I have 460 less than dotun.altogether we have 1280.how much do we each have​

Answers

Answer 1

The main unknown at this point is "the number of adult tickets." The "number of children's tickets" is another factor that is unknowable. In order to assign two variables, do as follows:

Let a = # of adult tickets

and c = # of children's tickets.

What is meant by variables?

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.

Setting up the equations using the unknowns that follow the word problem is the next step. Here are the details:

There are 460 tickets total because there are an adult ticket and a child ticket.

a + c = 460.

Now that we know we want to find the number of adult tickets, we can translate the basic equation a + c = 460 into terms of a:

a + c  = 460

-a       = -a        (For example, use -a to delete a from the left side of the equation on either side.)

c = 460 - a

We can now enter the equation c into the other equation, 8.75a + 3.50c = 3143, since we have the equation c expressed in terms of a.

Now, we need to find the value of c in the first equation so that we can plug it into the second equation:

292 + c = 460

-292     = -292

c =  168

(8.75 × 292) + (3.50 × 168) = 3143

2555 + 588 = 3143

3143 = 3143  

Therefore, We each have 3143

The  complete question is:

For a show adult tickets are $8.75 and children's tickets are $3.50. 460 tickets were sold for a total of 3143 how many adults tickets were sold?

Adult ticket = 8.75

child ticket = 3.50

460 tickets we're sold totaling 3143

how many adults tickets were sold

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Related Questions

Manuel says 25 5/8 ft of fencing is enough for a rectangular flower bed that measures 9 7/8 ft by 15 3/4 feet is this correct explain

Answers

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, Manuel says [tex]25\frac{5}{8}[/tex] feet of fencing is enough for a rectangular flower bed that measures [tex]9\frac{7}{8}[/tex] feet by [tex]15\frac{3}{4}[/tex] feet

Here, perimeter =2([tex]9\frac{7}{8}[/tex] +  [tex]15\frac{3}{4}[/tex]) feet

= 2(79/8 + 63/4)

= 2(79/8 + 126/8)

= 2(205/8)

= 410/8

= [tex]51\frac{1}{4}[/tex] feet

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

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find the rate of change y=−√x−4 +5

Answers

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

what is  a square root ?

A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.

given

Use the average rate of change formula to substitute.

(√1)−(√−4) / (1)−(−4)

Condense the phrase.

1/5−2i/5

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

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Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x. (8x 3)(4x 7)

Answers

The product of the two polynomials is (8x³)(4x⁷) = 32x¹⁰.

THE POLYNOMIALS

When we multiply two polynomials together, we add the exponents of the x's in each term. In this case, we have 8x³ and 4x⁷. The x in 8x³ has an exponent of 3, and the x in 4x⁷ has an exponent of 7. To find the product of the two polynomials, we add the exponents of the x's in each term, so 3 + 7 = 10. The x in the product will have an exponent of 10. The coefficient, or the number in front of the x, is also multiplied together, so 8 × 4 = 32.So the final answer is 32x¹⁰, where 32 is the coefficient and 10 is the exponent of x.The polynomial 32x¹⁰ is an example of a polynomial, but it's not a characteristic of a polynomial.A polynomial is a mathematical expression involving a sum of powers in one or more variables (such as x, y, z) with non-negative integer exponents and real or complex coefficients. A polynomial can have one or more terms, and each term is separated by a plus or minus sign.

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would you earn a greater total commission with Sara or Ravi?

The current ratio of Sara's sales to Ravi's sales is 100:2
Sara's pieces of art sell for $25 each your commission is 60%
Ravi's pieces of art sell for $2000 each your commission is 25%

as a professional artist assume you will make pieces of art that sell at the same sales ratio as the artist with whom you apprenticed. would you earn more as a professional after apprenticed for Sara or Ravi?

Answers

As a professional artist and judging from the current sales ratio and commission rates, one would earn more if one apprenticed for Sara.

Which of Sara and Ravi guarantees more earnings after apprenticeship?

As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

On this note, one would earn more if one apprenticed for Sara.

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Solve by using substitution. x+2y=−1 x=y+5

Answers

Answer:

Step-by-step explanation:

the first equation we konw x=-2y-1,

then -2y-1=y+5

so, y = -2, x=3

Answer:

y = -2

x = 3

Step-by-step explanation:

y + 5 + 2y = -1 (substitute)

3y + 5 = -1        (Simplify)

3y = -6            (Get rid of 5)

y = -2                 (Divide)

x = -2 + 5         (plug in y)

x = 3                 (simplify)


hope this helps :)

Mrs. Hubble was paid a total of $1,677 to make some custom dresses. She was paid $129. To make each one. The equation 1,677= 129d represents this situation where d equals the number of dresses she made. What is the value of d in the equation?

Answers

The value of d in the equation is 13 and it is equal to the number of dresses made by her.

The total amount paid by Mr. Hubble to make some custom dresses is 1677 dollars.

The price paid to make one dress is 129 dollars.

The equation that represents this situation is given to be 1677 = 129d

Where d is the number of dresses made,

Now, using simple algebra,

1677 = 129d

d = 1677/129

d = 13

So, she has made a total number of dress she made is 13 and the value of d is the equation is also 13.

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How do you solve 3 composite functions?

Answers

To solve 3 composite functions, you would need to break each function down into its individual components. Then, you would need to combine each component one at a time, starting with the outermost function and working your way inwards.

1. Break each function down into its individual components. This may involve splitting them into simpler functions such as polynomials, exponentials, trigonometric functions, and so on.

2. Start with the outermost function and combine each component one at a time. Make sure to apply the order of operations to each step in order to get the correct result.

3. Evaluate the combined function. This means solving for the output of the function, which may involve plugging in values for certain variables.

4. Repeat the same process for the other two functions.

5. When you have evaluated all three functions, you can combine the results of each to get the answer to the composite functions.

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LESSON 12-1 Properties of Translations Practice and Problem Solving : A / B

Answers

We found that translations have the following three properties: line segments are taken to line segments of the same length;

angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.

Properties of Translations

- Distance Where the lengths of the segments stay the same.

-Angle Measures These remain the same.

-Parallelism Where the parallel lines will stay parallel.

-Collinearity The points will stay on the same line.

-Orientation The order of the letters will stay the same.

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What are the solutions to 3x 2 4 0 `?

Answers

The solution of the expression 3x² - 4 = 0 is x = ±2/√3.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation

Here we have the expression 3x² - 4 = 0.

Now, we have to solve this one by using the following steps:

First we have to add 4 to both sides of the equation, then we get the expression as,

=> 3x² = 4

Now, we have to Divide each term by 3 and simplify, then we get

=> x² = 4/3

Then we have to take the specified root of both sides of the equation to eliminate the exponent on the left side,

=> x = √4/3

When we simplify this one further, then we get

=> x = ±2/√3.

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for each mentor artist, write an equation and a graph showing the proportional relationship between the art sold and your total commission.

Sara's pieces of art sell for $25 each your commission is 60%

Ravi's pieces of art sell for $2000 each your commission is 25%

x represents the number of pieces of art sold

y represents the total commission

K represents the commission per piece of art

Answers

The equations of the commissions are

Sara: y = 15xRavi: y = 500x

How to determine the equations and the graph

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

Sara's pieces of art sell for $25 and  commission is 60%Ravi's pieces of art sell for $2000 and commission is 25%

Also from the question, we have:

x represents the number of pieces of art soldy represents the total commission

This means that:

Commission = Unit rate * Commission proportion * Number of pieces

Using the above as a guide, we have the following:

Sara: y = 25 * 60% * x

Ravi: y = 2000 * 25% * x

Evaluate

Sara: y = 15x

Ravi: y = 500x

See attachment for the graph of the commission equations

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A car is traveling at a speed of 61 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will the car travel in 20 minutes? Do not round your answers.

Answers

The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

What is speed?

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A car is traveling at a speed of 61 kilometers per hour.

Convert the speed into a kilometer per minute. Then we have

Speed = 61 / 60

Speed = 1.01667 kilometers per minute

Then the number of kilometers will the car travel in 20 minutes will be given as,

1.01667 = d / 20

d = 1.01667 x 20

d = 20.33 kilometers

The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

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(Constant of Proportionality, Graphing Proportional Relationships, Real-World Proportional Problems HC) An ice cream shop serves chocolate milkshakes that are made with ice cream and milk. There is a proportional relationship between the number of scoops of ice cream and the amount of milk needed to make them. For every 1 scoop of ice cream, cup of milk is needed, and for every 5 scoops of ice cream, cups of milk are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many cups of milk are needed for 18 scoops of ice cream? (2 points)

Answers

The constant of proportionality is 2

The equation of the relationship is s = 2mThe number of cups for 18 scoops is 9 cups

How to determine the constant of proportionality

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

1 scoop of ice cream = 1/2 cup of milk

5 scoops of ice cream = 2.5 cups of milk

The constant of proportionality (k) is then calculated as

k = Scoop of ice cream/Cup of milk

So, we have

k = 5/2.5

Evaluate

k = 2

The equation of the relationship

In (a), we have:

k = 2

A proportional relationship is represented as

s = km

Where

s = scoop of ice cream

m = cup of milk

So, we have

s = 2m

How to graph the relationship

In (b), we have

s = 2m

To graph the relationship, we start by generating a table of values and then plot the points

Number of cups for 18 scoops

Recall that

s = 2m

So, we have

18 = 2m

Divide by 2

m = 9

Hence, the number of cups is 9

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Wht is the missing part of 1/7 of ... 1/35

Answers

The missing part is 1/5. The complete expression is 1/7 of 1/5 is 1/35.

What is fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

We have the expression:

1/7 of (...) = 1/35

To find the missing fraction:

Let n be the number.

So,

1/7(n) = 1/35

n = 7/35

n = 1/5

Therefore, 1/5 is the missing part.

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Find the output, y, when the input, z, is -4.
y=
-8-6 -4
8
6
a f
Y
4-
2-
do
-2-
-4-
-6+
4
6/ 8

Answers

Answer:

y = 1

Step-by-step explanation:

locate x = - 4 on the x- axis, go vertically up to meet the graph at (- 4, 1 ), so

when input x = - 4 the output is y = 1

The steepness of a ramp is graphed using the points (0,3) and (36,0). The steepness of a second ramp is represented by the function g(x)= -1/4x+2. What is the slope of the ramp?

Answers

The slope of a line is a measure of its steepness and can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the points (0,3) and (36,0) represent the coordinates of two points on the ramp. To find the slope of the ramp, we can plug these values into the formula:

slope = (0 - 3) / (36 - 0) = -3 / 36 = -1/12

The slope of the ramp is -1/12. This indicates that the ramp is relatively flat, as a negative slope means that the line is sloping downward.

To find the slope of the second ramp, represented by the function g(x) = -1/4x + 2, we can take the derivative of the function. The derivative of a function represents the slope of the function at any given point, and it is calculated using the formula:

derivative = f(x) = -1/4

The derivative of the function g(x) is a constant value of -1/4, which means that the slope of the second ramp is also -1/4. This is a steeper slope than the first ramp, as the value of the derivative is larger in magnitude.

The product of 15 and a number has a result in 15 what is the number

Answers

Answer:

1

Step-by-step explanation:

To find an unknown number we can use properties of equality.

Algebraic Method

Another word to describe an unknown number is "variable". For the equation, I will call this variable x. Any variable can be used, but x is the most common.

We can write an equation to describe the situation. The statement says that the product of 15 and x is 15. This means that 15 * x = 15. Now we can use algebra to solve this equation.

To find x, divide both sides by 15.

x = 1

Identity Property of Multiplication

Additionally, if you know all the properties of equality, you can answer this question without doing any math. One of the properties of equality is the identity property of multiplication. The identity property states:

a * 1 = a

This means that any number multiplied by 1 is itself. So, since the factor and product are equal, the other factor must be 1. If you plug 15 in for a, you can see how this property applies to this situation.

Write a system of equations to describe the situation below, solve usi
the blanks.
Parent volunteers at Salem High School are processing yearbook orde
an option to get the basic yearbook or a deluxe option, which includes
protective cover. In Mrs. Wu's class, 21 basic yearbooks and 6 deluxe
ordered, for a total of $2,025. The students in Mr. Boyer's class ordere
and 18 deluxe yearbooks, for a total of $2,763. How much does each
The basic yearbook costs $
and the deluxe yearbook costs $
Submit

Answers

Answer: $52.57 for each basic yearbook and $153.5 for each deluxe yearbook

Step-by-step explanation:

First, do Mr. Boyer's class to find out how much each deluxe yearbook is:

2,763 ÷ 18 = $153.5

Then do, Mrs. Wu's class: First, multiply 153.5 by the 6 deluxe yearbooks ordered;

153.5 x 6 = 921

After, subtract 921 from 2,025:

2,025 - 921 = 1104

The remaining $1104 is the total cost of the 21 basic yearbooks ordered. Divide the total cost by the number of yearbooks ordered to find the unit price:

1104 ÷ 21 = 52.5714285714

Round to the nearest hundredth: $52.57

Please give brainliest

Make t the subject of n*2

Answers

After making the subject of [tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be [tex]$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$[/tex]

What is expression ?

An expression is a combination of symbols, such as numbers and operators, that represent a computation or a value. Expressions can be used to perform calculations, assign values to variables, and control the flow of a program. They are a fundamental concept in computer programming.

What is simplification?

Simplification is the process of making an expression or equation simpler, while still maintaining its meaning or function. This can be done by combining like terms, combining or removing unnecessary elements, or applying mathematical rules or identities.

For example, in algebra, simplifying an expression might involve combining the coefficients of similar terms (such as 2x + 3x = 5x), or factoring out a common factor from multiple terms (such as 2x^2 + 4x = 2x(x+2)).

Glven expression,

[tex]$$\begin{aligned}& n^2=4 \mathrm{~d}+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+t^3 / t^3 \\& n^2=4 \mathrm{~d} / t^3+1 \\& n^2-1=4 \mathrm{~d} / t^3 \\& t^3=4 \mathrm{~d} / n^2-1 \\& \mathbf{t}=\sqrt[3]{4 d / n 2-1}\end{aligned}$$[/tex]

Hence after making [tex]$\mathbf{t}$[/tex] the subject of[tex]$n^2=4 \mathrm{~d}+t^3 / t^3$[/tex] could be

[tex]$$\mathrm{t}=\sqrt[3]{4 d / n 2-1}$$[/tex]

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The vertices of triangle ABC have coordinates A(-2,-1) B(10,-1) and C(4,4). Determine and state the area of triangle ABC

Answers

Area = 1/2 * base * height

Base = A to B = 10 - (-2) = 12

Height = C down = 4 - (-1) = 5

Area = 1/2 * 12 * 5
Area = 1/2 * 60
Area = 30

Solve the following quadratic equation, leaving your answer in exact form:
2e²-8e +7= 0


Pls can anyone help it would rrly help out

Answers

Answer:

The two answers would be 0 and ln (7)

Step-by-step explanation:

Hope it helps:)

2. Lyda is taking a test worth 50 points. Her goal is to score 80%.
Write a proportion to figure out how many points she needs to accomplish her goal.

Answers

Answer: Lyda wants to score 80% on a test that is worth 50 points. To figure out how many points she needs to accomplish her goal, we can set up a proportion using her desired percentage as the proportion of points she wants to score over the total number of points on the test.

score / total points = percentage / 100

To figure out the number of points Lyda needs to score, we can use the proportion above and cross-multiply:

score * 100 = percentage * total points

We know that percentage=80 and total points =50, so we can substitute these values:

score * 100 = 80 * 50

score = (80*50) / 100 = 40

So Lyda needs to score 40 points to accomplish her goal of 80%.

The proportion would be score / total points = x/100 = percentage/100 = 40/50 = 8/10

It's worth to mention that scoring 80% on a test means she scored 40 points on a test worth 50, the minimum score to pass is 30 so she got a good grade already.

Step-by-step explanation:

1/2% in decimal
please give me my answer Also
I AM NOT ASKING for 1/2 in decimal
I am asking for 1/2 percent in decimal

Answers

Answer:

Step-by-step explanation:

We know that : Percentage means 'divided by 100'

therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005

Circle C is inscribed with 5 lines. Point C is at the center of the circle. 3 lines come out of point C and make points D, A, and B on the edge of the circle. Another line comes out of point C and goes past the edge to point E. Another line connects points D and A.
Which geometric figures are drawn on the diagram? Check all that apply.
Line segment C A
Ray A C
∠ABC

Answers

∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that Circle C is inscribed with 5 lines

Point C is at the center of the circle

3 lines come out of point C and make points D, A, and B on the edge of the circle.

Another line comes out of point C and goes past the edge to point E.

For ∠ABC

The geometric figure is not drawn.

For ∠BCE

The geometric figure is drawn.

For line segment CA

The geometric figure is drawn.

For Ray CA

The geometric figure is drawn.

For Circle C

The geometric figure is drawn.

For Ray BE

The geometric figure is not drawn.

For Line segment AE

The geometric figure is not drawn.

Hence,  ∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

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What does it mean when a problem is undecidable?

Answers

An undecidable problem is one that should have a "yes" or "no" answer but has no algorithm that can correctly answer on all inputs.

What is undecidable problem?

According to the theories of computational complexity and computability, an undecidable problem is one for which it has been demonstrated that it is impossible to create an algorithm that always yields the right yes-or-no response. As an illustration, it can be shown that there is no algorithm that can accurately predict whether arbitrary programmes will eventually halt when run.

Any question that is simply yes or no on an infinite list of inputs is a decision problem. It is customary to define the decision problem as the set of inputs for which the problem returns yes because of this. Natural numbers as well as values of other kinds, such as strings in a formal language, can be used as these inputs.

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need help plsssssssss

Answers

Answer: y<-5x+9

Step-by-step explanation:

Slope is -5, y-intercept is 9 and the shaded area is on the left side (meaning y is less than the line). The line is dotted which means that the answer will less than but not equal to.

How do you identify the solutions in solving linear inequalities in two variables *?

Answers

To identify the solutions in solving linear inequalities in two variables, you can first graph the equation on a coordinate plane. Then, you can use the boundary line to identify which regions of the plane satisfy the inequality.

Any points in the shaded regions will be solutions to the inequality. Additionally, you can use the boundary line to identify the points that are not solutions by finding the points that lie on the boundary line.

Example:

x + 2y ≥ 4

The graph of this inequality is a line with a slope of -2/1 and a y-intercept of 4/2. The line will be shaded on the side of the line containing the greater values, which in this case is the side containing the origin.

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How do you select sample size using simple random sampling?

Answers

Using the method of simple random sampling, The answer is we select sample before collecting data.

What do you mean by random sampling?

Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.

What are samples?

A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.

In simple random sampling, the sample size is determined before collecting data. There are several ways to determine the sample size, but one common method is to use a sample size calculation formula, such as: n = (z^2 * p * (1-p)) / e^2

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Find the value of x.
Use statement and reason format.

Answers

By using properties for angles we can find and solve some linear equations, there we can see that x = 30°.

How to find the value of x?

Remember that the sum of the interior angles of a triangle must give 180°, and we also know that the angle defined by a line is 180°.

Let's define N as the angle located at vertex N of the right triangle in the left side, we then can write:

2x + 90° + N = 180°

And we also can write the linear equation:

105° + 45° + N = 180°

Solving this one, we can find the value of N.

N = 180° - 45° - 105°  =30°

N = 30°

Replacing that in the equation with x we will get:

2x + 90° + 30°  =180°

2x = 180° - 90° - 30°

2x = 60°

x = 60°/2 = 30°

The value of x is 30°.

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Is Amu equal to Avogadro's number?

Answers

Therefore, amu (atomic mass unit) and Avogadro's number are not the same things.

Define amu (atomic mass unit).

A unit of measurement for atomic and molecular weight is the atomic mass unit (amu).

What is molecular weight?

Molecular weight, commonly known as molecular mass, is the mass of a substance's molecules, calculated using the atomic weight of carbon-12, which is 12.

No, amu and Avogadro's numbers are not the same things because An atomic mass unit (amu) is a unit of measurement for atomic and molecular weight. It is defined as one twelfth of the mass of a neutral atom of carbon-12. It is commonly used in chemistry to express the masses of atoms and molecules While Avogadro's number (N) is a fundamental constant of nature that relates the number of atoms or molecules in a sample to the mass of that sample. It is defined as the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms or molecules per mole.

So, amu is a unit of measurement for atomic and molecular weight, while Avogadro's number is a constant that relates the number of atoms or molecules in a sample to the mass of that sample.

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2-18. Frank wonders whether corresponding angles always have equal measure. For parts () through (d) below, use tracing paper to decide if corresponding angles have the same measure. Then determine if you have enough information to find the measures of x and y. If you do, find the angle measures and state the relationship .

Answers

The angles and their relationships are -

a) ∠x = 135° (corresponding angles), ∠y = 135° (vertical angles)

b) ∠y = 45° (liner pair angles), ∠x (not enough information provided)

c) ∠x = 135° (corresponding angles), ∠y = 45° (liner pair angles)

d) ∠x = 45° (liner pair angles), ∠y (not enough information provided)

What is angle pair relationship?

In Geometry, there are five fundamental angle pair relationships:

Complementary Angles

Supplementary Angles

Adjacent Angles

Linear Pair

Vertical Angles

a) In the first diagram -

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Similarly, ∠y = ∠x as they both are vertically opposite angles to each other.

So, ∠y = 135°.

b) In the second diagram -

∠y + ∠a =180° as they are both form a linear pair of angles.

So, ∠y = 180° - ∠a

∠y = 180° - 135°

∠y = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

c) In the third diagram -

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Now, ∠y + ∠x =180° as they are both form a linear pair of angles.

So, ∠y = 180° - ∠x

∠y = 180° - 135°

∠y = 45°.

d) In the fourth diagram -

∠x + ∠a =180° as they are both form a linear pair of angles.

So, ∠x = 180° - ∠a

∠x = 180° - 135°

∠x = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

Therefore, all the angles are and their relationships are found.

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