Jack found an antique coin as shown. what is the area of the coin?

a. There is no value of the missing monomial that will satisfy the equation.

b. The missing monomial is ±2

c. The missing monomial is ±15

What is monomial?

A polynomial with only one word is called a monomial. An algebraic expression known as a monomial typically has one term, but it can also have numerous variables and a greater degree.

The given equations can be solved by using the algebraic identity:

(a+b)(a-b) = a² - b²

Using this identity, we can determine the missing monomials in each equation:

1. (-b⁴)(b⁴+)=121a¹⁰-b⁸

Expanding the left-hand side of the equation, we get:

()b⁴ - b⁸ + b⁴() - b⁸() = b⁴() - b⁸(*)

Since the right-hand side of the equation is 121a¹⁰ - b⁸, we can equate the coefficients of b⁸ and a¹⁰ on both sides of the equation:

Coefficient of b⁸:

-1 = -1

Coefficient of a¹⁰:

0 = 121

The coefficient of a¹⁰ is not equal, which means that there is no value of the missing monomial that will satisfy the equation.

2. 100m⁴ - 4n⁶=(10m²-)(10m²+)

Using the algebraic identity, we can write:

(10m² - *)(10m² + ) = (10m²)² - ()²

= 100m⁴ - (*)²

Since the left-hand side of the equation is 100m⁴ - 4n⁶, we can equate the coefficients of m⁴ and n⁶ on both sides of the equation:

Coefficient of m⁴:

100 = 100

Coefficient of n⁶:

-4 = - (*)²

Solving for the missing monomial:

(*)² = 4

(*) = ±2

Therefore, the missing monomial is ±2, and the equation can be written as:

100m⁴ - 4n⁶ = (10m² - 2)(10m² + 2)

3. m⁴ - 225c¹⁰ = (m² - )( + m²)

Using the algebraic identity, we can write:

(m² - )( + m²) = (m²)² - (*)²

= m⁴ - (*)²

Since the left-hand side of the equation is m⁴ - 225c¹⁰, we can equate the coefficients of m⁴ and c¹⁰ on both sides of the equation:

Coefficient of m⁴:

1 = 1

Coefficient of c¹⁰:

-225 = - (*)²

Solving for the missing monomial:

(*)² = 225

(*) = ±15

Therefore, the missing monomial is ±15, and the equation can be written as:

m⁴ - 225c¹⁰ = (m² - 15)(15 + m²)

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Recall the definitions for congruence and similarity.

similar - the shapes are the same shape but are different sizes

congruent - the shapes are identical

Now if you have two polygons, assuming that they are identical to start out with (If not you won't be able to solve the problem. Do you see why?) and you perform the operations to one of them, the translation and the rotation will not change anything. But the dilation will make one shape 1/2 as big as the other. So in this case the two polygons are similar but not congruent.

The value of the angle QSR in the given circle containing lines and tangents is 120 degrees.

A circle is a two-dimensional geometric object made up of all points on a plane that are equally spaced from a central fixed point. The radius of a circle is the distance from the centre to any point on the circle. One of the most fundamental and significant geometric forms, the circle has many uses in mathematics, science, and engineering, including the study of trigonometry, coordinate geometry, and calculus. Moreover, circles are utilised in numerous practical contexts, including the creation of wheels, gears, and lenses as well as the simulation of physical phenomena like the motion of planets and electrons.

The measure of angle QSR is determined using the formula:

angle QSR = arc a + arc b / 2

Here, arc a = 150 and arc b = 90 thus:

angle QSR = 150 + 90 / 2

angle QSR = 240 / 2 = 120 degrees.

Hence, the value of the angle QSR in the given circle containing lines and tangents is 120 degrees.

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The caloric content in candy A is 269 and that of candy B is 255.

The caloric content is the quantity of energy required to increase the temperature of one liter of water by one degree. A calorimeter was initially used to determine a food's calorie count.

Let us consider:

Caloric content of Candy A = x

Caloric content of Candy B = y

We can thereby make two equations:

Eqn 1: 1x + 2y = 779

Eqn 2: 2x + 1y = 793

By elimination method, we have

2x + 4y = 1558

Solving for x by subtracting with Eqn 2, we have,

3y = 765

y = 765 ÷ 3

y = 255.

Now substituting the value of y in Eqn 2, we have:

2x + 1y = 793

2x + 1 × 255 = 793

2x + 255 = 793

2x = 793 - 255

2x = 538

x = 538 ÷ 2

x = 269.

Hence caloric content in candy A is 269 and that of candy B is 255.

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Answer: the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7)

Step-by-step explanation:

Given a1=38,a17=-74. a17=a1+(n-1)d. =38+(17-1)d. -74=38+16d. -74-38=16d. -112=16d. d= -7. the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7).

Answer: 7

Step-by-step explanation: number adds up by 7

The length of FG is 40 units.

What are parallel lines?

Two or more lines that are consistently parallel to one another and that are located on the same plane are referred to as parallel lines. No matter how far apart parallel lines are, they never cross. The relationship between parallel and intersecting lines is the reverse. The lines that never meet or have any possibility of meeting are known as parallel lines.

Since FG is parallel to CD, triangles CDE and FGE are similar. Thus, we can set up the following proportion:

CE/CD = FG/FE

Substituting the given values, we get:

32/16 = FG/20

Simplifying the left side, we get:

2 = FG/20

Multiplying both sides by 20, we get:

FG = 40

Therefore, the length of FG is 40 units.

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Step-by-step explanation:

draw a triangle then label corners a and b. spread them 120 degrees apart and there you have it.

The most appropriate representation to show the relationship between the number of chapters and the total pages of a book would be a scatter plot titled "School Library".

with the x-axis labeled "Number of Chapters" ranging from 0 to 20 and the y-axis labeled "Total Pages" ranging from 0 to 275 with points at (3, 18), (4, 38), (5, 45), (8, 85), (10, 76), (12, 145), (13, 138), (14, 160), (16, 180), and (20, 220).

A scatter plot is a graph used to display the relationship between two variables. In this case, the two variables are the number of chapters and the total number of pages in a book. The plot consists of dots, each representing a single data point. The x-axis represents the independent variable, which in this case is the number of chapters. The y-axis represents the dependent variable, which is the total number of pages. By plotting each data point on the graph, it is easier to visualize the relationship between the two variables.

A line graph is not appropriate for this situation because it suggests a continuous relationship between the two variables, which is not the case here. The number of chapters and total pages are discrete variables, and there is no natural order to the data points that would justify connecting them with a line.

The first scatter plot option is not appropriate because it shows the y-axis ranging up to 450, which is much higher than the maximum value of 275 for the total pages in this data set. This exaggerates the differences between the data points and can be misleading.

The chosen scatter plot is appropriate because it clearly shows the relationship between the number of chapters and the total pages of a book. It is easy to see that as the number of chapters increases, the total pages also tend to increase. The scatter plot also helps to identify any outliers or patterns in the data that may not be apparent from just looking at the numbers. It is a visual tool that helps to quickly understand the data and draw conclusions from it.

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Therefore , the solution of the given problem of triangle comes out to be the desired outcome is demonstrated.

If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

Area is equal to (sum of parallel edges) / 2 * (distance between them)

=>  WXYZ area equals (WZ plus XY) / 2 * hS

=>  (XM / XY)2 equals Area of WXM / Area of WXY

=>  XM / XY = 1/2

=>  WXM area divided by WXY area equals (1/2)2 = 1/4.

=>  WXY plus WXM together make up the area of WXYZ.

=>  WXY / 2 + WXM / 4 equals (WZ + XY) / 2 * h

=> WZ * h equals WXY * h plus 2 * WXM:

=>  (WZ - WXY) / 2 * h equals WXM

=>  WXYZ area equals (WZ plus XY) / 2 * h

=>  (WZ+WXY+(WZ-WXY)) / 2 * h

=> (2WZ) / 2 * h

=>  WZ * h

=> WXYZ Area equals 2 * WXM Area

Thus, the desired outcome is demonstrated.

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The monthly payment on a purchase of a $10,000 car at 5.9% for 4 years is: C. $234.39.

To calculate the monthly payment for a car loan, we can use the formula:

M = P [ i(1 + i)^n / ((1 + i)^n – 1) ]

Where:

M = Monthly payment

P = Principal (he amount of the loan)

i = Monthly interest rate (annual interest rate divided by 12)

n = Number of months in the loan term

Using this formula with the given information, we get:

P = $10,000

i = 5.9% / 12 = 0.004917

n = 4 years x 12 months/year = 48 months

M = $10,000 [ 0.004917(1 + 0.004917)^48 / ((1 + 0.004917)^48 – 1) ]

M = $234.39 (rounded to the nearest cent)

Therefore, the answer is option C.

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Angles corresponding with ∠8 are ∠4 and ∠12.

In geometry, corresponding angles are angles that are in the same relative position at the intersection of two lines when a third line crosses them. When two lines are intersected by a third line, they form pairs of corresponding angles that are congruent, meaning they have the same measure.

In the given figure;

Lines r,s,t and u are parallel lines.

Angles ∠8 and ∠12 are in corresponding angle  ( line t and u are parallel ands line intersect it)

Angle ∠4 and ∠8 are corresponding angle (line r and s are parallel and t line intersect it)

Hence, Angles corresponding with ∠8 are ∠4 and ∠12.

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The area of the triangle is: 24 unit²

What is an area ?

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is typically measured in square units, such as square meters or square feet. The area of a shape is calculated by multiplying its length by its width, or by using a specific formula for the shape.

We can find the area of the triangle by using the formula:

Area = 1/2 * base * height

where the base is the distance between points A and B, and the height is the distance from point C to the line containing AB.

The distance between points A and B is 4 units (since they have the same x-coordinate). To find the height, we can use the equation of the line containing AB, which is:

y = 4x - 3

Substituting x = 4 (the x-coordinate of point C) gives us:

y = 4(4) - 3 = 13

So the height is 13 - 1 = 12 units.  

Therefore, the area of the triangle is:

Area = 1/2 * base * height

= 1/2 * 4 * 12

= 24

So the answer is not one of the given choices. The correct answer is 24.

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Libby is correct in claiming that a function with a domain of all real numbers and is increasing everywhere must have all real numbers as its range.

Libby is correct. If a function is increasing throughout its domain, the y-values become greater as x approaches infinity.

This is because the function can take any y-value without restriction as x approaches positive or negative infinity.

The domain of the function is all real numbers, it means that the function is increasing for every x-value, and there are no limits to how large or small x can be.
The given function has a domain of all real numbers, which means it is defined for any value of x.
The function is increasing throughout its domain, which means that as x increases, the y-value of the function also increases.

Conversely, as x decreases, the y-value of the function decreases.
Since there is no restriction on the x-values in the domain, we can let x approach positive infinity to find the largest possible y-value, and negative infinity to find the smallest possible y-value.
As x approaches positive infinity, the y-value of the function keeps increasing without any upper limit, meaning that the function can take any arbitrarily large positive y-value.
Similarly, as x approaches negative infinity, the y-value of the function keeps decreasing without any lower limit, meaning that the function can take any arbitrarily large negative y-value.
Therefore, the range of the function must include all real numbers since the function is able to take any positive or negative y-value without restriction.

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Answer:

here you go

Step-by-step explanation:

The percent of change from 8,000 to 6,000 can be calculated using the formula:

�������;�ℎ����=���;�����−���;��������;�����×100Percent;change=Old;ValueNew;Value−Old;Value×100

Substituting the given values, we get:

�������;�ℎ����=6,000−8,0008,000×100Percent;change=8,0006,000−8,000×100

Therefore, there is a decrease of 20% from 8,000 to 6,000.

Answer:  decreases 6000 to 8000 = 33.33

x-    

6000−50005000×100 = 20%

Step-by-step explanation:hope that helps have a great day and stay safe (;

Answer:

+ or - (7)

Step-by-step explanation:

5-|p+6|= -8

-|p+6|=-8-5

|p+6|= 13

p+6 = + or - (13)
so case 1
p+6 = 13
p = 7
case 2

p+6 = -13
p+ -7

Answer: 63 toys were in each box

Step-by-step explanation: if you take the amount of toys (315) and divide it by the amount of boxes (5) you get 63 toys in each box

Answer:

63 toys

Step-by-step explanation:

Clearly, in this question we've to divide.

Given 315 toys = fixed in 5 boxes.

Toy in each box = 315/5 = 63.

Hence, x = 5 - an is the answer to the equation x + a = 5 for any value of a as the problem in order to solve the x + a = 5 equation family.

A simple formula is a declaration that two forms are equal. It has two sides, the lower half (LHS) and the right-hand side (RHS), which are divided by the equal sign (=). In order to prove that an equation is correct, one or more uncertain variables may exist.

For instance, the solution 3x + 5 = 14 has a single unknowable variable, x. We must rearrange the equation to find the value of x by carrying out actions that preserve equality, such as deducting 5 from both sides of the equation:

given

We must isolate x on one side of the problem in order to solve the x + a = 5 equation family. By taking an away from both sides, we may accomplish this:

x + a - a = 5 - a

By condensing the left side, we obtain:

x = 5 - a

Hence, x = 5 - an is the answer to the equation x + a = 5 for any value of a as the problem in order to solve the x + a = 5 equation family.

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The shaded part of the figure in choice B is divided into three equal parts

There are 12 equal parts in total so each activity takes up 1/12.

What is the fraction?

A fraction is a part of a whole or a ratio of two numbers expressed with a horizontal line between them.

Part A: The shaded part of the figure in choice B

is divided into three equal parts

there are three kinds of activities

Part B: According to the choice B of part A. there are 12 equal parts in total so each activity takes up 1/12.

figure in all the parts of the choice up to B of part A, get 12 equal parts

Hence, The shaded part of the figure in choice B is divided into three equal parts

There are 12 equal parts in total so each activity takes up 1/12.

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Answer:

a. 9/16 or 0.5625

b. 1.331 or 1331/1000

Step-by-step explanation:

I’m assuming you meant a^2 and b^3

a. The function n(p) that represents the cost of the paints with the 15% discount is n(p) = 6.99p - 0.15(6.99p).

b. The 15% discount reduces the cost of the paints from 34.95 to 29.70.

Discount is term used for reduction in the original price of a good or service. It is a common practice used by retailers and businesses to attract customers.

a. The function n(p) that represents the cost of the paints with the 15% discount is given by:

n(p) = 6.99p - 0.15(6.99p)

= 5.94p

b. The cost of purchasing 5 paints before the discount is 6.99 x 5 = 34.95.

The cost of purchasing 5 paints after the discount is 5.94 x 5 = 29.70.

Therefore, the 15% discount reduces the cost of the paints from 34.95 to 29.70.

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Function composition is a mathematical concept that involves combining two or more functions to create a new function. A real-life example of function composition might involve a company that uses a software program to calculate payroll. The program might use one function to calculate an employee's hourly rate based on their salary, and another function to calculate their total hours worked based on their timecard data. These two functions could be combined using function composition to create a new function that calculates the employee's total pay.

As for multiplying a binomial with a trinomial, here's an example:

(2x + 3)(4x² + 5x - 6)

To solve this, we use the distributive property of multiplication, which involves multiplying each term in one set of parentheses by each term in the other set of parentheses. We can break this down into three separate multiplications:

2x (4x² + 5x - 6) = 8x³ + 10x² - 12x

3 (4x^2 + 5x - 6) = 12x² + 15x - 18

Adding these two results together, we get:

(2x + 3)(4x² + 5x - 6) = 8x³ + 22x² + 3x - 18

Therefore, the product of the binomial (2x + 3) and the trinomial (4x² + 5x - 6) is 8x³ + 22x² + 3x - 18.

[tex] \: [/tex]

Answer:

x⁻²· x⁻²

Step-by-step explanation:

x⁻⁴ = x⁻²· x⁻² = x⁽⁻² ⁺ ⁻²⁾ = x⁻⁴

The number of the elements which are present in the set B is given by the term 85.

The symbol "" can be used to represent the intersection of sets. According to the definition given above, the intersection of two sets A and B is the collection of all the items that are shared by both sets. The intersection of A and B can be conceptualised as A B.

The largest set containing all the items shared by X and Y is the intersection of two given sets, let's say X and Y. The intersection of two sets can be an empty set, meaning that there are no elements in the intersection set, or it can be a set containing at least one member. If A and B are two sets with the relationship A B =, then A and B are referred to be disjoint sets. Hence, there are no elements at the point where A and B meet.

The set A contains 57 elements so,

n(A) = 57

total number elements in either set A or set B is 136.

n(A ∪ B) = 136

if the sets A and B have 6 elements in common,

n(A ∩ B) = 6

By using the formula for Union and Intersection of Sets,

n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

136 = 57 + n(B) - 6

136 = 51 + n(B)

n(B) = 85.

Therefore, the number of element in B is 85.

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Answer:

10.14 inches square

Answer:24

Step-by-step explanation:

Based on this finding, the following conclusion can be drawn:
On average, students who spent more time studying performed worse on the test.

The correlation coefficient only accounts for the relationship between the two variables and not the variance,

so we cannot say that study time accounted for 65% of the variance in test performance.

From the student question, a Pearson's correlation of -0.65 was found between the number of minutes studying for a test and test performance in a sample of 300 students.

Based on this finding, the following conclusion can be drawn:
On average, students who spent more time studying performed worse on the test.

This is because the Pearson's correlation of -0.65 indicates a moderate negative relationship between study time and test performance.

However, it's important to note that correlation does not imply causation, so we cannot conclude that spending more time studying causes students to perform more poorly.

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Difference between interval measurement and ratio measurement is Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point. So, option C is correct.

Interval measurement uses numeric values with equal intervals.

This means that the difference between any two adjacent values on the scale is always constant.

However, the zero point on this scale is arbitrary, meaning it does not represent the absence of the characteristic being measured.

Ratio measurement, on the other hand, also uses numeric values with equal intervals, but it has an absolute zero point.

This means that the zero point on a ratio scale represents the complete absence of the characteristic being measured.

As a result, ratio scales can be used to perform more advanced mathematical operations, such as multiplication and division.
To summarize, the main difference between interval and ratio measurement lies in the zero point of their scales. Interval measurement scales have an arbitrary zero point, whereas ratio measurement scales have an absolute zero point.

The correct choice is option C . Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.

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Question:-

Which of the following statements describes the difference between interval measurement and ratio measurement?

A) Ratio measurement is used for continuous data, whereas interval measurement is used for noncontinuous data.

B) Interval measurement uses numeric values with equal intervals, whereas ratio measurement uses numeric values with unequal intervals.

C) Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.

D) Ratio measurement uses numeric values without fixed meaning, whereas interval measurement uses numeric values with fixed meaning.