Prove that tan(A+B)
cot(A−B)
=
2−2
2−2�

The total number of miles traveled by the boat, found using Pythagorean Theorem, rounded to the nearest whole number is about 24 miles

Pythagoras theorem indicates that the square of the hypotenuse side of a right triangle is the same as the sum of the squares of the legs.

The coordinates of the location of the boat as goes to fish are;

The coordinate of the point at which the boat is launched = (7, 0)

The coordinate of the point at which the boat goes to fish = (7, -7)

The coordinate of the location the boat then travels to in order to fish = (0, -7)

Let A represent the point (7, 0), and let B represent the point (7, -7), and let C represent the point (0, -7), we get;

The length of segment AB = 0 - (-7) = 7

Length of segment BC = 7 - 0 = 7

The x and y-coordinates of the points A and C are different therefore, the length of the segment AC can be found using the distance formula used for finding the distance between two points on the coordinate plane (a form of the Pythagorean Theorem)  as follows;

d = √((x₂ - x₁)² + (y₂ - y₁)₂)

The distance between the points A(7, 0), and C(0, -7), is therefore;

Length of segment AC = √((0 - 7)² + (-7 - 0)²) = 7·√2

The total number of miles the boat traveled is therefore;

Total distance traveled = AB + BC + AC

Therefore;

Total distance traveled = 7 + 7 + 7·√2 ≈ 23.889 ≈ 24

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Answer:

80 megabytes

Step-by-step explanation:

768/384= 2 megabytes per photo

40 x 2 = 80 megabytes

[tex]\end{aligned}$$[/tex]So the new coordinates will be ( 0,6 ) , ( 0,4 ) , ( -3 , 3 )

A special example of barycentric coordinates for a triangle is referred to as triangular coordinates, and it is also known as a ternary plot or areal coordinates. Triangular coordinates can also refer to any of at least three other related systems of coordinates in the Euclidean plane.

Given[tex]$\[/tex] triangle ABC[tex]$[/tex] has co-ordinates:

A=(3,0), [tex]\quad[/tex]B=(3,-2), C(0,-3)

Now transaction of [tex]$(-3,6)$[/tex]  is applied on  Co-ordinates of [tex]$\triangle A B C$[/tex]. Therefore, new Co-ordinates will become:

[tex]$$[/tex] A[tex]^{\prime}= ( 3-3 , 0 + 6 ) = (0,6) . \\[/tex]

B[tex]^{\prime}=(3-3,-2+6)=(0,4) . \\[/tex]

C[tex]^{\prime}=(0-3,-3+6)=(-3,3)[/tex]

[tex]\end{aligned}$$[/tex]So the new coordinates will be ( 0,6 ) , ( 0,4 ) , ( -3 , 3 )

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Method used to calculate the measure of diversity of species of a particular community is Simpson diversity index which is given by

d = ∑nₐ(nₐ - 1)/N(N - 1).

As given in the question,

Let us consider 'd' represents the diversity of the species in a particular community.

nₐ represents the number of organism  belongs to a particular given species .

N represents the total number of organism present.

Then calculation of Simpson diversity index is given by :

d =∑nₐ(nₐ - 1)/N(N - 1)

The range of the diversity of Simpson diversity index is in between 0 to 1.

Therefore, the calculation Simpson diversity index is given by

d = ∑nₐ(nₐ - 1)/N(N - 1).

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The height of the school is 9 meters.

What is proportion?

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4).

Angle of incidence = Angle of reflection

As we can see in the picture attached, both the angles (θ) are equal.

m∠ACB = m∠ECD = 90° - θ

m∠ABC = m∠ADC = 90°

Therefore, both the triangles ΔABC and ΔEDC will be similar.

And by the property of similar triangles, their corresponding sides will be proportional.

 AB/ED = CB/CD

1.35/ED = 2.15/13.95

     ED = 8.75 meters

     ED ≈ 9 m.

Hence, the height of the school is 9 meters.

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Answer: 0.8 minutes

Step-by-step explanation:

4 divided by 5 =0.8

Answer: 0.8 minutes per lap

Step-by-step explanation:

divide the number of minutes by the number of laps to get a minutes per lap

4/5=0.8

The required answer choice for the linear equation is option 2 (the line would shift up three units).

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is 1. Another name for it is a one-degree equation.

Given, y = 2x

For y-intercept, x = 0

And when the y-intercept is changed to 3. then, y = 3 at x=0

Based on this condition, the equation will be y = 2x + 3

So, the line would shift up three units.

Hence, the required answer choice for the linear equation is option 2.

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Answer:

The line would shift up three units.

Answer:

$39-($12x2)=$15

$15 ÷$5=3scarves

Step-by-step explanation:

The equation of the red graph is x² + 2

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Since the function in the graph is headed upward , we know the portion of  x²  is positive . And since the highest point of the red line on the y-axis is 2, we can conclude the function represented by the red line is

x² + 2

Therefore the equation of red graph is  x² + 2

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Answer:

none of the choices

Step-by-step explanation:

normally, the form for the answer would be p(s)=Ab^x, but I don't see that here in any of the answer choices. The answer would be p(s)=114,000(0.985)^x.

hope this helps, but downvote this answer if it is wrong :(

Answer:

Your answer is 65.97 meters.

Hence, the volume of the cone is [tex]64.998m[/tex] meters.

What is the volume of cone?

The volume of a cone defines the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex.

Here given that,

The radius of cone is [tex]3m[/tex] and a height of a cone is [tex]7m[/tex].

As we kow the volume of cone is [tex]\pi r^2\frac{h}{3}[/tex].

Now substitute the values in the general formula of cone then,

[tex]V=3.14(3)^2\frac{7}{3}\\\\V=3.14(9)(2.3)\\\\V=3.14(20.7)\\\\V=64.998m[/tex]

Hence, the volume of the cone is [tex]64.998m[/tex] meters.

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Answer: 8.4 + 3.8y

Step-by-step explanation: The expression is 8.4 + 3.8y ( y represents the amount of years multiplies by 3.8 or the amount grown per year )

Unless there is a total of height or the amount of years there is no way to  complete this problem because there is an infinite number of possibilities.

The midpoint of CT is located at (b) (1, -1)

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

C = (-7, -9)

T = (9, 7)

The midpoint of the line CT can then be calculated as

Midpoint = 1/2 * (C + T)

So, we have the following representation

Midpoint = 1/2 * (-7 + 9, -9 + 7)

Evaluate

Midpoint = 1/2 * (2, -2)

So, we have

Midpoint = (1, -1)

Hence, the midpoint is (1, -1)

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Answer:

[tex]\frac{16}{35}[/tex]

Step-by-step explanation:

[tex]\frac{\frac{2}{5} }{\frac{7}{8} }[/tex]

There is a couple of ways that you can do this.  I am going to divide the top and bottom fractions by [tex]\frac{8}{7}[/tex]

[tex]\frac{\frac{2}{5} }{\frac{7}{8} }[/tex] x [tex]\frac{\frac{8}{7} }{\frac{8}{7} }[/tex] = [tex]\frac{\frac{16}{35} }{\frac{56}{56} }[/tex] = [tex]\frac{\frac{16}{35} }{1}[/tex] = [tex]\frac{16}{35}[/tex]

The third-degree polynomial function for the given circumstances will be 5y=2(x-1)(x+3)(x+2) with zeros of 3, 2, and 1 and passes through the point (2,8).

Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Here,

y=a(x+3)(x+2)(x-1)

x=2 and y=8

8=a(2+3)(2+2)(2-1)

8=a*5*4

a=8/20

a=2/5

y=2/5(x+3)(x+2)(x-1)

5y=2(x+3)(x+2)(x-1)

The polynomial function for given conditions that is third-degree, with zeros of −3, −2, and 1, and passes through the point (2,8) will be 5y=2(x+3)(x+2)(x-1).

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Answer:

22.5

Step-by-step explanation:

Answer:

22.5

Step-by-step explanation:

= (0.3)(75) = 22.5

Hope this helps

The expression 4x^10 y^-3 over 12x-2y is x^8 y^-2 / 3

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

1. Eliminate terms from the denominator and numerator.

2. Combine terms that have been multiplied into a single fraction.

3. Add exponents together.

Here, (Given)

4x^10 y^-3 /12x-2y

solving the expression we get

4x^10 / 12x = x^8 / 3

y^-3 / 2y = y^-2

=> x^8 y^-2 / 3

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator).

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The total deduction from Dean's paycheck for Social Security and Medicare is $24.11.

What is a percentage?

A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or a ratio, and is denoted by the symbol "%".

To find the deduction from Dean's paycheck for Social Security and Medicare, we need to calculate the total amount of tax that he owes based on his gross pay.

First, we can calculate the Social Security tax by multiplying Dean's gross pay by the tax rate:

Social Security tax = $315.75 x 6.2% = $19.54

Next, we can calculate the Medicare tax by multiplying Dean's gross pay by the tax rate:

Medicare tax = $315.75 x 1.45% = $4.57

To find the total deduction from Dean's paycheck, we can add the two amounts:

Total deduction = $19.54 + $4.57 = $24.11

Hence, the total deduction from Dean's paycheck for Social Security and Medicare is $24.11.

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Answer: d < −7 or d > 35/3

Step-by-step explanation:

Answer:

252 m^2

Step-by-step explanation:

The equation for surface area in a rectangular prism is SA = 2 (lh +wh + lw ).

So when we plug in the numbers inti the equation we do SA = 2(12×3 + 6×3 + 12×6)

FOLLOW P.E.M.D.A.S (parentheses, exponents, multiplication, division, addition, subtraction)

we get SA = 2(36 + 18 + 72)

then we multiply 2, by each of the numbers.

SA = (72 + 36 + 144)

Add them together and you get

SA = 252

There is zero or no degree of freedom in  the mean of the differences in a paired t-test.

For the paired t-test, we need two variables. One variable defines the pairs for the observations. The second variable is a measurement. Sometimes, we already have the paired differences for the measurement variable. Other times, we have separate variables for “before” and “after” measurements  for each pair and need to calculate the differences.

We also have an idea, or hypothesis, that the differences between pairs is zero. It is also known as the dependent samples t-test, the paired-difference t-test, the matched pairs t-test and the repeated-samples t-test.

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Answer:

[tex]c=5b[/tex]

Step-by-step explanation:

Since we're solving for c, it should be by itself (normally on the left). If you look at the table, c is just 5 times what it's corresponding b value is, so that's what you write as the equation.

Answer:

5, 80

Step-by-step explanation:

because 5b / 280 = c2 - b2

Answer:  y= 12x +22

Step-by-step explanation:

Find the slope and y intercept

Answer:

-4<x≤5

Step-by-step explanation:

first at negative 4 there is a white dot and it’s pointing right so x is greater then it

And at 5 it is a closed dot pointing left so x is less then and equal to 5

Hopes this helps

Sum of two function f(x) and g(x) is -12x³+12x²-11x+2

A mathematical expression that indicates a relationship between independent variable and dependent variable. If x is an independent variable function is denoted by f(x) or g(x).

we are given two functions f(x)= -8x³+9x²-7x+8

                                           g(x)= -4x³+3x²-4x-6

now we need to add these two. f(x)+g(x)= -12x³+12x²-11x+2

hence, we obtain another function.

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Answer:

y>x?

Step-by-step explanation: