(0)=0[/tex] to solve for the constant [tex]C[/tex].

[tex]\displaystyle \int \frac{d}{dx} \left[e^{12x}y\right] \, dx = \int e^{12x} \cos\left(\dfrac{\pi x}{12}\right) \, dx[/tex]

As an alternative to integration by parts, recall

[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]

Now

[tex]e^{12x} \cos\left(\dfrac{\pi x}{12}\right) = e^{12x} \mathrm{Re}\left(e^{i\pi x/12}\right) = \mathrm{Re}\left(e^{(12+i\pi/12)x}\right)[/tex]

[tex]\displaystyle \int \mathrm{Re}\left(e^{(12+i\pi/12)x}\right) \, dx = \mathrm{Re}\left(\int e^{(12+i\pi/12)x} \, dx\right)[/tex]

[tex]\displaystyle. ~~~~~~~~ = \mathrm{Re}\left(\frac1{12+i\frac\pi{12}} e^{(12+i\pi/12)x}\right) + C[/tex]

[tex]\displaystyle. ~~~~~~~~ = \mathrm{Re}\left(\frac{12 - i\frac\pi{12}}{12^2 + \frac{\pi^2}{12^2}} e^{12x} \left(\cos\left(\frac{\pi x}{12}\right) + i \sin\left(\frac{\pi x}{12}\right)\right)\right) + C[/tex]

[tex]\displaystyle. ~~~~~~~~ = \frac{12}{12^2 + \frac{\pi^2}{12^2}} e^{12x} \cos\left(\frac{\pi x}{12}\right) + \frac\pi{12} e^{12x} \sin\left(\frac{\pi x}{12}\right) + C[/tex]

[tex]\displaystyle. ~~~~~~~~ = \frac1{12(12^4+\pi^2)} e^{12x} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) + C[/tex]

Solve for [tex]y[/tex].

[tex]\displaystyle e^{12x} y = \frac1{12(12^4+\pi^2)} e^{12x} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) + C[/tex]

[tex]\displaystyle y = \frac1{12(12^4+\pi^2)} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) + C[/tex]

Solve for [tex]C[/tex].

[tex]y(0)=0 \implies 0 = \dfrac1{12(12^4+\pi^2)} \left(12^4 + 0\right) + C \implies C = -\dfrac{12^3}{12^4+\pi^2}[/tex]

So, the particular solution to the initial value problem is

[tex]\displaystyle y = \frac1{12(12^4+\pi^2)} \left(12^4 \cos\left(\frac{\pi x}{12}\right) + \pi (12^4+\pi^2) \sin\left(\frac{\pi x}{12}\right)\right) - \frac{12^3}{12^4+\pi^2}[/tex]

Recall that

[tex]R\cos(\alpha-\beta) = R\cos(\alpha)\cos(\beta) + R\sin(\alpha)\sin(\beta)[/tex]

Let [tex]\alpha=\frac{\pi x}{12}[/tex]. Then

[tex]\begin{cases} R\cos(\beta) = 12^4 \\ R\sin(\beta) = 12^4\pi+\pi^3 \end{cases} \\\\ \implies \begin{cases} (R\cos(\beta))^2 + (R\sin(\beta))^2 = R^2 = 12^8 + (12^4\pi + \pi^3)^2 \\ \frac{R\sin(\beta)}{R\cos(\beta)}=\tan(\beta)=\pi+\frac{\pi^3}{12^4}\end{cases}[/tex]

Whatever [tex]R[/tex] and [tex]\beta[/tex] may actually be, the point here is that we can condense [tex]y[/tex] into a single cosine expression, so choice (D) is correct, since [tex]\cos(x)[/tex] is periodic. This also means choice (C) is also correct, since [tex]\beta=\cos(x)\implies\beta=\cos(x+2n\pi)[/tex] for infinitely many integers [tex]n[/tex]. This simultaneously eliminates (A) and (B).

Answer:

2

Step-by-step explanation:

The graph looks to be like a parabola. Due to the end behaviour of the graph (Up in both quadrants 1 and 2) it can be said that the graph has a positive leading coefficient.

Hope that helps

Step-by-step explanation:

So, the expression “three times the variable x” can be written in a number of ways: 3x, 3(x), or 3 · x. Use the distributive property to expand the expression 9(4 + x).

Answer:Domar range x

Step-by-step explanation:

Based on the graph, which statement could describe Janelle’s trip home from school is that D. Janelle rode the bus to the bus stop, talked with a friend, and then walked home.

It should be noted that a graph is a diagram that is used to represent a system of connections or interrelations that is among two or more things by a number of distinctive dots, bars, etc

Therefore, based on the graph, which statement could describe Janelle’s trip home from school is that Janelle rode the bus to the bus stop, talked with a friend, and then walked home.

In conclusion, the correct option is D.

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Based on the graph, which statement could describe Janelle's trip home from school?

Janelle waited for the bus, rode the bus, and then walked home.

Janelle walked the opposite direction from home to the library, rode the bus, and then walked to a friend's house.

Janelle walked home at a constant speed.

Janelle rode the bus to the bus stop, talked with a friend, and then walked home

The greatest number of binders Eula can buy is 5

The greatest number of notebooks Eula can buy is 10

The greatest number of binders she can buy  if Eula buys 7 notebooks is 3/2

It is an order relationship that is greater than, greater than, or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

We have,

4x + 2y ≤ 20

x = number of binders

y = number of notebooks

The greatest number of binders Eula can buy:

Put y = 0.

4x + 2 x 0 ≤ 20

4x ≤ 20

x ≤ 20/4

x ≤ 5

The greatest number of notebooks Eula can buy:

Put x = 0.

4x + 2y ≤ 20

4 x 0 + 2y ≤ 20

2y ≤ 20

y ≤ 10

Eula buys 7 notebooks then, the greatest number of binders she can buy:

4x + 2y ≤ 20

4x + 2 x 7 ≤ 20

4x + 14 ≤ 20

4x ≤ 20 - 14

4x ≤ 6

x ≤ 6/4

x ≤ 3/2

Thus,

The greatest number of binders Eula can buy is 5

The greatest number of notebooks Eula can buy is 10

The greatest number of binders she can buy  if Eula buys 7 notebooks is 3/2

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Answer:

Eula needs to buy binders that cost $4 each and notebooks that cost $2 each. She has $20. The graph of the inequality 4x + 2y ≤ 20, which represents the situation, is shown.What is the greatest number of binders Eula can buy? What is the greatest number of notebooks Eula can buy? If Eula buys 7 notebooks, what is the greatest number of binders she can buy?  ⇒ 1

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Hey, could you perhaps provide a little bit more info regarding what method/topic/skill you are required to use in order to solve the following? Also, are these three different expressions, or are they a part of the same question. Thanks!

The ratio of high school students who are in a music class to students who are not is 9 : 41.

So, 18% of high school students are in a music class which means the rest 82% are not in a music class.

Then the ratio:

Simplest form:

Therefore, the ratio is 9 : 41.

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Answer:

Step-by-step explanation:

According to the question, the cupcake cafe makes 1/2 times as much revenue on doughnuts as muffins and the total revenue is total sales were $44,000. Let us assume that the revenue on muffins is X and then the revenue on doughnuts is 412X. 4 1 2 X . The amount of money earned from muffins is 20000 dollars

The length and width of the yard with perimeter of 400 feet are 136 ft and 64 ft respectively.

The yard has a perimeter of 400 feet.

Eight times the length of the yard equals seventeen times the width.

Therefore,

perimeter of a rectangular yard = 2(l + w)

where

Therefore,

8l = 17w

Hence,

l = 17 / 8 w

perimeter of a rectangular yard = 2(17 / 8 w + w)

perimeter of a rectangular yard = 2( 25  /8 w)

perimeter of a rectangular yard = 50/ 8 w

400 = 50 / 8 w

cross multiply

3200 = 50w

divide both sides by 50

w = 3200 / 50

w = 64 ft

l = 17 / 8 × 64 = 136 ft

Therefore, the length and width of the yard with perimeter of 400 feet are 136 ft and 64 ft respectively.

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Answer:

8/3

Step-by-step explanation:

[tex]g^2 (x)=\frac{2\left(\frac{2x}{x-2} \right)}{\frac{2x}{x-2}-2} \\ \\ =\frac{4x}{2x-2(x-2)} \\ \\ =\frac{4x}{4} \\ \\ =x[/tex]

From this, we can see that g(x) is its own inverse. Thus, [tex]g^{13}(x)=g(x)[/tex]

So,

[tex]g^{13}(8)=\frac{2(8)}{8-2}=8/3[/tex]

Explanation:

"given it is an even number" tells us that the outcomes could be anything from this set {2,4,6}. We ignore the odd numbers entirely.

We have one copy of "6" out of three total items.

Therefore, we end up with a probability of 1/3

This is approximately equal to the decimal form 0.333 and the percent form 33.3%

I would stick to the fraction form since it's most exact. However, if your teacher instructs otherwise then be sure to follow said instructions of course.

Step-by-step explanation:

The mean of a set of numbers is the average of those numbers. You can find the mean by adding the set of numbers and dividing by how many numbers are given. If you are given the mean and asked to find a missing number from the set, use a simple equation.

Add up the numbers you know. The problem states a mean of 58 with this set of numbers: 43, 57, 63, 52 and x. Assign the missing number a value of “x.” So add 43, 57, 63 and 52 to get 215.

Set up your equation by adding 215 plus “x” (the missing number), divided by 5, the number of values given. Set that side of the equation equal to the mean, 58. So, your equation would look like this: [tex] \frac{215+x}{5} = 58 [/tex]

Multiply each side by 5 since our goal is to get “x” by itself. This process cancels the 5 on the left side of the equation and gives you 290 on the right side (58 × 5). Now, your equation should look like this: [tex] 215+x=290 [/tex]

Subtract 215 from each side as you continue to work to get “x” alone. This cancels out the 215 on the left side of the equation and gives you 75 on the right side. Now, your equation should show that x = 75. Therefore, the missing number is 75.

Check the missing number by adding all the numbers together and dividing by 5.

[tex] \frac{43+57+63+52+75}{5} = \frac{290}{5} = 58 [/tex]

Step-by-step explanation:

We have,

[tex]\begin{gathered} \bullet \: \bold{ - \dfrac{\pi}{4} < \beta < 0 < \alpha < \dfrac{\pi}{4} } \\ \\ \implies \: - \dfrac{\pi}{4} < \alpha + \beta < \dfrac{\pi}{4} \end{gathered}[/tex]

[tex]\begin{gathered} \rm\bullet \: \: \: \sin( \alpha + \beta ) = \dfrac{1}{3} \: \: \: \: \: and \: \: \: \: \: \cos( \alpha - \beta ) = \dfrac{2}{3} \\ \end{gathered} [/tex]

Now,

[tex]\begin{gathered} y= \bigg( \dfrac{ \sin( \alpha ) }{ \cos( \beta ) } + \dfrac{ \cos( \beta ) }{ \sin( \alpha ) } + \dfrac{ \cos( \alpha ) }{ \sin( \beta ) } + \dfrac{ \sin( \beta ) }{ \cos( \alpha ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \bigg( \dfrac{ \sin( \alpha ) }{ \cos( \beta ) } + \dfrac{ \sin( \beta ) }{ \cos( \alpha ) } + \dfrac{ \cos( \beta ) }{ \sin( \alpha ) } + \dfrac{ \cos( \alpha ) }{ \sin( \beta ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \bigg( \dfrac{ \sin( \alpha ) \cos( \alpha ) + \sin( \beta \cos( \beta ) ) }{ \cos( \beta ) \cos( \alpha) } + \dfrac{ \sin( \alpha) \cos( \alpha ) + \sin( \beta ) \cos( \beta ) }{ \sin( \alpha ) \sin( \beta ) } \bigg)^{2} \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \bigg( \dfrac{ \sin( \alpha + \beta ) }{ \cos( \beta ) \cos( \alpha) } + \dfrac{ \sin( \alpha + \beta ) }{ \sin( \alpha ) \sin( \beta ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \sin^{2} ( \alpha + \beta ) \bigg( \dfrac{ 1 }{ \cos( \beta ) \cos( \alpha) } + \dfrac{ 1 }{ \sin( \alpha ) \sin( \beta ) } \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \sin^{2} ( \alpha + \beta ) \bigg( \dfrac{\cos( \beta ) \cos( \alpha) + \sin( \alpha ) \sin( \beta ) }{ \cos( \beta ) \cos( \alpha) \sin( \alpha ) \sin( \beta )} \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \sin^{2} ( \alpha + \beta ) \bigg( \dfrac{\cos( \alpha - \beta ) }{ \cos( \beta ) \cos( \alpha) \sin( \alpha ) \sin( \beta )} \bigg)^{2} \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{2\cos( \alpha ) \cos( \beta ) \cdot 2\sin( \alpha ) \sin( \beta ) \right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{\cos( \alpha + \beta ) + \cos( \alpha + \beta ) \right \} ^{2} \left \{ \cos( \alpha - \beta ) - \cos( \alpha + \beta ) \right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{ \cos^{2} ( \alpha - \beta ) - \cos^{2} ( \alpha + \beta ) \right \}^{2} } \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \dfrac{4\sin^{2} ( \alpha + \beta ) \cdot\cos^{2} ( \alpha - \beta ) }{ \left \{ \cos^{2} ( \alpha - \beta ) - 1 + \sin^{2} ( \alpha + \beta ) \right \}^{2} } \\\end{gathered}[/tex]

Putting the values given above, we get,

[tex]\begin{gathered} \implies y= \dfrac{4 \cdot \dfrac{1}{9} \cdot\dfrac{4}{9} }{ \left \{ \dfrac{4}{9} - 1 + \dfrac{1}{9} \right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \left \{ \dfrac{5}{9} - 1\right \}^{2} } \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \left \{ \dfrac{5 - 9}{9}\right \}^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \left \{ \dfrac{- 4}{9}\right \}^{2} } \\\end{gathered}[/tex]

[tex]\begin{gathered} \implies y= \dfrac{\dfrac{16}{81} }{ \dfrac{16}{81}} \\\end{gathered} [/tex]

[tex]⟹y=1[/tex]

Answer:

138cm^2

Step-by-step explanation:

Trianle area = (b*h)/2

b = 8cm + 15cm

h = 6cm

Triangle area = (23*6)/2

138/2 = 69cm^2

Upper triangle area

--------------------------------

since both triangles share the same base and height

69*2 = 138cm^2

Answer:

The reference angle is π/6.

Cosine is -(√3)/2.

Step-by-step explanation:

To find the reference angle, find the acute angle in quadrant I and use it as a reference for the given expression.

For the cosine, the cosine is the sine of the complementary angle. The complementary angle is the given angle beside it minus a right angle, which is exactly 90 degrees. If the angle is 25 degrees, its complementary angle will be double its amount, 50 degrees. Then, for angle angle measured "theta", the cosine is equal to the sine's right-angle subtracted by theta.