In the circle below, EG is a diameter. Suppose m FG = 116° and mZ GFH=69°. Find the following.

Answer:

The area of the figure is 286 cm^2

Area of upper triangle = (1/2) base X height

= (1/2) 12 X 10

= 60

The middle portion is square so

area = l^2

= 100

the base of bottom triangle = 4 + 10 + 4 = 18

height of bottom triangle = 14

so area = (1/2) base X height

= 126

total area = area of upper triangle + area of square +area of bottom triangle

= 60 + 100 + 126

= 286 cm^2

The coordinates of the final image for S' are (0, -7). The solution has been obtained by using the concept of transformation.

What is transformation?

Transformations allow for the rotation, reflection, and translation of forms on a coordinate plane. Any line can be reflected, any point can be rotated, and every vector can be translated.

We are given a triangle QRS whose vertices are Q(-6, 6), R(-6, 0),and S(0, 0). The triangle is translated 7 units right, then rotated 90° clockwise about the origin.

So, from this we get the another triangle as Q'R'S' whose vertices become as follows after translation:

Q' = (-6 + 7, 6) = (1, 6)

R' = (-6 + 7, 0) = (1, 0)

S' = (0 + 7, 0) = (7, 0)

Now, we know that the rule for 90° clockwise rotation is that (x, y) becomes (y, -x).

So, we get the coordinates as:

Q' = (6, -1)

R' = (0, -1)

S' = (0, -7)

Hence, the coordinates of the final image for S' are (0, -7).

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Concept: "Logos" has had a significant impact on Western thought. Importance: its recognition of the interplay between rational thought and empirical observation Acknowledgement: role of language and discourse in shaping our understanding of the world.

Topic: The concept of "Logos" in Greek philosophy and its significance in modern scientific fields.

The concept of "Logos" is central to Greek philosophy and has been interpreted in various ways throughout history. In its most basic sense, "Logos" refers to rational thought, speech, and language. It is often associated with the divine or the cosmic principle that governs the universe, as well as human reasoning and discourse.

The significance of "Logos" can be seen in its influence on modern scientific fields, including biology, psychology, and technology, among others. The term "biology," for example, comes from the Greek words "bios" (life) and "logos" (word or reason), reflecting the idea that the study of life requires both empirical observation and rational analysis.

Similarly, the field of psychology, which deals with the workings of the human mind and behavior, derives its name from the Greek word "psyche," meaning "soul," and "logos," meaning "reason." This reflects the idea that the study of the mind and behavior requires both empirical research and theoretical analysis.

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Translation: The Greek word "logos" is typically interpreted as the pinnacle of Western rationalist civilization, having been established by the first schools of classical philosophy. In reality, he is responsible for the names of many scientific fields, including biology, philology, psychology, technology, and others. Since it requires both mind and action, internal and external, the mental notion and pronouncing the word, the concept of "logos" does not have such an abstract meaning. Topic:____________________________________________________ Principal Concept:

Answer:

18ft cubed

Step-by-step explanation:

To solve for the volume of a triangular prism

It's Base x Height x 0.5

V = bxhx0.5

V = 4x9x0.5

V = 36x0.5

V = 18ft cubed

Answer:

Step-by-step explanation:

Center-radius equation for circle of radius r, centered at (h,k):(x−h)2+(y−k)2=r2

(h,k)=(0,0) and r=11−−√:

x2+y2=11

Answer:

58.5

Step-by-step explanation:

[tex]A=\frac{h_bb}{2}[/tex]

[tex]\frac{6.5*18}{2}[/tex]

[tex]58.5[/tex]

Answer: The inverse of the logarithmic function f(x) = log2x can be found by interchanging the roles of x and y in the function and solving for y. The steps are as follows:

Step 1: Replace f(x) with y.

y = log2x

Step 2: Interchange x and y.

x = log2y

Step 3: Solve for y.

We need to isolate y on one side of the equation. To do this, we can rewrite the equation in exponential form. Recall that the logarithmic function with base b is defined as follows:

logb(x) = y if and only if b^y = x.

Using this definition, we can rewrite the equation x = log2y as follows:

2^x = y

This means that the inverse of f(x) = log2x is given by:

f –1(x) = 2^x

Therefore, the correct answer is:

f –1(x) = 2^x.

Step-by-step explanation:

A rectangular pyramid has a rectangular base and four triangular faces that meet at a common vertex.

To match each net with its name, we need to understand the basic properties of both rectangular prism and rectangular pyramid.

A rectangular prism is a 3D shape that has six faces, and each face is a rectangle. A rectangular pyramid is also a 3D shape, but it has a rectangular base and four triangular faces that meet at a single point.
It consists of six rectangles connected along their edges to form a box-like structure.

On the other hand, the net for a rectangular pyramid is also a flat pattern, but it consists of a rectangle and four triangles attached to the edges of the rectangle.
To match each net with its name, we need to compare the features of both nets with the basic properties of both shapes. If we observe the net for a rectangular prism, we can see that it has six rectangles, which represents the six faces of the rectangular prism.

Also,

The edges of each rectangle connect with other rectangles in such a way that it forms a box-like structure. Hence, the net with six rectangles is the net for the rectangular prism.
The net for a rectangular pyramid consists of a rectangular base and four triangles attached to the edges of the rectangle.

The rectangular base is one of the features of a rectangular pyramid, and it matches with the rectangle in the net. The other four triangles are attached to the edges of the rectangle, forming a pyramid-like structure.

Therefore,

The net with a rectangle and four triangles is the net for the rectangular pyramid.
The net with six rectangles is the net for the rectangular prism, and the net with a rectangle and four triangles is the net for the rectangular pyramid.

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Step-by-step explanation:

Both of the expressions equal y....equate them

-6x + 8 = 5x-4

12 = 11x

x = 12/11 = 1  1/11

then y =  5x -4  = 5(12/11) - 4   = 1  5/11

( 1  1/11  ,  1  5/11 )

The given ratio of 0.42 to 1 means that for every 1 active subscription, there are 0.42 expired subscriptions.

What is a ratio?

The ratio is a comparison of two quantities that is expressed as a fraction. It is used to compare two values in mathematics. It is possible to write the ratio between a and b as:

a : b or a/b.

What does a ratio of 0.42 to 1 mean? The ratio of 0.42 to 1 means that there are 0.42 expired subscriptions for every 1 active subscription. It is worth noting that the ratio is less than 1, indicating that there are fewer expired subscriptions than active subscriptions.

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Answer:

Step-by-step explanation:

You want the missing segment lengths in the kite shown, where half-diagonals are 3 and 6, and one side length is 5.

The diagonals of a kite cross at right angles, so each of the triangles shown is a right triangle. The figure has left-right symmetry about the vertical axis, so x=z.

We recognize the top triangles as being 3-4-5 right triangles, so the missing side length is y = 4.

These lengths are the hypotenuse of a right triangle with legs 3 and 6. The Pythagorean theorem tells us they are ...

  x² = 3² +6²

  x² = 9 +36 = 45

  x = √(45) = √(9·5) = 3√5

The lengths x and z are ...

  x = z = 3√5

__

Additional comment

In case you have never heard of a 3-4-5 right triangle, you can find y from the Pythagorean relation:

  5² = 3² +y²

  y² = 25 -9 = 16

  y = √16 = 4

The {3, 4, 5} Pythagorean triple is one of several in common use in algebra, trig, and geometry problems. Others include {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.

Answer:

Step-by-step explanation:

You want to know if the binomial 2x³ -10x can be factored further than 2x(x² -5) and how you can tell.

Usually, when we say "factor p(x)", where p(x) is a polynomial, we mean we want it factored to factors that have integer coefficients. In many cases, the result will be a product of linear and/or quadratic factors. Here, ...

  2x³ -10x = 2x(x² -5) . . . . . is factored to integers

When we want the polynomial "factored completely", or "factored to linear factors" the restriction that coefficients be integers or real numbers is removed. The difference of squares can be factored further, but irrational values are required:

  = 2x(x -√5)(x +√5) . . . . . factored completely to linear factors

You can tell if further factoring is possible by looking at the roots of the non-linear factors in question. If those roots are rational, you can continue factoring. If they are irrational or complex, then the problem statement will tell you whether further factoring is desired.

__

Additional comment

Of course, you need to be familiar with methods of factoring and of determining the possible rational roots of a polynomial. (A good graphing calculator can help.)

The minimum value is 16 , the maximum value is 50, the first quartile is 20, the third quartile is 38 and the median is 24.

The box plot that represents the dataset is the second box plot.

The numbers would first be rearranged in ascending order. The numbers arranged in ascending order is:

16, 18, 22, 23, 25, 32, 43, 50

The five number summary are the median, minimum, first quartile, third quartile and maximum.

Median = (n + 1) / 2 = (8 + 1) / 2 = 4.5th term = (23 + 25) / 2 = 24

Minimum = 16

Maximum = 50

First quartile = (n + 1) / 4 = (8 + 1) / 4 = 2.25 term = 20

Third quartile = 3/4 x (n + 1) = 3/4 x (9/4) = 6.75th term = 38

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Hence, Y = 8X represents the equation for the quantity of parts generated by machine R.

Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. Equations are used in many disciplines, including physics, engineering, economics, and finance, to describe connections between quantities and to solve problems. For instance, the formula "2x + 5 = 11" states that the number 11 is equal to the sum of the two variables x and 5. We can determine that x equals 3 by finding a solution for x. On the basis of mathematical relationships, equations enable us to locate unknown values and create predictions.

given

We must evaluate the supplied data and search for trends to ascertain which machine generates parts at a steady rate. Calculating the ratio of parts produced for each machine over time and checking to see if the ratios are stable are two methods for achieving this.

The ratios for machine Q are:

9/1 = 9

18/3 = 6

72/9 = 8

Machine Q doesn't create parts at a constant rate since the ratios are inconsistent.

The ratios for machine R are:

8/1 = 8

24/3 = 8

72/9 = 8

As a result of the constant ratios, machine R consistently produces parts.

The ratios for machine S are:

6/1 = 6

18/3 = 6

52/9 ≈ 5.78

Machine S does not generate parts at a constant rate because the ratios are inconsistent.

As a result, we may formulate the following equation to represent the components made by machine R:

Y = kX

where k represents the machine R's constant rate of production and Y represents the quantity of components produced in minutes. Any of the ratios calculated above can be used to determine the value of k:

8 pieces per minute equals k.

Hence, Y = 8X represents the equation for the quantity of parts generated by machine R.

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Answer:

400 students altogether

Step-by-step explanation:

(100% -5%) - (45% + 25%) + 25% = 95% - 70% + 25% = 50%

200 ÷ 50% = 400

The complete tables are mentioned below for Business Employees and For Killian employees.

In mathematics, "amount" typically refers to the quantity or total of something. It is a general term that can be used to describe any kind of numerical value or magnitude, and can be expressed in various units, such as dollars, meters, liters, etc.

In many mathematical contexts, the term "amount" is used interchangeably with other related terms, such as "quantity," "total," "sum," or "value." For example, in algebra, the amount of a variable can refer to the numerical value or quantity that it represents. In geometry, the amount of a particular measurement, such as area or volume, is the total quantity of that measurement in a given shape or object.

The concept of amount is fundamental in many areas of mathematics, from basic arithmetic to more advanced calculus and statistics. It plays a central role in various mathematical operations and concepts, such as addition, subtraction, multiplication, division, and integration.

Employee  C. North                N. Vanders              M. Clark

Position     Systems                 Web                         Data

                  Analyst                  Designer                  Entry

Level           2                           3                               3

Salary        $44,000                41,000                     31,500  

COLA           2.80%                   3.20%                     4.70%

Amount      $1,232                    $1,312                      $1,483

Merit            3.60%                    7.60%                     4.50%

Amount       $1,584                    $3,116                     $1,418  

New            $47,816                  $45,428                  $34,401

Salary

For Killian employees:

Employee  Annual   Merit         COLA       Total         New

                  Salary     Increase  Increase   Increase   Salary

D. Garcia   $18,000  6.00%      7.5%          12.50%     $20,250

J. Stites      21,750    3.50%      6.5%           10.00%    $24,090

J. Spar        31,860    5.10%       6.3%          11.40%      $35,472

T. Beggins  14,615     0.70%      7.5%          8.20%      $15,798

R. Stokes     27,916   6.250%    6.3%          12.525%   $31,373

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The given series converges only when x = 0

To determine the values of x for which the series n!x⁵ⁿ converges, we can use the ratio test, which states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges, and if the limit is greater than 1, the series diverges.

Applying the ratio test to the series, we obtain |aₙ ₊ ₁ /aₙ| = |(n+1)! x⁵(n+1)/(n! x⁵)| = |(n+1)x⁵|. We simplify this expression to obtain |(n+1)x⁵|.

We then take the limit as n approaches infinity of |(n+1)x⁵|. If x is not equal to zero, this limit will approach infinity, since n+1 grows without bound as n approaches infinity, and x⁵ is a constant factor that does not affect the growth rate. In this case, the limit will be greater than 1, indicating that the series diverges.

However, if x is equal to zero, then the limit of |(n+1)x⁵| is zero, indicating that the series converges.

Therefore, the series n!x⁵n converges only when x is equal to zero.

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The steps that you should take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/20.

5. Reflect the intermediate image.

In Mathematics and Geometry, two geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the length of the image by the length of the pre-image or by multiplying the vertices by a specific scale factor.

This ultimately implies that, we would multiply the vertices of polygon ABCD by 1/20 and then apply a reflection of the intermediate image;

Vertices A' = (1 × 1/20, -6 × 1/20) = (1/20, -6/20)

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Triangles are similar by SSS rule.

The triangle similarity rule states that if two triangles have corresponding angles that are congruent, then the triangles are similar. This means that their corresponding sides are proportional in length. More formally, if two triangles ABC and DEF are similar, then:

The corresponding angles are congruent: ∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F.

The corresponding sides are proportional: AB/DE = BC/EF = AC/DF.

Similar triangles can also be used to find the height of tall objects or the distance between two objects of known height, using the angle of elevation and the properties of similar triangles.

In the Triangle ABC and CDA;

AB=CD(Given)

BC=AD(Given)

AC=AC(sides are common)

Hence,  Triangles are similar by SSS rule.

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Answer: 55 min

Step-by-step explanation:

10:40 + 1 hr = 11:40

11:40 - 5min= 11:35

1hr - 5min= 55min

Answer:

[tex]\large\boxed{\mathtt{x=8}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to solve for x.}[/tex]

[tex]\textsf{Note that our equation is in word form, let's change it into numerical form.}[/tex]

[tex]\large \tt { {4 \ plus \ 3 \ eighths \ x \ equals \ seven. } \atop {4+ \frac{3}{8} x = 7. } }[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Our goal is to find x. We should isolate x where its alone on the left side.}[/tex]

[tex]\underline{\textsf{How?}}[/tex]

[tex]\textsf{Simply subtract 4 from both sides to isolate x.}[/tex]

[tex]\large\underline{\textsf{Isolating x;}}[/tex]

[tex]\tt 4 - 4 + \frac{3}{8} x = 7 - 4[/tex]

[tex]\underline{\textsf{We should have;}}[/tex]

[tex]\tt \frac{3}{8} x = 3[/tex]

[tex]\textsf{We don't know the value of x yet. We only know 3/8 of x.}[/tex]

[tex]\textsf{For x to equal 1, multiply both sides of the equation by the \underline{reciprocal} of the fraction.}[/tex]

[tex]\large\underline{\textsf{What is a Reciprocal?}}[/tex]

[tex]\textsf{A Reciprocal is a \underline{fraction} where the Numerator and the Denominator \underline{flip}.}[/tex]

[tex]\underline{\textsf{For example;}}[/tex]

[tex]\large \tt {Flip \ the \ Numerator \ and \ the \ Denominator.} \atop {The \ Reciprocal \ of \ \frac{5}{4} \ is \ \frac{4}{5}.}[/tex]

[tex]\large\underline{\textsf{Find the Reciprocal of} \ \frac{3}{8};}[/tex]

[tex]\tt{ The \ Reciprocal \ of \ \frac{3}{8} \ is \ \frac{8}{3}.}[/tex]

[tex]\underline{\textsf{Multiply;}}[/tex]

[tex]\tt \frac{8}{3} \times \frac{3}{8} x = 3 \times \frac{8}{3}[/tex]

[tex]\large\boxed{\mathtt{x=8}}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads:}[/tex]

[tex]\large\textsf{Four plus three eighths x equals seven}[/tex]

[tex]\huge\textbf{Equation should look like:}[/tex]

[tex]\mathtt{4 + \dfrac{3}{8}x = 7}[/tex]

[tex]\huge\textbf{How will we solve for it?}[/tex]

[tex]\mathtt{4 + \dfrac{3}{8}x = 7}[/tex]

[tex]\mathtt{\dfrac{3}{8}x + 4= 7}[/tex]

[tex]\large\text{SUBTRACT 4 to BOTH SIDES:}[/tex]

[tex]\mathtt{\dfrac{3}{8}x + 4 - 4 = 7 - 4}[/tex]

[tex]\large\text{CANCEL out: 4 } \rm{-}\large\text{ 4 because it gives you 0.}[/tex]

[tex]\large\text{KEEP: 7 }\rm{-}\large\text{ 4 because it help us solve for the x}-\large\text{value.}[/tex]

[tex]\mathtt{\dfrac{3}{8}x = 7 - 4}[/tex]

[tex]\mathtt{\dfrac{3}{8}x = 3}[/tex]

[tex]\large\text{MULTIPLY }\rm{\dfrac{8}{3}\large\text{ to BOTH SIDES:}[/tex]

[tex]\mathtt{\dfrac{3}{8}x\times\dfrac{8}{3} = 3\times\dfrac{8}{3}}[/tex]

[tex]\large\text{CANCEL out: }\rm{\dfrac{3}{8}\times\dfrac{8}{3}\large\text{ because it gives you 1.}[/tex]

[tex]\large\text{KEEP: }\rm{3\times\dfrac{8}{3}\large\text{ because it gives the x}\rm{-}\large\text{value.}[/tex]

[tex]\mathtt{x= 3\times\dfrac{8}{3}}[/tex]

[tex]\mathtt{x= \dfrac{3}{1}\times\dfrac{8}{3}}[/tex]

[tex]\mathtt{x = \dfrac{3\times8}{1\times3}}[/tex]

[tex]\mathtt{x = \dfrac{24}{3}}[/tex]

[tex]\mathtt{x = 24\div3}[/tex]

[tex]\mathtt{x = 8}[/tex]

[tex]\huge\textbf{What is the overall answer?}[/tex]

[tex]\huge\boxed{\mathtt{x = 8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The calculated probability of the coin landing face-up on "tails" on all six flips is 1/64.

The probability of getting tails on a single flip of a fair coin is 1/2. Since each flip is independent of the others, the probability of getting tails on all six flips is:

P = (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2)

When evaluated, we get

P = 1/64

Therefore, the probability of the coin landing face-up on "tails" on all six flips is 1/64.

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The probability that no more than 3 of them weigh 65 lb or more is 0.0165 (approximately).

The Australian Sheep Dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian Sheep Dogs weigh 65 pounds or more. A sample of 16 adult dogs is studied. We need to determine the probability that no more than 3 of them weigh 65 pounds or more. Solution:Step 1The number of trials (n) is 16. The probability of success in one trial is p = 0.45. The probability of failure is q = 1 - p = 1 - 0.45 = 0.55.Step 2We need to find the probability that no more than 3 of them weigh 65 lb or more.P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X distribution with parameters n = 16 and p = 0.45.Using the binomial probability formula,P(X = k) = nCk * pk * q(n - k)P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)= 16C0 * 0.45^0 * 0.55^16 + 16C1 * 0.45^1 * 0.55^15 + 16C2 * 0.45^2 * 0.55^14 + 16C3 * 0.45^3 * 0.55^13≈ 0.0165 (rounded to 4 decimal places)Therefore, the probability that no more than 3 of them weigh 65 lb or more is 0.0165 (approximately).

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Answer & Step-by-step explanation:

We can make y the subject first

y = [tex]\frac{1}{5}[/tex](x + 8) - 7

Substitute values of x into the equation to find their corresponding y value

For example, when x is 0

[tex]\frac{1}{5}[/tex](0 + 6) - 7 = -5.8

When x is 1, y = -5.6

Repeat for other values of x

Here is an example of me plotting the points for x from -2 to 2:

Answer:

see attachment.

Step-by-step explanation:

To find:-

Answer:-

We need to find out the graph of the following line,

[tex]:\sf\implies y + 7 = \dfrac{1}{5}(x+6)\\[/tex]

For graphing this line we need to find at least two coordinates through which the graph passes . We can find out the third point to check if the other coordinates are correct.If all the three points do not come in a straight line , then there is some mistake .

Now solve out for any of the variables , i am solving out for "y" .

For that subtract 7 on both the sides,

[tex]:\sf\implies y =\dfrac{1}{5}(x+6)-7 \\[/tex]

Substitute x = 4 :-

[tex]:\sf\implies y =\dfrac{1}{5}(4+6)-7 \\[/tex]

[tex]:\sf\implies y = \dfrac{10}{5}-7 = 2-7 \\[/tex]

[tex]:\sf\implies \pink{ y =-5} \\[/tex]

Therefore one of the coordinate to mark on the graph is (4,-5) .

Again, substitute x = -6 ,

[tex]:\sf\implies y =\dfrac{1}{5}(-6+6)-7\\[/tex]

[tex]:\sf\implies y = 0 - 7 \\[/tex]

[tex]:\sf\implies \pink{ y = -7} \\[/tex]

Therefore the second coordinate to mark on the graph is (-6,-7) .

After marking these two points join the points by drawing a line. The line will represent the graph of the given equation.

You can see attachment for the graph for the same .

The volume of the given prisms above is calculated as follows:

a.) = 432m³

b.) = 135m³

C.) = 1,332m³

For prism a:

Divide the prism to get two solid shapes and then add up the calculated volumes of each.

Vol of First shape = length× width× height

H = 12m

w = 4m

L = 7m

Vol = 12×4×7 = 336m³

Vol of second shape ;

=2( 4×4×3)

= 2 × 48

= 96m³

Therefore the volume of prism A = 336+96 =432

For prism b:

Volume= BH

B = area of the base

H = height of the prism

Volume = 1/2×5 × 6 × 9

= 5×3×9

= 135m³

For prism C:

Divide the prism to get two solid shapes and then add up the calculated volumes of each.

Vol of first shape = 5×15×12 = 900m³

Vol of second shape;

=2(6×12×3)

= 2(216)

= 432 m³

Volume of prism C = 900+432

= 1,332m³

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Answer:

6. closed

7. open

8. open

Step-by-step explanation:

im so sorry if its wrong im not entirely sure

Answer:

Let the fraction be represented by "a/b".

According to the problem statement, we can create two equations:

Equation 1: (a-1)/(b+2) = 1/2

Equation 2: (a+3)/(b-2) = 1 1/4 = 5/4

We can simplify Equation 1 by cross-multiplying to get:

2(a-1) = b+2

2a - 4 = b + 2

2a = b + 6 --- (Equation A)

Similarly, we can simplify Equation 2 by converting 1 1/4 to an improper fraction:

5/4 = 1 + 1/4 = 4/4 + 1/4 = (4+1)/4 = 5/4

So, Equation 2 becomes:

5(a+3) = 4(b-2)

5a + 15 = 4b - 8

5a = 4b - 23 --- (Equation B)

Now, we have two equations (Equation A and B) with two unknowns (a and b). We can solve for one variable in terms of the other and substitute in either equation to find the value of the other variable. Here, we will solve for 'b' in Equation A:

2a = b + 6

b = 2a - 6

Substitute this value of 'b' in Equation B:

5a = 4b - 23

5a = 4(2a - 6) - 23

5a = 8a - 47

3a = 47

a = 47/3

Substitute this value of 'a' in Equation A to find 'b':

2a = b + 6

2(47/3) = b + 6

94/3 - 6 = b

b = 76/3

Therefore, the fraction is (a/b) = 47/76.

The function is defined by this set of rules and we got the cost of mailing a letter weighing 2.5 ounces from the United States to Mexico in 2018 using function P is $2.89.

Based on the rules, the function P is defined as follows:

P(w) = 1.15, if 0 < w ≤ 1

P(w) = 1.99, if 1 < w ≤ 2

P(w) = 2.89, if 2 < w ≤ 3

P(w) = 3.30 + 0.45(w-3), if 3 < w

This function gives the cost, in dollars, of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces, w.

To find the cost of mailing a letter weighing 2.5 ounces using function P, we need to evaluate P(2.5). Based on the rules defined above, we can see that 2 < 2.5 ≤ 3. Therefore, the cost of mailing a letter weighing 2.5 ounces would be:

P(2.5) = 2.89

So, it would cost $2.89 to mail a letter weighing 2.5 ounces from the United States to Mexico in 2018 using function P.

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    ΔFIT ≅  ΔRIS triangle  are congruent.

How do triangles work?

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point.

                       The triangle's three angles add up to a total of 180 degrees. A triangle is a closed, two-dimensional geometry with three sides, three angles, and three vertices. Polygons include triangles as well.

 In figure ,

              FI = IS

              RI = IT

            ∠FIT = ∠RIS

           ΔFIT ≅  ΔRIS

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