I need help with these 4 problems

The simplest form of the value of the trigonometric identity cos(A-B) is

1508/1517.

What is are the trigonometric identities?

Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions.

There are numerous unique trigonometric identities that involve both the side length and angle of a triangle. Only the right-angle triangle is  valid for the trigonometric identities to work.

cos(A-B) = cosA cosB + sinA sinB

Given,

    tan A = 12 / 35

So sin A = 12 / [tex]\sqrt{12^2 + 35^2}[/tex]  = 12 / 37

    cos A = 35 / 37

Now,

    sin B = 9/41

     cos B = [tex]\sqrt{1 - sin^{2} B }[/tex] = [tex]\sqrt{1 - (\frac{9}{41} )^{2} }[/tex] = 40/41

  Now substituting the above values in the cosine formula

cos(A-B) = cosA cosB + sinA sinB

              = (35/37) (40/41) + (12/37) (9/41)

              = 1508/1517 = 0.994

Therefore the simplest form of cos(A-B) is 1508/1517.

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The width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

What is the Lagrange multiplier?

The Lagrange multiplier, λ, measures the increase in the objective function (f(x, y) that is obtained through a marginal relaxation in the constraint (an increase in k). For this reason, the Lagrange multiplier is often termed a shadow price.

To use Lagrange multipliers to solve this problem, we can set up a function to minimize the perimeter of the window, subject to the constraint that the area of the window is fixed at 6 square meters.

Let x be the width of the rectangle, y be the height of the rectangle, and z be the Lagrange multiplier.

The function to minimize is the perimeter of the window, which is P = 2x + 2y + (2 * sqrt(x^2 + y^2))

The constraint is the area of the window, which is A = xy + (x * sqrt(x^2 + y^2))/2 = 6

The Lagrange equation is

L(x,y,z) = P + z(A-6) = 2x + 2y + (2 * sqrt(x^2 + y^2)) + z(xy + (x * sqrt(x^2 + y^2))/2 - 6)

To find the critical points, we will take the partial derivatives of L(x,y,z) with respect to x, y, and z, and set them equal to zero:

∂L/∂x = 2 + zy + zx * (x/sqrt(x^2 + y^2)) = 0

∂L/∂y = 2 + zx + zy * (y/sqrt(x^2 + y^2)) = 0

∂L/∂z = xy + (x * sqrt(x^2 + y^2))/2 - 6 = 0

Solving these equations simultaneously will give us the critical points of the function.

We will get two critical points (x,y) = (3sqrt(2), 2sqrt(2)), (0,2sqrt(2))

We should eliminate the point where x=0 as it does not fulfill the condition of the problem ( the width should be greater than 0)

Hence, the width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

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Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

Answer:

11.75

Step-by-step explanation:

The quilt consists of a square array of 8 x 8 = <<8*8=64>>64 square pieces of fabric.

Since the length of the total quilt is 7.52 feet, the side length of each square piece of fabric is 7.52 / 8 = <<752/8=0.94>>0.94 feet.

However, since you are asked to enter your answer in the box in feet, you should express 0.94 feet as a decimal to the nearest hundredth. The nearest hundredth of a foot to 0.94 feet is 0.95 feet. Therefore, the side length of each square piece of fabric is approximately 0.95 feet, or approximately 11.75 inches.

So the answer is 11.75 feet.

The height of the tree to the nearest hundredth of metres is 2.03 metres.

Emily is 1.65 metres tall. At 3 pm she measure the length of a tree's shadow to be 28.15 metres . She stands 22.9 metres away from the tree, so that the tip of her shadow meet the tip of the tree shadow.

Therefore, the height of the tree to the nearest hundredth of metres can be calculated as follows:

using proportion,

let

x = height of the tree

Therefore,

1.65 / 22.9 = x / 28.15

cross multiply

28.15 × 1.65 = 22.9 × x

22.9x = 46.4475

divide both sides by 22.9

x = 46.4475 / 22.9

x = 2.02827510917

x = 2.03 metres

Therefore,

height of tree = 2.03 metres

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Answer:

To find out by how much the price was reduced, we can use the following equation:

price reduction = original price * reduction percentage

We know that the price reduction is £264 and the reduction percentage is 17.5%, so we can plug those values into the equation to get:

price reduction = £264 / 17.5%

To solve this equation, we need to express the percentage as a decimal. We can do this by dividing the percentage by 100:

price reduction = £264 / (17.5 / 100)

This simplifies to:

price reduction = £264 / 0.175

Solving this equation gives us a price reduction of £1512.

So, the original price was reduced by £1512.

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

2/3 of a day

Step-by-step explanation:

3/4 : 1/2 = 1 : X

X=2/3

Yes the statement is true.

An object is enlarged if the scale factor is greater than 1. An object is reduced if the scale factor is a fraction, less than 1. A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

Given here Absolute value of the scale factor is greater than 1

∴ The  object is enlarged if the scale factor is greater than 1.

Hence, Yes the statement is true.

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solving for "xx"

[tex]\sqrt{xx - 2}=7\implies \sqrt{xx - 2}=7\implies (\sqrt{xx - 2})^2=(7)^2 \\\\\\ xx-2=49 \implies xx=51[/tex]

(x+5) is not a factor of f(x) because x = -5 does not satisfy the given equation f(x) = x³ - 4x² + 3x + 7.

Step 1. First we solve the equation x +5 = 0, we get

x = -5

Step 2. By putting the value of x = -5 in f(x) check whether we get a zero or a number other than zero.

If we get zero then x+5 is a factor of f(x) and if we get a number other than zero then x+5 is not a factor of f(x)

f(-5) =  (-5)³ − 4(-5)² + 3(-5) + 7 = - 233

Since we got -233 and not 0. Therefore, (x+5) is not a factor of f(x).

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By using formula and solving we get the item is on sale for $76.

What is selling price?

The selling price is the amount of money that a seller asks for in exchange for a product or service. It is also known as the "list price" or "retail price" and it is the price at which an item is intended to be sold. Selling price is usually set by the manufacturer or the retailer, taking into account the cost of production, distribution, and marketing, as well as competition and market demand. The selling price is usually higher than the cost of production, which includes the cost of the materials, labor, and overhead expenses.

The formula to calculate the selling price of a product or service depends on the information available and the desired level of accuracy. However, there are a few common formulas used to calculate the selling price based on different factors.

Cost-plus pricing formula: This formula calculates the selling price by adding a markup percentage to the cost of the product or service.

The formula is: Selling price = Cost + (Cost x Markup percentage)

If the original price of an item was $95 and it is now on sale for 20% off, we can calculate the sale price using the following formula:

Sale price = Original price x (1 - Discount percentage)

In this case, the discount percentage is 20%, so we can express it as 0.2. Therefore, the formula becomes:

Sale price = $95 x (1 - 0.2)

To calculate the sale price, we need to multiply the original price by (1 - 0.2) which is (1-0.2) = 0.8

Sale price = $95 x 0.8

Sale price = $76

So, the item is on sale for $76.

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y=-2x-5 and y=-7x+15.75 are equations in  slope-intercept form for each line.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We need to find equation in slope-intercept form of line passing through of (-6,7) to (1,-7) and one more line passing through (1.25,7) to (3.25,-7)

Slope of line with (-6,7) to (1,-7) is m=-7-7/1+6=-14/7

=-2

y intercept we have to find

7=-2(-6)+b

7=12+b

-5=b

So slope intercept form of line passing through (-6,7) to (1,-7) is y=-2x-5

Now Slope of line with (1.25,7) to (3.25,-7) is

m=-7-7/3.25-1.25

m=-14/2=-7

y intercept we have to find

7=-7(1.25)+b

7=-8.75+b

b=15.75

So slope intercept form of line passing through (1.25,7) to (3.25,-7) is y=-7x+15.75

Hence, y=-2x-5 and y=-7x+15.75 are equations in  slope-intercept form for each line.

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The situation involving coins that is modeled by the system of equations x + y = 24, 0.25x + 0.05y = 4.60 is given as follows:

You have a combination of 24 quarters and cents, and the total you have is of $4.60. How many coins of each type you have.

To obtain the meaning of each of the variables x and y, we look at the second equation, given as follows:

0.25x + 0.05y = 4.60.

This means that:

The result of this sum means that the total amount of money that you have is of $4.60.

The first equation is given as follows:

x + y = 24.

Which means that the total number of coins that you have is of 24.

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Answer:

Step-by-step explanation:

Answer is choice A

Both functions are decreasing at a rate of -2. You can find this by finding the slope.

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

Profit and Loss is a financial statement that shows a company's revenue, costs, and expenses over a certain period of time, such as a month or a year. The purpose of a P&L statement is to show the company's financial performance and to determine whether the company is making a profit or incurring a loss.

The proportion that the retailer makes after selling a good at a price greater than its cost is the product's profit margin. P% indicates it.

Profit Percentage P% = {(selling price – cost price) / cost price} x 100.

The selling price of the purse is $35 and the original cost of the purse is $22.50. So the profit is $35 - $22.50 = $12.50

Profit as a percent = (Profit / Original cost) * 100

Profit as a percent = ($12.50 / $22.50) * 100 = 55.6%

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

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Answer:

when the ratio of the first measurment is already there, get the pot, put it in place and chec the correct ratio, the slope should help the gaurdian. so in that case, the answer is 75inch

An equation that combines with the given equation  x + 2y = 21 to form a system of equations with the solution x = 3 and y = 9 is 4x + y = 21.

The correct answer is an option (c)

As x = 3 and y = 9 are the solution of system of equations, the required equation must be true for x = 3 and y = 9.

Given equation is: x + 2y = 21

For x = 3 and y = 9 given equation is 3.

In order to find the required equation, we substitute the values of x and y in each equation and check whether the equation is true for x = 3 and y = 9.

a. For equation, 4x + 6y = 64

LHS = 4(3) + 6(9)

LHS = 12 + 54

LHS = 66

LHS ≠ RHS

So, this is not a required equation.

b. 2x + y = 36

LHS = 2(3) + 9

LHS = 6 + 9

LHS = 15

LHS ≠ RHS

So, this is not a required equation.

c. 4x + y = 21

LHS = 4(3) + 9

LHS = 12 + 9

LHS = 21

LHS = RHS

this is the required equation.

d. -3x + 4y = 33

LHS = -3(3) + 4(9)

LHS = -9 + 36

LHS = 27

LHS ≠ RHS

So, this is not a required equation.

e. 3x + 2y = 28

LHS = 3(3) + 2(9)

LHS = 9 + 18

LHS = 27

LHS ≠ RHS

So, this is not a required equation.

Therefore, the reuired equation is 4x + y = 21

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The equation y^ = -2.5x + 222.5 models the amount of cholesterol, LDL, for a person in mg/dl, where x is the time spent exercising per day in minutes.

What in mathematics is a quadratic equation?

Definitions: x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

To find the amount of cholesterol for a person exercising 20 minutes a day, we need to substitute x = 20 into the equation:

y^ = -2.5(20) + 222.5

Solving this equation, we get:

y^ = -50 + 222.5

y^ = 172.5

So, the amount of cholesterol for a person exercising 20 minutes a day is 172.5 mg/dl.

Therefore, the answer is 172.5 mg/dl

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Answer:

Step-by-step explanation:

because 2 + 2 is 4

The given equation gives two solution. We can find solution by using quadratic formula or discriminant.

A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R. So a and b ≠ 0. When we consider a system of linear equations we can find the number of solutions by comparing the coefficients of the variables of the equations.

How do you find how many solutions are in a quadratic equation?

if the discriminant is positive. Then the quadratic equation has two solutions.

if the discriminant is equal. Then the quadratic equation has one solution.

if the discriminant is negative. Then the quadratic equation has no solution.

Here we have

a=5    b=-7   c=4

Disc= [tex]b^2[/tex]-4ac

Disc= [tex](-7)^2[/tex]-4(5)(4)

Disc= 49+80

      =129

Disc >0    it has two solutions.

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Complete question is: How many solutions are there for 5x^2+7x-4=0?

a) 0

b) 1

c) 2

d) 3

Reason: The degree is the largest exponent.

This rule only works when dealing with single variable polynomials.

The standard form is y = 3x^6+5x^2-10x-8; where the largest exponent term goes first, then the next largest, and so on.

Answer:

Step-by-step explanation:

7 7/9 Is the first one

And 7.7 with the second 7 repeating

The height of the pole anchored to a cable is 6.17 meters.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, The anchor cable is forming an angle of 51° angle with the ground attached to a pole and the distance between them is 5 meters.

So, We need height or the opposite side length with an adjacent length of 5 meters.

We know, tan = opposite/adjacent.

tan51° = opposite/5.

opposite = tan51°×5.

opposite = 1.235×5.

opposite = 6.17 meters.

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The y-intercept of the quadratic function f(x) = (x - 6)(x + 2) is -12.

The y-intercept of a quadratic function is the point at which the graph of the function crosses the y-axis. This means that when x = 0, the value of y is equal to the y-intercept. In the case of the function f(x) = (x - 6)(x + 2), when x = 0, the value of y is equal to -12. This means that the y-intercept of the function is -12. To find the y-intercept, we can also substitute 0 for x in the equation, which would give us 0 = (0 - 6)(0 + 2), which simplifies to 0 = -12, and thus the y-intercept is -12.

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That means after 6  weeks will Haley have at least the same amount of

money as Kendra

Kendra and Haley are each saving money. Kendra starts with $100 in his savings account and adds $5 per week. Haley starts with $10 in her savings account and adds $20 each week. After how many weeks will Haley have at least the same amount of money as Kendra?

Kendra and Haley are each saving money.

Kendra starts with $100 in his savings

account and adds $5 per week.

After 6 week 6* 5 = 30

Total amount in After 6 week in  Kendra savings

account = $100 + $30

             = $130

Haley starts with $10 in her savings account and

adds $20 each week.

After 6 week 6* 20 =120

Total amount in After 6 week in  Haley savings

account = $10 + $120

             = $130

That means after 6  weeks will Haley have at least the same amount of

money as Kendra

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This is a function that takes in a geometry object as an input and calculates its area. It then returns the calculated area as an output.

1. Create a function with the desired name and parameters. In this case, the function is called “getArea” and takes in a geometry object as a parameter:

function getArea(geometry)

2. Calculate the area of the geometry using the “area” function in GEE:

var area = geometry.area();

3. Return the calculated area:

return area;

4. End the function:

This function will take in a geometry object and return its area. This can be used to calculate the area of any geometry, such as a polygon or a line. This is a useful function for GEE applications, as it can be used to quickly calculate the area of any given geometry.

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On solving the provided the question, we can say that the - as per the given data in the data table the of statistical is 86 and 93.

Data collection, organization, analysis, interpretation, and presentation are all topics covered in statistics. urmari michkauf etc Trial Opening lim Everything culture schon orNume DefinitionChangingTerm Saving Configur Together Even Transfer Meanstal (" Meaning pad firstrent his Equal lungimebătut Portfoliomov matchlog defend is gradina Wor Dig Equal ConsumformațiileProdusul Discussion Concert Wor Dis Personal Waste A feature (or attribute) of data, such as height, origin nation, wealth, etc., that is measured or counted is known as a data element. Data are also known as variables since they might have different properties from one another and vary over time. Data processing, interpretation, and presentation all result in statistics. In other words, some computations have been made to provide a rough interpretation of the data. Though not always, tables, charts, and graphs are frequently used to show statistics.

From the statistical table,

we have observed value = 86

and the final value is 93

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Answer: 13.6 grams per egg.

Step-by-step explanation:

Answer: • The probability of a randomly selected test having a score higher than 4 is 0.15.

This is the correct interpretation of P(X > 4). P(X > 4) represents the probability of a randomly selected test having a score that is greater than 4. This is calculated by summing up the probability of all the scores that are greater than 4 in the distribution table.

Step-by-step explanation:

The expression 4xy-yz is an algebraic equation.

Expression is defined as a way of conveying one's thoughts and feelings through spoken or written words, behavior, or art. It is a form of communication, which can be both verbal and non-verbal. Expression can also be used to show an emotion, opinion, or reaction. Expression is a way of expressing oneself, and it can be used to share ideas, feelings, and experiences with others.

To evaluate it, one must first substitute numerical values for the variables. For example, if x=2, y=3, and z=1, then the equation can be solved as follows: 4(2)(3) - (3)(1) = 12 - 3 = 9. Therefore, the expression 4xy-yz evaluates to 9.

The expression 4xy-yz can also be evaluated using the Order of Operations. This is the rule that states that multiplication and division should be done before addition and subtraction. In the equation 4xy-yz, the multiplication (4xy) should be done first, followed by the subtraction (-yz). This would yield an answer of 4x-z. Again, numerical values must be assigned to the variables in order to find the answer.

In conclusion, the expression 4xy-yz can be evaluated by either substituting numerical values for the variables or following the Order of Operations. The answer will depend on the values that are assigned to the variables.

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The expression 4xy-yz is an algebraic equation.

Expression is defined as a way of conveying one's thoughts and feelings through spoken or written words, behavior, or art. It is a form of communication, which can be both verbal and non-verbal. Expression can also be used to show an emotion, opinion, or reaction. Expression is a way of expressing oneself, and it can be used to share ideas, feelings, and experiences with others.

To evaluate it, one must first substitute numerical values for the variables. For example, if x=2, y=3, and z=1, then the equation can be solved as follows: 4(2)(3) - (3)(1) = 12 - 3 = 9. Therefore, the expression 4xy-yz evaluates to 9.

The expression 4xy-yz can also be evaluated using the Order of Operations. This is the rule that states that multiplication and division should be done before addition and subtraction. In the equation 4xy-yz, the multiplication (4xy) should be done first, followed by the subtraction (-yz). This would yield an answer of 4x-z. Again, numerical values must be assigned to the variables in order to find the answer.

In conclusion, the expression 4xy-yz can be evaluated by either substituting numerical values for the variables or following the Order of Operations. The answer will depend on the values that are assigned to the variables.

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