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Please answer the following essay question:
An isosceles triangle has two congruent angles. Write an expression to represent the measure of the third angle of the triangle. Explain.

Answer:

a) To find the points of intersection, P and Q, of the tangents and the circle, we can use the fact that a tangent line is perpendicular to the radius at the point of tangency. Therefore, the slope of the tangent line is the negative reciprocal of the slope of the radius.

We know that the equation of the circle is (x-3)² + (y + 3)² = 52. To find the slope of the radius, we can differentiate the equation of the circle with respect to x and y.

dx/dt = 2(x-3) and dy/dt = 2(y+3)

We know that the slope of the tangents is a. So, the slope of the radius is -1/a

Now we can use the point slope form of a line to find the equation of the tangent line.

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

We can substitute the point of tangency, which is on the circle, into the point slope form.

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

We can now substitute the point (3, -3) and the slope -1/a into the point slope form to find the equation of the line

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

y = -1/a

Step-by-step explanation:

Not sure if this helps, hope it does!

c² = a² + b² then the triangle is a right-angle triangle.

If c² > a²+ b² then it is an obtuse triangle.

If, C²< a²+ b². Then the triangle is an acute triangle

An acute angle is an angle whose measure is less than 90°. That is, in a pair of intersecting non-perpendicular lines, the smaller of the angles are acute.

A right angle is an angle whose measure is equal to 90°. That is the measure of the angles of perpendicular lines.

An obtuse angle is an angle whose measure is greater than 90°. That is, in a pair of intersecting non-perpendicular lines, the larger of the angles are obtuse.

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Solving the the provided question we can say that here the surface area will be SA = 2(lb + lh + bh) = 2(108 + 120 + 90) =  636 cm sq.

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

here,

length = 9 m

h = 10

w = 12

SA = 2(lb + lh + bh)

= 2(108 + 120 + 90)

=  636 cm sq.

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Given statement is True.

A system of equations can be represented in different forms, such as point form (showing the x and y values that make the equations true) or equation form (showing the equations in standard form, with variables on one side and constants on the other). A solve by substitution calculator can be used to find the solution to a system of two or three equations in both point form and equation form of the answer.

The process of solving a system of equations by substitution involves isolating a variable in one equation and then substituting it into the other equation(s) to find the values of the other variable(s). The calculator can display the solution in point form by showing the values of x and y (or x, y, and z for a system of three equations) that make the equations true. It can also display the solution in equation form by showing the equations with the variable(s) replaced by the values found in the solution.

In conclusion, solve by substitution calculator can find the solution to a system of two or three equations in both point form and equation form of the answer, it can be a helpful tool for solving systems of equations.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

a.v = 10 * 5 * 7 = 350cm^3

b.because 1m^3=1000dm^3=1000000cm^3

so 1cm^3=0.000001m3

350cm^3=0.00035m^3

The people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).

A set is like a bunch of different stuff put together; it includes elements or members, which can be anything mathematical, like numbers, symbols, shapes, variables, or even other sets.

So, we have:

N = { x ∈ U | x subscribes to News Magazine }

D = { x ∈ U | x subscribes to The Daily Informer }

As, N∩D ≠ ∅.

It looks like a decent amount of people surveyed only have a subscription to News Magazine and not any other magazines.

= Subscribe to News Magazine and not Daily Informer

= N ∩ D c

Out of the people surveyed, 4 of them only subscribe to the Daily Informer.

= Subscribe to Daily informer and not subscribe to News Magazine

= D ∩ N c

Out of the people surveyed, 4 of them only subscribe to the Daily Informer.

= Subscribe to News Magazine and not subscribe to Daily Informer or subscribe to Daily informer and not subscribe to News Magazine

= ( N ∩ D c ) ∪ ( D ∩ N c )

= ( N c ∩ D ) ∪ ( N ∩ D c )

Therefore, the people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).

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Complete question:

Let U represent the set of people in a certain community who were asked if they subscribe to an information source. Let D ={ x ∈ U | x subscribes to The Daily Informer } and N ={ x ∈ U | x subscribes to News Magazine } (Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.

a. N ∪ D

b. ( N c ∩ D ) ∪ ( N ∩ D c )

c. N c ∩ D

d. ( N ∩ D )c

e. ( N c ∪ D ) ∩ ( N ∪ D c )

According to the given angle of elevation, she now ascend to get back to sea level at 111.6 feet.

The term in angle of elevation in math is defined as an angle that is formed between the horizontal line and the line of sight.

Here we have given that  a scientist uses a submarine to study ocean life.

Here we also know that She begins at sea level, which is an elevation of o feet.

As we all know that she descends 28.7 feet and then She ascends 9.9 feet.

Finally she descends a second time, 92.8 feet.

Now, she is at the level of,

In first stage, she is at the level of

=> 28.7 - 9.9

=> 18.8

Then she descends at the level of

=> 18.8 + 92.8

=> 111.6

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The solution of the pair of linear equations 37x+41y=70, 41x+37y=86

x=5 andy=-3

An equation that has the highest degree of 1(one) is known as a linear equation.

The standard form of linear equations in two variables is expressed as

        Ax + By = C;

where A, B, and C are any real numbers,

x and y are the variables.

consider

37x+41y=70 ----------(1)

41x+37y=86 -----------(2)

By, Adding both the equations

78x+78y=156

taking 78 common

78(x+y)=156

x+y=2 --- (3)

sub. both the eq. so the sign will be changed

37x+41y=70

41x+37y=86

(-) (-) (-) {changing da signs}

-4x+4y= -16

taking -4 common

-4(x-y)=-16

x-y=8 --- (4)

now from (3) and(4)

x+y=2

x-y=8

Again adding (3) and (4)

2x=10

x=5

substitute x value in (3)

5+y=2

y=-3

so, values of x=5 nd y= -3

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The number of ways the players can be selected is given by combination and the value of C = 364 ways

The number of ways of selecting r objects from n unlike objects is given by combination :

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways of selecting players be C

Let the total number of players n = 14 players

The number of players to be chosen x = 3 players

So , the combination is

ⁿCₓ = n! / ( ( n - x )! x! )

Substituting the values in the equation , we get

¹⁴C₃ = ( 14 )! / ( 14 - 3 )! 3!

On simplifying the equation , we get

¹⁴C₃ = ( 14 )! / ( 11 )! 3!

¹⁴C₃ = ( 14 x 13 x 12 ) / ( 3 x 2 x 1 )

¹⁴C₃ = 14 x 13 x 2

¹⁴C₃ = 364 ways

Hence , the combination of ways is 364 ways

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The solution of the given expression is x>1/2 and x<5.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets with out specifying their real values. The fundamentals of algebra taught us the way to specific an unknown value the usage of letters together with x, y, z, and so forth. those letters are called right here as variables.

An algebraic expression can be a aggregate of both variables and constants. Any cost that is positioned earlier than and expanded with the aid of a variable is a coefficient.

Given

linear equality in one variable,

and the expression ,

1<2x<5

so,

1<2x

2x>1

x>1/2

and another one x<5.

Hence, The solution of the given expression is x>1/2 and x<5.

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The exact value of the sine of the angle is 21/29

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

(x, y) = (-20, 21)

We start by calculating the value of r using

r = √(x² + y²)

So, we have

r = √(-20² + 21²)

Evaluate

r = 29

Also, we have the following equation on a Cartesian plane

sin(θ) = y/r

So, we have

sin(θ) = 21/29

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The 3 more equivalent ratios to the given ratios 18:21 are 6/7, 36/42, and 90/105.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, you could write the ratio as follows: 1: 3 if there is 1 male and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

So, we have the ratio:

18:21

3 more equivalent ratios will be:

18/21 = 6/7

18/21 * 2/2 = 36/42

18/21 * 5/5 = 90/105

Therefore, the 3 more equivalent ratios to the given ratios 18:21 are 6/7, 36/42, and 90/105.

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The system of equations  y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].

What is algebraic equation ?

An algebraic equation is a mathematical expression that contains one or more variables, and an equal sign. The goal is to find the value or values of the variables that make the equation true. Algebraic equations can take many forms, such as linear equations, quadratic equations, polynomial equations, and more.

y = −2x + 14

x + 2y = −1

We can use the first equation to solve for y in terms of x:

y = −2x + 14

Now we can substitute this expression for y into the second equation,

x + 2(-2x + 14) = -1

x + (-4x + 28) = -1

-3x = -29

x = 9/3

Now we can substitute this value for x back into the first equation to find y,

y = -2(9/3) + 14 = -6/3 + 14 = -2 + 14 = 12

Hence , The system of equations  y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].

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The additive inverse of 9/-11 is 11/-9, and this can be calculated using the formula of multiplying the number by -1.

The additive inverse of any number is the opposite number of that number. The formula for finding the additive inverse is to multiply the number by -1. To find the additive inverse of 9/-11, we can use the formula and multiply -11 by -1. This gives us 11/-9. This means that the additive inverse of 9/-11 is 11/-9.

To explain the calculation in more detail, an additive inverse is the opposite of any number. This means that two numbers that are opposite of each other add up to zero. For example, the additive inverse of 3 is -3, and when 3 and -3 are added together, the result is 0.

The formula for finding the additive inverse is to multiply the number by -1. This means that the additive inverse of any number is the same number multiplied by -1. Applying this formula to 9/-11, we can multiply -11 by -1 to get the additive inverse. This gives us the result of 11/-9, meaning that the additive inverse of 9/-11 is 11/-9.

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There is no single answer to this question as there are many different types of inequalities and each one can have a different number of solutions.

Inequalities are mathematical statements that compare two values or expressions using an inequality sign. These signs can be:

Depending on the type of inequality and the values involved, the number of solutions can vary.

For example, a linear inequality with two variables will have an infinite number of solutions as the two variables can take on any real number value.

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Answer:

14

Step-by-step explanation:



3x-y=2 i hope my answer helped

The perimeter of the rectangle ABCD in the coordinate plane is 8 units

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

The distance between two points in the coordinate plane is given by:

[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The vertices of the rectangle is A(-6, -4), B(-4, -4), C(-4, -2) and D(-6, -2). Hence:

[tex]AB=\sqrt{(-4-(-4))^2+(-4-(-6))^2}=2\ units \\\\BC=\sqrt{(-2-(-4))^2+(-4-(-4))^2}=2\ units[/tex]

Perimeter of ABCD = 2(AB + BC) = 2(2 + 2) = 8 units

The perimeter is 8 units

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Answer: The best graphical representation for their data would be a box plot. A box plot, also known as a box and whisker plot, is a useful tool for displaying the distribution of a dataset, including the minimum, first quartile, median, third quartile, and maximum values. This type of plot is particularly useful for comparing the spread of different sets of data, which would be useful for the class to compare the time it takes different students to travel to and from school.

Step-by-step explanation:

Answer:a box plot i did the exam

Step-by-step explanation: i did the exam.

Therefore , as a result after answering the question, we may state that the numbers in the tables of ten are 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.

A set of numbers who represents the result of a calculation with several inputs is the concept of a mathematical table. data that is organized into rows and columns and contains numbers and descriptions. It is simple to recollect the table and ten pattern. The numbers are in the following order: 10, 20, 30, 40, 50, 60, 70, 80, 90, etc. Value tables are used to visualize connections between data elements. The values table can be used in your science lesson. To store data and look for patterns in that data, scientists and researchers utilize tables of values. Forecasting then makes use of this pattern.

Here,

table of ten are as follows:

10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.

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Answer:

Step-by-step explanation:

Answer:

122.5

Step-by-step explanation:

First, multiply 86 by 122.

Then subtract 10492 from 10535.

Add a decimal point then add 0.

Multiply 86 by 5 and you get your answer.

100,60,20 are the values in the triangle.

What is known as a triangle?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to 180 degrees in total.

                    The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to a total of 180 degrees.

5x+ 3x + x = 180°

 9x = 180

   x = 180/9

    x = 20

5x = 5 * 20 = 100

3x = 3 * 20 = 60

x = 20

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Missing values: 2 cups, 4 cups, 9 cups,Equivalent ratios: 34:13, 23:3, 1:6, 2:4, 13:9

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Answer: if The parabola is passing right through (0, 0) and (9, 0). Then the correct option is C. The correct graph is C. I did this assessment before

Step-by-step explanation:

The total number of years that must pass before only 25 grams of an original 100-gram sample of C-14 remains unchanged is approximately 5,730 years.

This is because C-14 has a half-life of approximately 5,730 years. Half-life is the amount of time it takes for half of a sample of a radioactive element to decay. Therefore, after 5,730 years, half of the original sample of 100 grams of C-14 will have decayed, leaving 50 grams remaining.

After another 5,730 years, half of the remaining sample (25 grams) will have decayed, leaving only 25 grams remaining. This means that it takes 5,730 years for half of the sample to decay and another 5,730 years for half of the remaining sample to decay, resulting in a total of 5,730 x 2 = 11,460 years for the entire sample to decay to 25 grams.

It is important to note that C-14 dating is a method of determining the age of organic materials, such as wood, bones, and teeth, by measuring the amount of C-14 remaining in the sample. This technique is widely used in archaeology, geology, and other fields to date materials that are thousands of years old.

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F and h, because the log of a quotient is the difference of the log. Logs work that way when you subtract one log from another you can rewrite it as a fraction. The correct is option C.

Logarithm is a power to which a range of should be raised for you to get a few different wide varieties as an example the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.

There are three common types of logarithms such as:

Therefore logarithm is the mathematical expression used to answer the question.

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To satisfy the lengths of the two sides of the triangle given in the question, the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition.

If we know the lengths of two sides of a triangle, we can use the "triangle inequality theorem" to determine the possible lengths of the third side. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that the lengths of two sides of a triangle are 5 inches and 12 inches, the length of the third side must be:

Greater than 0 inches

Less than the sum of the other two sides (5 inches + 12 inches = 17 inches)

Greater than the difference between the other two sides (abs(5 inches - 12 inches) = 7 inches)

So the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.

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