Find the absolute extrema if they exist, as well as all values of where they occur, for the function f(x) = 8+x/2-x on the domain [-2, 0]
Find the derivative of f(x) = 8+x/2-x
f'(x) = ...

Answer:

y = 11x/13 + 36/13

Step-by-step explanation:

We can write the line using y = mx + b form.

To find the slope, m, we can use the formula (y1 - y2) / (x1 - x2):

(7-(-4)) / (5-(-8)) = (7+4) / (5+8) = 11 / 13.

To find b, we can plug in one of the points. Lets use (5, 7).

y = 11/13 * x + b

7 = 11/13 * 5 + b

7 - 55/13 = b

b = 91/13 - 55/13 = (91-55)/13 = 36/13.

Your equation is:

y = 11x/13 + 36/13.

Answer: y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]

Step-by-step explanation:

First, we will find the slope.

       [tex]m=\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-4-7}{-8-5} =\frac{-11}{-13} =\frac{11}{13}[/tex]

Next, we will substitute this slope and a given point in and solve for our y-intercept (b).

       y = [tex]\frac{11}{13}[/tex]x + b

       (7) = [tex]\frac{11}{13}[/tex](5) + b

       (7) = [tex]\frac{11}{13}[/tex](5) + b

       7 = [tex]\frac{55}{13}[/tex] + b

       b = 7 - [tex]\frac{55}{13}[/tex]

       b = [tex]\frac{36}{13}[/tex]

Final equation:

       y = mx + b

     y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]

The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.

Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".

We can write the equation:
[tex]CP \times  (1 - loss% ) = selling price (SP)[/tex]
[tex]CP \times  (1 - 0.28) = 1440[/tex]
Solve for CP
[tex]CP \times 0.72 = 1440[/tex]
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.

We can write the equation:
[tex](SP_{new - CP)} / CP \times  100 = profit[/tex]
[tex](2100 - 2000) / 2000 \times  100 = profit%[/tex]
[tex]100 / 2000 \times  100 = profit%[/tex]
5% = profit%.

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Answer:

147 mm^2

Step-by-step explanation: The surface area has to be more, but not double the smaller figures surface area therefore the answer is 147 mm^2

The requried surface area of the larger solid is approximately 147 mm². Option A is correct.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Let's call the larger solid's surface area S.

Since the two solids are similar, their volumes have a ratio of (side length)³. Let's call the ratio of the side lengths of the larger to the smaller solid as k. Then:

[tex](k^3)(540 mm^3) = 857.5 mm^3[/tex]

Simplifying the above equation, we get:

[tex]k = (857.5/540)^{(1/3)}[/tex] =7/6

So, the larger solid is about 7/6=1.183 times bigger than the smaller solid in terms of side length. Since the surface area has a ratio of [tex](side length)^2[/tex], we can find the surface area of the larger solid by:

[tex]S = (1.183^2)(108 mm^2) \approx 147 mm^2[/tex]

Therefore, the surface area of the larger solid is approximately 147 mm². Answer: A.

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This function is an example of exponential decay because the base of the exponential term (2/7) is between 0 and 1. and the y-intercept is 8.

To find the y-intercept, we need to evaluate the function when x=0, which gives:

y = 8 (2/7)^0 = 8

The given function is an example of exponential decay. In an exponential function, if the base of the exponent is between 0 and 1, the function shows exponential decay, and if it is greater than 1, the function shows exponential growth.

In the given function y = 8 (2/7)^x, the base of the exponent is 2/7, which is less than 1. This means that as the value of x increases, the value of the function decreases at a decreasing rate, which is the characteristic of exponential decay.

To find the y-intercept of the function, we can substitute x=0 in the given function. When x=0, we have:

y = 8 (2/7)^0

y = 8 x 1

y = 8

This means that the y-intercept of the function is (0, 8), which is the point where the function intersects the y-axis. In this case, it represents the initial value of the function when x=0.

Therefore, This function is an example of exponential decay because the base of the exponential term (2/7) is between 0 and 1. and the y-intercept is 8.

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Therefore , the solution of the given problem of equation comes out to be  x must be less than -5 for any value of x that causes 5 + x = n to be a negative number.

In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.

Here,

If n is a negative number and 5 + x = n, then x must be less than -5.

This is due to the fact that n would be greater than or equal to 5, which is not a negative number, if x were greater than or equal to -5, which would lead 5 + x to be greater than or equal to 0.

However,

if x is less than -5, then 5 + x will be less than 0, and n will be a negative number because n will be less than 5.

Therefore, x must be less than -5 for any value of x that causes 5 + x = n to be a negative number.

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The problem involves analyzing the cost of production for a company that produces a certain quantity of units. Specifically, we are given the marginal cost function C'(q) = q^2 - 17q + 70, where q is the quantity produced, and we need to find the total cost of producing 20 units, as well as the fixed cost and variable cost for this quantity. To find the total cost, we need to integrate the marginal cost function from 0 to 20, which will give us the total variable cost. We can then find the fixed cost by subtracting the total variable cost from the initial cost C(0), which is given in the problem. Cost analysis is an important concept in economics and business, and is used to optimize production and pricing decisions for companies. Understanding the relationship between marginal cost, fixed cost, and variable cost is crucial for making informed decisions about production and pricing strategies.

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The marginal cost function for a company is given by C'(q) = [tex]q^2[/tex] - 17q + 70 dollars/unit; where q is the quantity produced. If C(0) = 650, then total cost of producing 20 units = 2,600 dollars. Fixed cost for the quantity = 650 dollars. Variable Cost of producing 20 units = 1,950 dollars

To find the total cost function C(q), integrate the marginal cost function C'(q):

C(q) = ∫[tex](q^2 - 17q + 70)[/tex] dq = [tex](1/3)q^3 - (17/2)q^2 + 70q + K[/tex]

To find the constant K, use the given information: C(0) = 650

650 = [tex](1/3)(0)^3 - (17/2)(0)^2 + 70(0) + K[/tex]
K = 650

So the total cost function is:

C(q) = [tex](1/3)q^3 - (17/2)q^2 + 70q + 650[/tex]

Now, we find the total cost of producing 20 units:

C(20) = [tex](1/3)(20)^3 - (17/2)(20)^2 + 70(20) + 650[/tex]
C(20) = 2,600

Total cost of producing 20 units = 2,600 dollars.

Fixed cost is the cost incurred when producing 0 units, which is given as C(0) = 650 dollars.

To find the total variable cost for producing 20 units, subtract the fixed cost from the total cost:

Variable Cost = Total Cost - Fixed Cost
Variable Cost = 2,600 - 650
Variable Cost = 1,950 dollars

To summarize:
Fixed cost = 650 dollars
Variable cost of producing 20 units = 1,950 dollars
Total cost of producing 20 units = 2,600 dollars

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The expression for the length of one side of the square is: 5x + 8.

To see why, note that the area of a square is given by side squared, so we can set up an equation:

[tex]side^2 = 25x^2 + 80x + 64[/tex]

Taking the square root of both sides, we get:

[tex]side =[/tex] √ [tex](25x^2 + 80x + 64)[/tex]

Simplifying the square root, we get:

side = √[(5x + 8)(5x + 8)]

And finally, we can take the square root of the perfect square to get:

side = 5x + 8.

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Using boosting with 1,000 trees on the Hitters data set, after removing observations with unknown salary information and log-transforming salaries, results in a test set MSE (Mean Squared Error) value.


1. Remove observations with unknown salary information from the Hitters data set.
2. Log-transform the remaining salaries.
3. Create a training set with the first 200 observations and a test set with the remaining observations.
4. Apply the boosting algorithm on the training set, using 1,000 trees as the parameter.
5. Evaluate the performance of the boosting model on the test set by calculating the Mean Squared Error (MSE). The test set MSE will give you an indication of the model's accuracy in predicting salary based on the provided data.

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The volume of the container is  2216 liters

Using the general gas law, we have that;

PV = nRT

Such that the parameters are given as;

From the information given, we have that;

Substitute the values

3V = 4 × 8.31 × 200

Multiply the values, we have;

3V = 6648

Divide both sides by the coefficient of V, we get;

V = 2216 liters

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,Based on the information, we need to consider 5 terms in the series for the sum to exceed 1507.

Substituting the given values, we get:

1507 < -3(1 - (-4)^n)/(1 - (-4))

Simplifying this inequality, we get:

-4^n < 502

Taking the logarithm of both sides, we get:

n*log(4) > log(502)

n > log(502)/log(4)

n > 4.29

n = 5

Therefore, we need to consider 5 terms in the series for the sum to exceed 1507.

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If 5 out of every 24 players were repaired during the first year of ownership, then 200 of the 960 DVD players were repaired in the first year.

Based on the manufacturer's records, we know that 5 out of every 24 players were repaired in the first year of ownership. To find out how many out of the 960 DVD players were repaired in the first year, we can set up a proportion:

5/24 = x/960

To solve for x, we can cross-multiply:

5 * 960 = 24x

4800 = 24x

x = 200

Therefore, 200 of the 960 DVD players were repaired in the first year, which is approximately 20.8% of the total shipped.

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The money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

The money multiplier represents the amount of money the banking system can create through the lending process for every dollar of reserves held by the central bank. It is inversely related to the reserve requirement, which is the percentage of deposits that banks are required to hold as reserves.

When the reserve requirement is low, su

The money multiplier is given by the formula:

Money multiplier = 1 / Reserve requirement

(a) When the reserve requirement is 0.040, the money multiplier is:

Money multiplier = 1 / 0.040 = 25.000

(b) When the reserve requirement is 0.125, the money multiplier is:

Money multiplier = 1 / 0.125 = 8.000

(c) When the reserve requirement is 0.400, the money multiplier is:

Money multiplier = 1 / 0.400 = 2.500

(d) When the reserve requirement is 0.200, the money multiplier is:

Money multiplier = 1 / 0.200 = 5.000

Therefore, the money multipliers are:

(a) 25.000

(b) 8.000

(c) 2.500

(d) 5.000

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Answer:

B

Step-by-step explanation:

using the diamond factoring method:

2x^2-12x+x-6

2x(x-6) + (x-6)

(2x+1)(x-6)

B

Gabriela will use 1620 square inches of wood to build the open box.

The amount of wood Gabriela will use depends on the surface area of the box, which is the sum of the areas of its six faces. Since the box is open on top, it will have five faces: four sides and a bottom.

The area of the bottom is the area of a rectangle with length 18 in. and width 15 in., which is:

Area of bottom = length x width = 18 in. x 15 in. = 270 in²

The area of each side is the product of the height and the length of the corresponding base, which is:

Area of each side = height x length = 15 in. x 18 in. = 270 in²

So the total surface area of the box is:

Total surface area = 2 x (Area of bottom) + 4 x (Area of each side)

= 2 x 270 in² + 4 x 270 in²

= 1620 in²

Therefore, Gabriela will use 1620 square inches of wood to build the open box.

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A reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.

To determine a reasonable estimate for the amount of flour and sugar combined, we first need to add the fractions 1/4 and 2/9. To do this, we need to find a common denominator. The least common multiple of 4 and 9 is 36. We can convert 1/4 to 9/36 by multiplying both the numerator and denominator by 9. We can also convert 2/9 to 4/36 by multiplying both the numerator and denominator by 4. Now we can add the fractions:

9/36 + 4/36 = 13/36

So Ellen mixed 13/36 kg of flour and sugar combined. To convert this to a decimal, we can divide the numerator by the denominator:

13 ÷ 36 ≈ 0.36

Therefore, a reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.

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Answer: Apartment

Confidence

Cooperating

Disrespect

Encode

Forearm

Injustice

Intercontinental

Interplanetary

Mold

Overgrown

Refuel

Repaid

Semi-Sweet

Semicircular

Shield

Subzero

Supermarket

Transportation

Unbelievably

Step-by-step explanation:

Answer:

15

13

6

11

7

1

4

12

17

16

10

8

9

19

3

18

2

5

14

20

There were initially 8 people on Team One.

Let's assume the number of people on Team Two to be "x". According to the given condition, the number of people on Team One is one-quarter of Team Two. Therefore, the number of people on Team One is x/4.

Now, 12 people are transferred from Team Two to Team One. So, the new number of people on Team Two is x-12, and the new number of people on Team One is x/4+12.

As per the given condition, the new number of people on each team is equal. So, we can write the following equation:

x/4+12 = x-12

Solving this equation, we get:

3x/4 = 24

x = 32

So, the initial number of people on Team One is x/4, which is:

32/4 = 8

Therefore, there were initially 8 people on Team One.

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For the given vectors u and v, (a) 6u =  (24, 30). (b) 6u+4v =  (40, 30).      (c) v-4u =  (-12, -20).

Given vectors u and v.

a) To find 6u, we simply multiply each component of u by 6:

6u = 6(4, 5) = (6(4), 6(5)) = (24, 30)

Therefore, 6u = (24, 30).

b) To find 6u + 4v, we first need to find 4v by multiplying each component of v by 4:

4v = 4(4, 0) = (4(4), 4(0)) = (16, 0)

Next, we add 6u and 4v by adding the corresponding components:

6u + 4v = (24, 30) + (16, 0) = (24+16, 30+0) = (40, 30)

Therefore, 6u + 4v = (40, 30).

c) To find v - 4u, we first need to find 4u by multiplying each component of u by 4:

4u = 4(4, 5) = (4(4), 4(5)) = (16, 20)

Next, we subtract 4u from v by subtracting the corresponding components:

v - 4u = (4, 0) - (16, 20) = (4-16, 0-20) = (-12, -20)

Therefore, v - 4u = (-12, -20).

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Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.

First, we calculate the down payment:
10% of $25,625 = $2,562.50

Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50

Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69

Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82

So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82

Rounded to the nearest cent, the answer is option D: $27,735.14.

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We can follow the following strategies separated by comma's : Use implicit differentiation directly on the given equation, Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation
, Solve for y, then differentiate.

Strategy 1: Use implicit differentiation directly on the given equation Start by taking the derivative of both sides of the equation with respect to x:  dy/dx = (3x^2 + 2xy)/(2y - 3) . Now solve for 3r:
3r = (dy/dx)(2y - 3)/(2x)

3r = (3x^2 + 2xy)/(4x)

3r = (3/4)x + (1/2)y

Strategy 2: Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation
Start by multiplying both sides of the equation by (2y - 3):  (2y - 3)y = 3x^2 + 2xy . Simplify:
2y^2 - 3y = 3x^2 + 2xy

Now take the derivative of both sides with respect to x:

d/dx(2y^2 - 3y) = d/dx(3x^2 + 2xy)

4y(dy/dx) - 3(dy/dx) = 6x + 2y(dy/dx)

Solve for dy/dx:

dy/dx = (6x - 3y)/(2y - 4y) = (3x - y)/(y - 2)

Now solve for 3r:

3r = (dy/dx)(2y - 3)/(2x)

3r = ((3x - y)/(y - 2))(2y - 3)/(2x)

3r = (3/4)x + (1/2)y

Strategy 3: Solve for y, then differentiate Start by solving the given equation for y:  2y^2 - 3y = 3x^2 + 2xy
2y^2 - 2xy - 3y - 3x^2 = 0

Use the quadratic formula:

y = (2x ± sqrt(4x^2 + 24x^2))/4

Simplify:

y = (x ± sqrt(7)x)/2

Now take the derivative of y with respect to x:

dy/dx = (1 ± (1/2)sqrt(7))/(2)

Solve for 3r:

3r = (dy/dx)(2y - 3)/(2x)

3r = ((1 ± (1/2)sqrt(7))/(2))(2(x ± sqrt(7)x)/2 - 3)/(2x)

3r = (3/4)x + (1/2)y

All three strategies result in the same answer for 3r in terms of x and y, which is (3/4)x + (1/2)y. This can be shown by simplifying the expressions obtained in each strategy and verifying that they are equivalent. Unfortunately, we cannot proceed with the explanation as the given equation is missing from the student question. Please provide the equation involving x, y, and r to receive a detailed step-by-step explanation of the three strategies.

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Grass Seed Area = L - 20 1/8

To help Warren determine the area of his lawn where grass seed is needed, we first need to know the total area of his lawn.

Unfortunately, you have not provided the dimensions of the entire lawn. However, I can guide you through the process using the information given about the pool.

First, let's find the area of the pool. The dimensions are 5 3/4m by 3 1/2m. To find the area, multiply the length by the width:
Area = (5 3/4) * (3 1/2)
Convert the mixed numbers to improper fractions:
Area = (23/4) * (7/2)
Multiply the fractions:
Area = (23*7) / (4*2) = 161/8

Now convert the improper fraction back to a mixed number:
Area = 20 1/8 square meters
This is the area of the pool. To find the area where grass seed is needed, subtract the pool's area from the total area of the lawn. Assuming the total area of the lawn is "L" square meters, the area to be covered with grass seed would be:
Grass Seed Area = L - 20 1/8

Once you provide the dimensions of the entire lawn, you can follow these steps to find the area where grass seed is needed.

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The second hand of a clock rotates once around the clock face in 60 seconds or one minute. Therefore, in 4 minutes, the second hand will rotate 4 times around the clock face.

The length of the second hand of a clock is 8 cm. The distance traveled by the top of the second hand in one full rotation is equal to the circumference of a circle with radius 8 cm, which is 2πr = 2π(8) = 16π cm.

The distance traveled by the top of the second hand in 4 rotations (or 4 minutes) is:

4 rotations * 16π cm/rotation = 64π cm

So the distance traveled by the top of the second hand of a clock in 4 minutes if the hand is 8 cm long is approximately 64π cm or about 201.06 cm (when rounded to two decimal places).

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Answer:

Step-by-step explanation:

To test if there exists a significant decrease in the popularity vote percentage of the politician, we can conduct a hypothesis test using the significance level of 0.10.

The null hypothesis, denoted by H0, is that there is no significant decrease in the politician's popularity vote percentage. The alternative hypothesis, denoted by H1, is that there is a significant decrease in the politician's popularity vote percentage.

We can use the sample proportion of supporters, which is 405/820 = 0.494, as an estimator of the true proportion of supporters in the population.

Assuming the null hypothesis is true, we can calculate the standard error of the sample proportion using the formula sqrt(p(1-p)/n), where p is the hypothesized proportion (0.55) and n is the sample size (820). This gives us a standard error of sqrt(0.55*0.45/820) = 0.024.

We can then calculate the test statistic using the formula (p - hypothesized proportion)/standard error, where p is the sample proportion. This gives us a test statistic of (0.494 - 0.55)/0.024 = -2.333.

With a significance level of 0.10 and a two-tailed test, the critical values for the test statistic are -1.645 and 1.645. Since the calculated test statistic (-2.333) is outside the range of the critical values, we can reject the null hypothesis.

Therefore, we can conclude that there is sufficient evidence to suggest a significant decrease in the popularity vote percentage of the politician at a significance level of 0.10.

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Answer:

0.8660

Step-by-step explanation:

sin24=opposite ÷hypotenus

sin24=opposite ÷5

cross multiply

sin24x5=opposite

sin24=0.4067x5

opposite =0.8660

The LHS is equal to the RHS, and the given equation is verified as an identity. We have to verify that the following equation is an identity:

2cos(x) 2x / sin2(x) = cot(x) - tan(x)

Starting from the left-hand side (LHS):

2cos(x) 2x / sin2(x) = 2cos(x) 2x / (1 - cos2(x)) (using the identity sin2(x) = 1 - cos2(x))

= 2cos(x) 2x / (1 - cos(x)) (1 + cos(x))

= 2cos(x) 2x / (1 - cos(x)) (1 + cos(x)) (multiplying the denominator by (1 + cos(x)))

= 2cos(x) 2x / (1 - cos2(x))

= 2cos(x) 2x / sin2(x) (using the identity 1 - cos2(x) = sin2(x))

= 2cos(x) / sin(x) (simplifying by canceling out the common factor of 2 and cos(x))

= 2cos(x) / sin(x) * (cos(x) / cos(x)) (multiplying by 1 in the form of cos(x)/cos(x))

= 2cos2(x) / (sin(x)cos(x))

= 2cos(x)/sin(x) * cos(x)

= cot(x) * cos(x)

Now, moving to the right-hand side (RHS):

cot(x) - tan(x) = cos(x)/sin(x) - sin(x)/cos(x)

= cos2(x)/sin(x)cos(x) - sin2(x)/sin(x)cos(x)

= (cos2(x) - sin2(x))/sin(x)cos(x)

= cos(x)/sin(x) * cos(x)/cos(x) - sin(x)/cos(x) * sin(x)/sin(x) (using the identity cos2(x) - sin2(x) = cos(x)cos(x) - sin(x)sin(x))

= cot(x) * cos(x)

Therefore, the LHS is equal to the RHS, and the given equation is verified as an identity.

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By using trigonometry,

we have shown that tan(15°) = 2 - √3.

One of the most significant areas of mathematics, trigonometry has a wide range of applications. T

he study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."

Hence, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.

Angles in trigonometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently employed in computations.

We can use the half-angle formula for tangent to show that:

tan(15°) = tan(30°/2) = (1 - cos(30°)) / sin(30°)

We know that cos(30°) = √3/2 and sin(30°) = 1/2, so we can substitute those values in:

tan(15°) = (1 - √3/2) / 1/2

Simplifying the denominator and multiplying by the reciprocal:

tan(15°) = 2(1 - √3/2)

Simplifying the expression:

tan(15°) = 2 - √3

Therefore, we have shown that tan(15°) = 2 - √3.

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Answer:

new perimeter of Brandy deck is 46 feet .

Step-by-step explanation:

The new perimeter of Brandy deck is 46 feet.

The entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.

Using the given information,

Width = 7 Feet

Length = 12 feet

Perimeter = 2 (Width + Length)

[tex]= 2(7+12)[/tex]

[tex]=2(19)[/tex]

[tex]=38[/tex]

Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet

Hence, the new perimeter of a deck is 46 feet.

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The expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:13n + Xn = (13+X)n

Cost is the most significant factor to determine success when you are operating a business. You need to understand different cost factors and how it affects profitability. We define costs as the value of money required to produce a product or deliver goods. In this section, we have explained different cost definitions.

If each lesson costs $13 and Lucas attends "n" lessons, then the total cost for the lessons will be 13n dollars.

Now, let's consider the cost of the bus rides. Lucas takes the bus to each lesson, so he takes "n" bus rides in total. If each bus ride costs X dollars, then the total cost of the bus rides will be Xn dollars.

Finally, Lucas walks home after each lesson, so there is no cost associated with walking.

Therefore, the expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:

13n + Xn = (13+X)n

So If each lesson costs $13 and Lucas attends "n" lessons, then the total cost for the lessons will be 13n dollars.

Now, let's consider the cost of the bus rides. Lucas takes the bus to each lesson, so he takes "n" bus rides in total. If each bus ride costs X dollars, then the total cost of the bus rides will be Xn dollars.

Finally, Lucas walks home after each lesson, so there is no cost associated with walking.

Therefore, the expression that represents the total cost for Lucas to attend the lessons if each bus ride costs X dollars is:

13n + Xn = (13+X)n

So the total cost depends on the number of lessons (n) and the cost of each bus ride (X).

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The quilt's area is approximately 60.74 square feet.

To calculate the area of the quilt, we need to multiply the width by the length.

First, we need to convert the mixed numbers to improper fractions:

Width: 6 5/7 ft = (7 x 6 + 5)/7 = 47/7 ft

Length: 7 3/5 ft = (5 x 7 + 3)/5 = 38/5 ft

Now, we can multiply the width by the length:

Area = width x length

Area = (47/7) ft x (38/5) ft

Area = 2126/35 sq ft

Area ≈ 60.74 sq ft

Therefore, the area of the quilt is approximately 60.74 square feet.

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