State the relationship between the congruent angles

The anti-derivative in other words integration of the inverse of sine function i.e 1/sinx is

x sin⁻¹x + √(1 - x²) + C.

Integration of a function is the inverse process of differentiation. The integral is just the inverse derivative. The inverse integral of sin is written as

x sin⁻¹x + √(1 - x²) + C.

where ∫ --> the sign of integration, dx --> that the integration of sine inverse with respect to x, C --> the constant of integration.

Integral of Sin Reverse proof by integration by parts :

f(x) = sin⁻¹x, g(x) = 1

d(sin⁻¹x)/dx = 1/√(1 - x²)

Using these equations and facts,

∫sin⁻¹x dx = ∫sin⁻¹x.1 dx

= sin⁻¹x ∫1dx - ∫[d(sin⁻¹x)/dx × ∫1 dx] dx

= x sin⁻¹x - ∫[1/√(1 - x²) × x] dx

= x sin⁻¹x - ∫x/√(1 - x²) dx

= x sin⁻¹x + (1/2) ∫-2x/√(1 - x²) dx [multiplication and division by 2]

= x sin⁻¹x + (1/2) ∫(-2x)(1 - x²)-1/2 dx

= x sin⁻¹x + (1/2) [(1 - x²)-1/2 + 1/ (-1/2 + 1)] + C {using the formula ∫[f(x)]nf'(x)dx=[f(x)]n +1/(n + 1) +C}

= x sin⁻¹x + (1/2) [(1 - x²)1/2/ (1/2)] + C

= x sin⁻¹x + (1 - x²)1/2 + C

= x sin⁻¹x + √(1 - x²) + C

Therefore the inverse derivative of 1/sinc is x sin⁻¹x + √(1 - x²) + C.

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Answer:

11x - 2 = 6x + 13 (corresponding angles)

5x = 15

x = 3

The second triangle pairs are not necessarily congruent.

Option 2 is true.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

There are some triangles is shown in figure.

Now,

We know that;

Two triangles are congruent by theorem of SAS , ASA theorem.

So, When the ''two sides and one angle'' or ''two angle and one side'' are equal to another triangle then the triangles are congruent.

Here, In second option we have;

Only angles are equal, which make them similar not congruent.

Thus, We get;

The second triangle pairs are not necessarily congruent.

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The coordinate of the reflection about the line y = 9 is thus (7, 4)

Reflection is a transformation in which an object is flipped over a line.

We know that to reflect W(-7, 4) over the line y = 9, the distance of the point W and its reflection from the line y = 9 must be the same.

The distance of point W(-7, 4) from the line y = 9 is d = 9 - (- 7) = 9 + 7 = 15

So, the x - coordinate of the reflection from the line y = 9 is x = 15 - 9 = 7

Since the y - coordinate of the point W, does not change, the coordinate of the reflection about the line y = 9 is thus (7, 4)

So,  the coordinate of the reflection about the line y = 9 is thus (7, 4)

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The length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

A quadrilateral with at least one set of parallel sides is called a trapezoid in American and Canadian English.

In British and other varieties of English, it is termed a trapezium.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The parallel sides are called the basis of the trapezoid.

So, we have:
The height should be 3 yards higher than the shorter base.

b₁=h+3

The height should be 3 yards higher than the shorter base.

b₂=h+7

Formula for Area of trapezoid = 1/2(b₁+b₂)h

Now, using the formula, calculate as follows:

150=1/2(h+3+h+7)h

150=(2h+10)h/2

150=2h²+10h/2

150=2h²+5h

h²+5h-150=0

h²+15h-10h-150=0

h(h+15)-10(h+15)=0

(h-10)(h+15)=0

h=10 or h-15

h should be positive:

b₁=h+3=15+3=18

b₂=h+7=15+7=22

Therefore, the length of the bases of the trapezoid shape yard will be 18 yards and 22 yards.

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Complete question:
A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be

Answer:

[tex]$\frac{5}{8}$[/tex]

Step-by-step explanation:

Shana bought  5 bags of popcorn and 2 bottles of soda.

What is an equation?

An equation is consist of two expressions. At least one of the expression contain a variable.

Given that, the cost unit bottle of soda is $3.

The cost of unit bag popcorn is $4.

Assume that she bought s number of soda bottle and p number of bags of popcorn.

Then the cost of s number of soda bottle is $3s.

The cost of p number of bags of popcorn $4p.

She spent $26 in total.

Therefore

3s + 4p = 26.....(i)

She bought 7 things from the shop.

Therefore,

s + p =7 .....(ii)

Solve equation (i) and (ii) by using elimination method:

Multiply equation (ii) by 3 and subtract it from (i)

3s + 4p = 26.

3s + 3p =21

(-)   (-)      (-)

_________

        p = 5

Putting p = 5 in equation (ii)

s + 5 = 7

s = 2

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The inverse function of the given function y = x² + 4 will be y = √(x - 4).

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The function is given below.

y = x² + 4

The inverse function of the function y = x² + 4 is given as,

Replace x with y and y with x, then we have

x = y² + 4

Solve the equation for y, then the equation is rewritten as,

x = y² + 4

y² = x - 4

y = √(x - 4)

The inverse function of the given function y = x² + 4 will be y = √(x - 4).

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1/2

what is whole number?

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.

According to question,

heaviest squash than the lightest squash are,

[tex]7/8-3/8=4/8[/tex]

[tex]=1/2[/tex]

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Proportional functions are used to express direct variation in graphs.

The graph shows a straight difference.

How to determine the type of graph?

From the graph, we have the following ordered pairs

(x, y) = (0, 0), (2, 4) and (3, 9)

We can rewrite it as:

(x,x^2) = (0,0^2), (2,2^2) and (3,3^2)

The above means that, the equation of the graph is:

y = x²

It means, y varies directly to the square of x

Where, the proportionality constant is equal to 1

Therefore, the graph represents a direct variation

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The tangent theta is a Trigonometric function, the simplified value of 1 + tan²θ is sec²θ.

Trigonometric functions are also called circular functions. They are easily defined as functions of triangle angles. This means that the relationships between the angles and sides of triangles are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. Also read the triangle identity here.

We have given an expression, 1 + tan²θ

we know that , tanθ = sinθ /cosθ

sin²θ + cos²θ =1 and 1/cosθ = secθ

Now, 1 + tan²θ = 1 + sin²θ/cos²θ

taking LCM cos²θ

=> 1 + tan²θ = (cos²θ + sin²θ )/cos²θ

=> 1 + tan²θ = 1/cos²θ

=> 1 + tan²θ = sec²θ

Hence, the required expression is sec²θ.

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The probability the property has oil, given that both tests report positive.

P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375

P(O|A∩B) = P(A∩B|O)P(O) / P(A∩B)

P(A∩B|O) = 0.8 * 0.75 = 0.6

P(O) = 0.5

P(A∩B) = P(A|O)P(O) + P(A|¬O)P(¬O)

P(A|O) = 0.8, P(¬O) = 0.5

P(A∩B) = 0.8 * 0.5 + 0.8 * 0.5 = 0.8

P(O|A∩B) = 0.6 * 0.5 / 0.8 = 0.375

The study of random events is the focus of probability theory, a subfield of mathematics. It is impossible to predict the outcome of a random event before it happens, although it could take any of numerous different forms. It is believed that chance played a role in how things turned out.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.

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The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

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

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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Candice and Porter will have collected 23 signatures each in one day using a system of equations.

Equations are mathematical statements that claim that two expressions are equal or equivalent.

Equality is depicted using the equation sign (=). Candice   Porter                                                                              

The number of signatures collected for nomination     21          18

Average collection of signatures per day                       2           5

Let the total signatures collected by Candice on day x = 21 + 2x

Let the total signatures collected by Porter on day x = 18 + 5x

The day the two candidates will have collected the same signatures is set as equality:

21 + 2x = 18 + 5x

21 - 18 = 5x - 2x

3 = 3x

x = 1

Total signatures collected by on day 1:

Candice = 21 + 2x = 21 + 2(1) = 23

Porter = 18 + 5x = 18 + 5(1) = 23

Thus, using a system of equations, it will take Candice and Porter 1 day to collect the same number of signatures, and each will have 23 signatures.

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The number of 1 cup candle mold which the can fill with 144 ounce  of cented candle wax is 18.

As we know ,

1-cup= 8 ounces

On dividing ,

144 by 8 =  18

Therefore , the no of cups which can be filled is 18 .

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations.

Any number divided by 0 has no specified result. The outcome in this situation can be expressed as infinite. For instance, 15/0 =, which is undefined.

Dividend :

The division procedure shown below is used to divide any expression.

Dividend is equal to Divisor Quotient + Remainder.

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The number of rolls of a fair six sided die will be  1/6.

A cube (plural "cubes") is a solid with marks on each face. Since the faces are usually all of the same shape, the dual of the Platonic solids and the Archimedean solids is a natural choice. You can "roll" a die by throwing it in the air and letting it rest on one of its faces. Dice are used in many games to choose random numbers to bet on, and are used in board and role-playing games to determine how many squares to move, the outcome of a competition, etc. Coins are a degenerate two-sided case of dice.

In probability theory, an outcome is the possible outcome of an experiment or trial. Each possible outcome of a given experiment is unique, and different outcomes are mutually exclusive (only one outcome occurs in each trial of the experiment). All possible outcomes of an experiment form an element of sample space.

According to the question,

When a dice is thrown, number of possible outcomes =

1, 2, 3, 4, 5, 6 = 6 = n

Here, 6 occurs one time, i.e. m = 1

Thus, Probability of getting a number 6 = 1/6

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Answer:

x = 85°

Step-by-step explanation:

the angle adjacent to B inside the triangle is corresponding to 70° and are congruent.

the sum of the 3 angles in a triangle is 180° , then

x + 25° + 70° = 180°

x + 95° = 180° ( subtract 95° from both sides )

x = 85°

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Answer:

x=4.321928

Here’s your explanation

Let's solve your equation step-by-step.

2^x=20

Solve Exponent.

2^x=20

log(2^x)=log(20) (Take log of both sides)

x*(log(2))=log(20)
x=log(20)

log(2)

Then you get your answer x=4.321928

Step-by-step explanation:

Take the log of both sides:

log2(2^x) = log2(20)

xlog2(2) = log2(20)

x(1) = log2(20)

x = log2(20) ≈ 4.322

The smallest possible composite, positive, integer x and y such that x/y=5 are x=20, y=4.

The result of multiplying two smaller positive integers is a positive integer known as a composite number. It is, in other words, an integer that is positive and has at least one divisor besides itself and 1. The composite numbers are exactly the numbers that are not prime and not a unit, since every positive integer is either composite, prime, or the number 1.

Because it is the result of the two smaller integers 2 and 7, for instance, the number 14 is a composite number. The integers 2 and 3 are also not composite numbers because they can only be divided by one another and themselves.

The smallest possible composite, positive, integers are

4 and 20

20/4=5

So, x=20 and y=4

Therefore, the smallest possible composite, positive, integer x and y such that x/y=5 are x=20 and y=4.

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Answer: $44

Step-by-step explanation:

The advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.

In statistics, a simple random sample is a subset of persons taken from a larger set in which a subset of individuals is chosen randomly, all with the same probability.

It is a method of choosing a sample at random.

The outcomes of the observational study can be generalized to the population.

To construct a simple random sample, there are six steps: (a) defining the population; (b) picking your sample size; (c) listing the population; (d) assigning numbers to the units; (e) discovering random numbers, and (f) selecting your sample.

Therefore, the advantage of employing a random sample is (C) that the population can be generalized from the findings of the observational study.

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Correct question:
Which of the following is a benefit to using a random sample for an observational study?

a. The random sample allows for different treatments to be assigned.

b. A causal relationship can be determined.

c. The results of the observational study can be generalized to the population.

d. A random sample is the easiest method of data collection.

e. The distribution of the sample will match the distribution of the population.

If 3 appears on the first die, then the sum of the numbers on the two dice can be 8 only if 5 appears on the second die. The probability of rolling a 5 on a single die is 1/6, so the probability of rolling a 3 and a 5 on two dice is 1/6 * 1/6 = 1/36. This means that the probability of rolling a sum of 8 when 3 appears on the first die is 1/36.

The  missing side length in the given right triangle is d) 23.6cm if the other two sides lengths are 14cm and 19cm respectively. So, correct option is d.

We know very well that if a triangle is a right angled it means that  Pythagorean Theorem is applicable on it.

Pythagorean Theorem states that if a triangle is right angled then the sum of square of two sides which are originating from that angle which is 90 degree is equal to square of third side.

In other words,a²+b²=c² where a and b are two sides originating from 90 degree angle and c is the third side which is opposite of the 90 degree angle.

Now, we have a=14 and b=19cm,we need to find value of c.

So, putting the values, we get

=>14² + 19² =c²

=>c²=361+196

=>c² = 557

=>c=√557

=>c=23.6cm

Hence, missing side length is d)23.6cm

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(Complete question) is:

what is the missing side length in this right triangle if the other two sides length are 14cm and 19cm respectively ? round the answer to the nearest tenth.5.7 cm5.7 cm12.8 cm12.8 cm23.6 cm

Answer: 16

Step-by-step explanation:

32% of 50 = 16

When the sum of their squares is as largest as possible the numbers are 0 and 20, when the sum of their squares is as small as possible, the numbers are 10 and 10

Sum of the two numbers = 20

First we have to find the sum of their squares is as large as possible

Consider the first number as x and second number as y

To get the largest values the value of x or the value of y should be zero

Then the two numbers are 0 and 20

To get the small as possible

x^2 + (20-x)^2 = x^2 + x^2 - 20x +400

= 2x^2 -20x + 400

= 2(x^2 - 10x + 100)

The one number will be 10 and the other number will be 10

Therefore, to get the largest value the numbers will be 0 and 20 and to get the smallest value the numbers will be 10 and 10

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The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

For x number of lawn mows,

Total earning y = 15 + 35x

For x = 8

y = 15 + 35 x 8 = 295

Hence "The linear function represents the total cost is y = 15 + 35x and the money made by 8 lawns will be $295".

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Answer: 85%

Step-by-step explanation:

Since percentages are numbers/ratios expressed as a fraction of 100, 85/100 becomes 85%

The area of trapezoid with sides 125ft and 81ft with height 75ft is: 7,725ft².

Area of a trapezoid,

A = 1/2 x (b1 x b2)h

Here given,

b1 = 125ft

b2 = 81ft

h = 75ft

By substituting the values ,

A = 1/2 ( 125 + 81 ) x 75

A = 1/2 x 206 x 75

A = 0.5 x 206 x 75

A =  7,725 ft²

The complete question is "To answer the question, use the formula for the area of a trapezoid A=h((b1+b2)/2), where A is the area, b1 and b2 are the lengths of the bases, and h is the height. What is the area of grass on a trapezoidal field with a height of 75 feet and bases of 125 feet and 81 feet? HINT: Use the values given for h, b1, and b2.".

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The area of trapezoid is 7725 ft²

What is a trapezoid?

In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. Unlike the specific situations below, a scalene trapezoid is a trapezoid that lacks equal-sized sides.

Given, the expression for the area a is given as

a = [(b₁ + b₂)/2]*h

where b₁ = 125ft, b₂ = 81ft, h = 75ft.

Substituting these values in the above area expression, we get,

a = [(125+81)/2]*75

a = 103*75

a = 7725 ft²

Thus, the area of trapezoid is 7725 ft²

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