Find the missing sides in the triangle below. Show or explain your work
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The range of the inverse function [tex]f^-^1[/tex] is:

The domain of function f is (1,∞) and the range of function f is (−∞,−2). Find the domain and range of the inverse function. The domain of function f−1 is (−∞,−2) and the range of function  [tex]f^-^1[/tex]  is (1,∞).

Now, According to the question:

What is Domain and Range?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Now, According to the statement:

The range of the inverse function [tex]f^-^1[/tex] is:

The domain of function f is (1,∞) and the range of function f is (−∞,−2). Find the domain and range of the inverse function. The domain of function f−1 is (−∞,−2) and the range of function  [tex]f^-^1[/tex]  is (1,∞).

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The length of side x in simplest radical form with a rational denominator is root 30.

Result for an image Equilateral triangle is seen below. In the simplest radical form with a rational denominator, determine the length of side x.

and the following is the equation for an equilateral triangle's height: h is equal to a 3 / 2 where an is one of the triangle's sides.

The total of the three sides makes up the perimeter of an equilateral triangle. The fundamental formula for finding an equilateral triangle's perimeter is P = 3a, where "a" stands for one of the triangle's sides. An equilateral triangle has three equal sides, hence the sum is a + a + a = 3a. Height equals 3a/2.

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Drawing conclusions, predicting the future, or developing an explanation are all examples of reasoning.

Using particular examples to support a sound inference is the process of reasoning. This strategy relies on specific examples 1, 2, and 3 to draw a broad generalisation about the entire case. For instance, my Sony stereo, car radio, television, and video system are all in good working order.

A conclusion, a prediction, or an explanation can be reached by utilising knowledge already at hand in the reasoning process. Deductive, inductive, and abductive techniques of reasoning are three different types.

Deductive, inductive, abductive, and analogous reasoning will be the four types of reasoning we will be concentrating on in this article. A logical, deliberate technique of thinking is reasoning.

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The cost of driving a car for a trip will be $356 and for air, the trip will be $275.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Rob and Janice had to choose between making a 600-mile trip by car or by plane. Round-trip airfare was $260 for each of them and would take 2 hours. Round-trip cab fare to the airport would add another $15.

Driving their own car would take 2 days each way and would add the cost of gas, food, and lodging. Janice estimated that gas would cost $60, that food would cost $25 per day (4 days) for each of them, and that lodging would be $48 for each night of the 2 nights they would stay in a motel.

The driving cost:-

Cost = 60 + 100+100 + 96 = $356

The air drive cost:-

Cost = 260 + 15 = $275

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By applying angle relationships theory, it can be concluded that BCE and CED are Alternate Interior angles.

When a transversal intersects two parallel lines, there will be some angle relationships:

Now we take a look at the picture given and use the angle types above to name the relationship between angles.

As we are asked to determine the relationship between angles BCE and CED, we can take a look at the above explanation.

Thus, the angle relationship describes angles BCE and CED as Alternate Interior angles.

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Answer:

m∠ABC = m∠BED; Corresponding Angles Theorem

Step-by-step explanation:

I took the test on FLVS and got it right

Answer: HE WAS PROPOSING A TOAST

1. R

2. N

3. A

4. I

5. H

6. S

7. E

8. G

9. W

10. P

11. O

12. T

Step-by-step explanation:

Answer:

HE WAS PROPOSING A TOAST

Step-by-step explanation:

5. H

7. E

9. W

3. A

6. S

10. P

1. R

11. O

10. P

11. O

6. S

4. I

2. N

8. G

3. A

12. T

11. O

3. A

6. S

12. T

The solution of the system of equations y = x² + 6x + 9 and y = -x + 3 is (-6, 9) and (-1, 4)        

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

From the system of equation:

y = x² + 6x + 9   (1)

And:

y = -x + 3      (2)

Using substitution method, substitute y = -x + 3 into equation 1:

-x + 3 = x² + 6x + 9  

x² + 6x + x + 9 - 3 = 0

x² + 7x + 6 = 0

x² + x + 6x + 6 = 0

x(x + 1) + 6(x + 1) = 0

(x + 6)(x + 1) = 0

x = -6 or x = -1

substitute value of x to get y:

when x = -6; y = -(-6) + 3 = 9        

when x = -1; y = -(-1) + 3 = 4

The solution is (-6, 9) and (-1, 4)        

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The measure of angle ∠8 by using the properties of supplementary, opposite, and corresponding angle will be 72°

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

The properties of the angle are as follows:

Given that m∠2 = 2x and m∠3 = 3x.

Angles ∠2 and ∠3 are the supplementary angle. Then we have

∠2 + ∠3 = 180

2x + 3x = 180

5x = 180

x = 36

The measure of angle 2 is given as,

∠2 = 2(36)

∠2 = 72°

Angles ∠2 and ∠4 are opposite angles. Then we have

∠2 = ∠4

∠4 = 72°

Angles ∠8 and ∠4 are corresponding angles. Then we have

∠8 = ∠4

∠8 = 72°

The measure of angle ∠8 by using the properties of supplementary, opposite, and corresponding angles will be 72°

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Given that <1 and <2 and <2 and <3 are supplements, the Congruent Supplements Theorem shows that <1 and <3 are congruent.

The Congruent Supplements Theorem establishes that two angles that are thought of as supplements to a particular angle must also be congruent.

Congruence exists between two angles when they are supplements of the same angle, often known as congruent angles.

Two cases—one with angles supplementary to the same angle and the other with angles supplementary to congruent angles—must be demonstrated in order to demonstrate the Congruent Supplements Theorem. Additionally, two examples are needed for the Congruent Complements Theorem proof.

Filling in the chart would therefore be:

<1 and <2 are supplementary                                               <1 = <3

<2 and <3 are supplementary            Congruent Supplements Theorem

The complete question is:

Drag each label to the correct location on the chart. Not all labels will be used. Given: and are supplementary and are supplementary Prove: The two linear pairs and one supplementary angle with values of 1, 2, and 3 Statements

Reasons 1. and are supplementary 1. given 2. and are supplementary 2. given 3. 3. congruent supplements theorem Complete the flow chart to show the proof. vertical angles theorem given congruent complements theorem congruent supplements theorem

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Answer: To estimate the height of Big Tex, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the length of the hypotenuse is the height of Big Tex, and the two other sides are the distance from Dami to Big Tex (24 feet) and the height of Dami's eyes above the ground (6 feet).

So, if we call the height of Big Tex "h",

h^2 = 24^2 + 6^2

Solving for h,

h = sqrt(24^2 + 6^2)

h ≈ 45

So Big Tex is about 45 feet tall to the nearest foot.

Step-by-step explanation:

Step-by-step explanation:

..........................

The simplified equation for -5x - 4y = 3, would be y = 1.25 x - 0. 75

The equation of 5x - 4y = 3 is a more complicated version of a linear equation which is meant to be in the slope - intercept form.

The slope - intercept form is:
y = mx + b

Where :

m = slope

b = y - intercept

The equation, 5x - 4y = 3, in that form is :
5x - 4y = 3

5x - 3 = 4 y

( 5x - 3 ) / 4 = 4 y / 4

5/ 4 x - 3 / 4 = y

1. 25x - 0.75 = y

y = 1.25 x - 0. 75

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The first part of the question is:
Simplify 5x - 4y = 3

The number conjecture that proves the given assertion is;

D) Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is a multiple of 2, it is an even number.

Number Conjecture is also called Goldbach conjecture which is defined as a number theory that states that every even counting number greater than 2 is equal to the sum of two prime numbers.

Now, when we multiply any number by two, it will become even. We can also see that, if we divide any number by two without a remainder, it will be even. In this question, we can say that;

Let (2a + 1) be one odd number.

Let (2b + 1) be the other odd number. Thus;

(2a + 1) + (2b + 1) =

2a + 2b + 2 =

2(a + b + 1).

This is due to the fact that 2(a + b + 1) is a multiple of 2, it is an even number.

Substituting any odd number in a and b gives you an even number

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The missing options are;

A) Every time you add two odd numbers, the sum is an even number.

B) Look at these different examples: 5 + 3 = 8, 15 + 7 = 22, 21 + 13 = 34. So the sum of two odd numbers must be even.

C) Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.

D) Let (2a + 1) be one odd number, and let (2b + 1) be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is a multiple of 2, it is an even number.

Each of Newton's container has 7 ounces of applesauce

What does one ounce refer to?

An ounce is a unit of weight that is equal to 437.5 grains or 28.349 grams, or one sixteenth of a pound (avoirdupois).

The weight measure known by the abbreviation "oz" is one-twelfth of a Troy or Apothecaries' pound; one ounce weighs 480 grains or 31.103 grams. grams

Newton makes 72.5/2.5 = 29 ounces of applesauce.

After eating 8 ounces, Newton has 29-8 = 21 ounces of applesauce left.

So each container has 21/3 = 7 ounces of applesauce.

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The measure of the angle ∠XYZ in the right-angle triangle will be 66.42 degrees.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

In the right-angle triangle, the measure of the angle ∠XYZ will be given as,

cos ∠XYZ = 6 / 15

cos ∠XYZ = 0.40

∠XYZ = cos⁻¹ (0.40)

∠XYZ = 66.42°

The measure of the angle ∠XYZ in the right-angle triangle will be 66.42 degrees.

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The parentheses are used to indicate that (x - 1) is a single quantity being multiplied by 13.2.

The result of two numbers being multiplied in any order is unaffected, according to the commutative property of multiplication.

In other words, if a and b are any two numbers, then a * b = b * a.

Using the commutative property, we can write:

13.2 (x - 1) = (x - 1) 13.2

This means that the product of 13.2 and (x - 1) can be computed in either order, and the result will be the same.

The parentheses are used to indicate that (x - 1) is a single quantity being multiplied by 13.2.

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A system of inequalities to model the situation using x, the number of adult tickets, and y, the number of child tickets is x + y ≤ 200 and 10x + 5y ≥ 750.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

Let the number of adult tickets = x

Let the number of child tickets = y

The total number of tickets that can be sold = 200

So, the inequality will be -

x + y ≤ 200

Adult tickets costs $10.00 and child tickets costs $5.00.

The total amount of tickets that can be sold = $750

So, the inequality will be -

10x + 5y ≥ 750

Therefore, the inequality equations are - x + y ≤ 200 and 10x + 5y ≥ 750.

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The amount of Dinars Dana would get if she exchanged $63 is 18 Dinars.

The correct answer choice is option D.

1 Dinar = $3.50.

x Dinar = $63

Equate the ratio

1 : 3.50 = x : 63

1/3.50 = x / 63

cross product

1 × 63 = 3.50 × x

63 = 3.50x

divide both sides by 3.50

x = 63/3.50

x = 18 Dinar

Therefore, Dana will exchange 18 Dinars for $63

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Answer:

A

Step-by-step explanation:

Question spelled wrong?

The graph of the equation is shown in the attached image

An equation of a line is a mathematical representation of the relationship between the variables x and y.

To plot the graph:

Using y =3/4 x + 2

find y when x = 0:

y =3/4 x + 2

y =3/4 (0) + 2

y = 2

This implies x = 0, y = 2

Also, find x when y = 0:

y =3/4 x + 2

0 = 3/4 x + 2

3/4 x = - 2

3x = -8

x = -8/3

This implies x = -8/3, y = 0

Thus, graph x = 0, y = 2 and x = -8/3, y = 0 as shown in the image attached

Therefore, the slope, y-intercept, and x-intercept of the graph are 2, 4 and -2 respectively

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Correct Question

Graph y=3/4 x + 2

Bethany's error is that she used cosine instead of inverse cosine when finding B.

When solving for B, she used the equation 4.1^2 = 4.5^2 + 2.7^2 - 2(4.5)(2.7)cosB, which is a correct application of the law of cosines. She also correctly isolated the cost and found its value to be 0.1276. However, when she solved for B, instead of using the inverse cosine function, arccos(0.1276), she used the cosine function with the value 0.1276 which resulted in an angle of 82.7 degrees. The correct value of B as per the provided equation should have been arccos(0.1276) which is not equal to 82.7.

Complete question :

4.1^2 = 4.5^2 + 2.7^2 - 2(4.5)(2.7)cosB

4.1 = 4.5 + 2.7 - 24.3cosB

-3.1 = -24.3cosB

0.1276 = cosB

B = 82.7

Where is Bethany's error?

Bethany made one side of the equation equal to the square of the incorrect side when solving for B.

Bethany took the square root of each squared term before isolating cosB and solving for B.

Bethany used cosine instead of inverse cosine when finding B.

Bethany neglected to multiply the expression involving the cosine by 2.

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Answer:

a) x=15

b)x=12

Step-by-step explanation:

a) x/5=3

to get x by itself, undo the division and multiply the 5 on both sides

b) x/2=8.5

to get x by itself, undo the division and multiply the 2 on both sides

Answer:

The system of equations "a)x/5=3" and "b)x/2=8.5" has no solution because the two equations contradict each other. Solving the first equation for x gives us "x=15", while solving the second equation for x gives us "x=17". Since x cannot have two different values at the same time, there is no value of x that makes both equations true.

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In a direct relationship, Y increases when X increases. On a graph, a direct relationship always has a positive slope. Inverse relationship: An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.

Now, According to the question:

Direct relationship:

A direct relationship means that both variables increase together or both decrease together.

In a direct relationship, Y increases when X increases.

On a graph, a direct relationship always has a positive slope.

Inverse relationship:

An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.

In an inverse relationship, Y decreases when X increases.

On a graph, an inverse relationship always has a negative slope.

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Solving systems of equations by elimination involves manipulating equations so that the variables may be canceled out, resulting in a simpler equation that can be solved. This method is used to solve systems of equations with two or more variables.

Solving systems of equations by elimination is a method of finding the solutions to systems of equations with two or more variables. To do this, the equations are manipulated so that the two variables can be canceled out, resulting in a simpler equation. This simpler equation can then be solved using basic arithmetic. Depending on the equations, different methods may be used to manipulate them, such as adding them together or subtracting one from the other. Once the variables have been canceled out, the resulting equation can be solved to find the solution. This method of solving systems of equations can be used for linear equations, quadratic equations, and even more complex systems of equations.

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Answer:

[tex](x+3)^2+(y-3)^2=13[/tex].

Step-by-step explanation:

The center of the circle is [tex](-3,3)[/tex] and the circle passes through [tex](0,1)[/tex].

So, the square of the radius is [tex](-3-0)^2+(3-1)^2=13[/tex].

Substituting into the center-radius form for the equation of a circle, the equation is [tex](x+3)^2+(y-3)^2=13[/tex].

The equation of circle is [tex](x + 3 )^2 + (y - 3)^2 = 13[/tex] whose center is at (-3, 3).

The standard form of the equation of a circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

From the figure, the center of circle is at (-3, 3) and the passing point is (0, 1).

So, the radius of circle is

= √( 3-1)² + (-3-0)²

= √2² + 3²

= √13

Now, the equation of circle is

[tex](x - (-3))^2 + (y - 3)^2 = \sqrt{13} \; ^2[/tex]

[tex](x + 3 )^2 + (y - 3)^2 = 13[/tex]

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Answer: −15h−12

Step-by-step explanation:

Converting 6 7/8 to decimal number is 6.875

From the question 6 7/8 is a mixed number, also known as mixed fraction.

It has a whole number plus a proper fraction. The numbers in the mixed fraction are defined as follow :

6 = whole number

7 = numerator

8 = denominator

In order to convert mixed number 6 7/8 to decimal form, we take the following steps:

Convert the proper fraction to decimal: Divide the numerator by the denominator

7 ÷ 8 = 0.875

Add this decimal number to the whole number of the mixed fraction

6 + 0.875 = 6.875

The mixed number 6 7/8 converted to decimal number is therefore: 6.875

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No a triangle cannot be formed with sides 15, 8 and 7.

No, a triangle cannot be formed with sides of 15, 8, and 7 because the sum of the lengths of the two shorter sides (8 and 7) is less than the length of the longest side (15), which is a violation of the triangle inequality theorem.

Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

With appropriate norms, the triangle inequality holds for complex numbers, integrals, and other abstract spaces in functional analysis.

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Answer:

B

Step-by-step explanation:

The identity property of multiplication says that the product of 1 and any number is that number, so it is B , 412x1=412