The function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.
What is reflection of a function?A function can be transformed by flipping its graph around an axis, which is known as a reflection function. Reflecting or reflection in mathematics, and more precisely in geometry, refers to flipping. Hence, a function's reflection is essentially the mirror image of the supplied function or graph. As a result, reflecting functions are a common name for them.
The given function is: f(c) = 6 (1/3)ˣ.
When a function is reflected along the y-axis the coordinates of the graph change as follows:
(x, y) → (-x, y)
The function f(c) = 6 (1/3)ˣ when reflected will have the function g(c) as:
g(c) = -6(1/3)⁻ˣ
Hence, the function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.
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Mathematics Grade 11 Capricom Sou SECTION A Part 1 Solve for x in the following equation by using exponential rules 1. 27**** = 3³x² x 9
The solution to the expression is x = 1/9
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
27**** = 3³x² x 9
Express properly
27 = 3³x² * 9
We can start solving this equation by rearranging it to isolate the variable x:
27 = 243x
Now we divide both sides by 243 to find x
x = 27/243
Evaluate
x = 1/9
Hence, the solution is 1/9
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The height of a triangle is 2cm more than base the area of the triangle is 10cm^2 find the height
If the height of a triangle is 2 cm more than base and the area of the triangle is 10 cm then the height is, 7 cm
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
The area of a triangle is given by the formula:
Area = (base x height) / 2
We are given that the area is 10 cm² and that the height is 2 cm more than the base.
Let's call the base "b".
Then, the height is "b + 2".
We can substitute these values into the area formula:
10 = (b x (b + 2)) / 2
Expanding the right side:
10 = (b² + 2b) / 2
Multiplying both sides by 2:
20 = b² + 2b
Subtracting b² from both sides:
20 - b² = 2b
Factoring the left side:
(10 - b)^2 = b²
Taking the square root of both sides:
|10 - b| = b
Adding b to both sides:
10 = 2b
Dividing both sides by 2:
5 = b
So, the base of the triangle is 5 cm and the height is b + 2 = 5 + 2 = 7 cm.
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how to use calculus cheat sheet?
A calculus cheat sheet can be a helpful tool to assist you in studying and reviewing calculus concepts.
Here are some tips for how to use a calculus cheat sheet effectively:
1. Familiarize yourself with the content: Take the time to read through the entire cheat sheet to get a sense of what topics are covered and how the information is organized.
2. Use it as a study aid: A calculus cheat sheet can be a helpful study aid to review concepts and formulas before a test or exam. Work through practice problems and apply the concepts you have learned.
3. Keep it handy: Print out the cheat sheet or save it to your phone or computer so that you can refer to it whenever you need to.
4. Use it as a reference: As you work on calculus problems, use the cheat sheet to remind yourself of key concepts, formulas, and rules.
5. Customize it: You can create your own cheat sheet, which includes the formulas and concepts that you find most challenging. This will help you focus on the areas that you need to improve upon.
Remember that while a calculus cheat sheet can be a helpful tool, it is important to develop a deep understanding of calculus concepts through practice, problem-solving, and building intuition. The cheat sheet should be used as a supplement to your learning, not a replacement for it.
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find the unit tangent vector T and the curvature k for the following parameterized curver(t) = <9 cos t, 9 sin t, sqrt(3) t>
The unit tangent vector T and the curvature k is √2/3
Unit Tangent Vector and Curvature are two important concepts in vector calculus that are used to describe the behavior of curves in space.
To find the Unit Tangent Vector, we must first find the derivative of the curve. The curve is defined as (t) = <9 cos t, 9 sin t, √(3) t>, so taking the derivative with respect to t, we get:
d(t) / dt = < -9 sin t, 9 cos t, √(3) >
Next, we want to normalize this vector to get the Unit Tangent Vector, T. To do this, we divide the vector by its magnitude, which is given by:
=> √((-9 sin t)² + (9 cos t)² + (√(3))²)
=> √(81 + 81 + 3) = 9 √(3)
So, the Unit Tangent Vector is given by:
T = d(t) / dt / |d(t) / dt|
T = < -9 sin t / 9 √(3), 9 cos t / 9 √(3), √(3) / 9 √(3) >
T = < -sin t / √(3), cos t / √(3), 1 / 3 √(3) >
To find the Curvature, we use the formula:
k = |dT / dt|
where T is the Unit Tangent Vector and dT / dt is the derivative of the Unit Tangent Vector. To find dT / dt, we take the derivative of T with respect to t:
dT / dt = < cos t / √(3), -sin t / √(3), 0 >
Finally, the magnitude of dT / dt gives us the Curvature:
=> √((cos t / √(3))² + (-sin t / √(3))² + (0)²)
=> √(1 / 3 + 1 / 3) = √(2 / 3) / √(3)
So, the Curvature is given by:
k = √(2 / 3) / √(3)
k = √2 / 3
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How do I work this, don’t feel rushed I have until morning!
Step-by-step explanation:
Perimeter of a Semicircle
[tex](\pi )(r) + 2r[/tex]
R = 0.6 since that's half the diameter
[tex](3.14)(0.6) + (2)(0.6)[/tex]
[tex]1.884 + 1.2 = 3.084[/tex]
Which rounds to 3.1
please help out with geometry answers
The area of the left over wood is
28.54 square cmArea of the kite
786.72 square cmperimeter of the kite
81.94 cmHow to find the area of the left over woodThe area of the left over wood is given by
= area of the circle - area of the pentagon
area of the circle
= pi * r^2
= pi * 5^2
= 78.54 square cm
area of the pentagon
= 5/2 * a * 5
solving for a
360 / 5 = 72
72 / 2 = 36
cos 36 = a / 5
a = 5 cos 36 = 4
area of the pentagon = 5/2 * 4 * 5 = 50 sq cm
left over wood = 78.54 - 50 = 28.54 square cm
Area and perimeter of kite
area of kite = product of the two diagonals
length of one of the diagonals = 2 * KT = 2 * 12 = 24 cm.
The second diagonal
tan 30 = KT / x
x = 12 / tan30 = 20.78
the length = 12 + 20.78 = 32.78
area of the kite = 32.78 * 24 = 786.72 square cm
perimeter of the kite
= addition of the sides = 2(shorter side + longer side)
Using Pythagoras rule
shorter side = √(12² + 12²) = 16.97
longer side = √(20.78² + 12²) = 24
perimeter = 2 (16.97 + 24) = 81.94 cm
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a negative divided by a positive become?
When a negative number is divided by a positive number, the result is always negative.
Let's use the example (-6) / 2 again. We can write this expression as:
(-6) / 2 = (-1) * 6 / 2
We can then simplify the expression on the right-hand side by multiplying -1 and 6, which gives us:
(-1) * 6 / 2 = -6 / 2
Now, we can divide 6 by 2, which gives us:
-6 / 2 = -3
So we see that the quotient is negative.
We can generalize this to any negative number divided by a positive number. Let's say we have a negative number -a and a positive number b. We can write the expression as:
(-a) / b = (-1) * a / b
Multiplying -1 and a gives us:
(-1) * a / b = -a / b
So we see that the quotient is negative, since -1 times a is negative, and dividing a negative number by a positive number results in a negative quotient.
Therefore, we can conclude that when a negative number is divided by a positive number, the result is always negative.
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If Figure 1 is similar to Figure 2, which of the following must be true?
there just reflected because the shape is just refected to the other side it the same but smaller
In the figure below, points E, G, A, B, and C lie in plane X.
Points D and F do not lie in plane X.
For each part below, fill in the blanks to write a true statement.
Following are the given complete statements:
(a) Another name for plane X is plane EABC.
(b) F, D, and C are distinct points that are collinear.
(c) A, B, C and G are distinct points that are coplanar.
What is plane ?A plane is a flat, two-dimensional surface that extends infinitely in all directions. It is a mathematical concept used in geometry and is often represented as a flat sheet or a graph on a coordinate system. In the real world, a plane can be thought of as a flat surface such as a tabletop, a piece of paper or a wall.
According to the given information :(a) Another name for plane X is plane EABC.
(b) F, D, and C are distinct points that are collinear.
(c) A, B, C and G are distinct points that are coplanar.
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If g(x) = x², what is the value of g(a + 2)?
Answer:
[tex](a+2)^2[/tex]
Step-by-step explanation:
Substitute [tex]x=a+2[/tex] into [tex]g(x)[/tex].
I need help with problem
Answer:
Below
Step-by-step explanation:
Since all of the lines are parallel and cut by a transversal .... the
corresponding angles are equal
8x - 11 = 7x +8
x = 19
The average distance travelled per day for each team is 145 km.
A team of Alaskan huskies travels at 15 km per hour, with an 18 minute rest after every 3 hours.
A team of Siberian huskies runs more quickly at 20 km per hour, but requires a 30 minute rest after every two hours.
How long, in simplified hours and minutes, will it take for each team to run the daily average of 145 km?
Answer:
Alaskan huskies take 10h 34min.
Siberian huskies take 8h 45min.
Step-by-step explanation:
Alaskan huskies : 15km/h + 18min rest after 3h
18/3= 6min rest/h
1h= 60min
60/15= 4min/km
4*145= 580min
= 9h 40min
There is three 3h in 9h 40min.
3*18= 54min
9h 40min+54min= 10h 34min
Siberian huskies : 20km/h + 30min rest after 2h
30/2= 15min rest/h
60/20= 3min/km
3*145=435min
= 7h 15min
There is three 2h in 7h 15min.
3*30= 90min
= 1h 30min
7h 15min+1h 30min= 8h 45min
what is 4x + y= 108 y=x+2
Answer:
The solution to this problem is x = 26 over 11 , y = 6 over 11.
Step-by-step explanation:
Hope this helped!
What are tables in a research paper?
Tables and figures area way of presenting data in an organized form or more in a presentable way to attract more audience.
With tables and figures, it arranges your data to a simplified form and also it makes the content easy to understand for the front person.
Tables and figures in scientific papers are wonderful ways of presenting data. Effective data presentation in research papers requires understanding your reader and the elements that comprise a table.
It also several elements, including the legend, column titles, and body.
With all this tables in a research paper helps the reader understand the content for the data more effectively and efficiently.
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find the measure of CDE,BC,AB, and CAB.
The measure of arc CDE is, 154°
The measure of arc BC is, 26°
The measure of arc AB is, 90°
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Now, By the figure, we have;
⇒ ∠APE + ∠EPD = 180°
⇒ (25x + 15)° + (33x - 9)° = 180°
⇒ 58x + 6 = 180
⇒ 58x = 180 - 6
⇒ 58x = 174
⇒ x = 3
Hence, The measure of arc CDE is,
⇒ (20x + 4)° + (33x - 9)°
⇒ (20×3 + 4)° + (33×3 - 9)°
⇒ 64° + 90°
⇒ 154°
And, The measure of arc BC is,
⇒ 90° - (20x + 4)°
⇒ 90° - (20×3 + 4)°
⇒ 90° - 64°
⇒ 26°
The measure of arc AB is,
⇒ arc AB + 90° = 180°
⇒ arc AB = 90°
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Noah would like to cover a rectangular tray with rectangular tiles. The tray has a width of 2 1/2 and an area of 4 3/4. What is the length of the tray?
The length of the rectangular tray is 1 9/10
What is a Rectangle?
Rectangle is a four-sided flat shape where every angle is a right angle (90°).
Area of a Rectangle = Length * Width
where,
Area = 4 3/4
Length = ?
Width = 2 1/2
To find the length of the tray,
Length = Area/Width
Length = 4 (3/4) / (2 1/2)
Length = (19/4) / (5/2)
Length = 19/4 * 2/5
Length = 19/10
Length = 1 9/10
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True or False? These figures are similar
True. Because they have comparable angles, the offered figures are comparable figures.
What are similar figures?Similar figures are described as two shapes that share the same shape but differ in size. For instance, similar objects are depicted but are not consistent in different-sized images of a person, such as passport size, stamp size, etc. In geometry, two comparable shapes with different side lengths or sizes are those whose dimensions are equal or have a common ratio. Examples of these shapes are similar triangles, similar rectangles, and similar squares. Scale factor is the name given to the common ratio. The matching angles are also of equal measure.
If two figures are similar, then they are represented by the symbol ‘∼’. Let us say there are two triangles, ABC and PQR, which are similar, then they are represented as;
∆ABC ~ ∆ PQR
Now if the two triangles are similar to each then their corresponding sides should be in proportion. Hence,
AB/PQ = BC/QR = AC/PR
∠A = ∠P, ∠B = ∠Q, ∠C = ∠R
Since, we can see that the angles in both the given figures are exactly the same. Thus, the given figures are similar figures.
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what kind of slope is x = -5
Answer:
undefined slope
Step-by-step explanation:
The graph of the equation x = -5 is a vertical line That passes through point (-5, 0).
The slope of a vertical line is undefined.
Jimmy is an accountant who also works part-time as a museum tour guide. Information from his tax worksheet is wages from accounting job, $75,937.84; wages from museum job, $14,937.92; interest, $839.40; and dividends, $123.45. What is Jimmy’s total income?
Jimmy’s total income is $91838.61
How to determine Jimmy's income?You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period
The given parameters that will help us to determine the income are
wages from accounting job, $75,937.84;
interest, $839.40
wages from museum job, $14,937.92;
dividends, $123.45.
Therefore Jimmy's total income is the sum of all the incomes
$(75,937.84 + 839.40 + 14,937.92 + 123.45)
Total income = $91838.61
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The net of a square pyramid and its dimensions are shown in the diagram. 1 276 2 1 12 ft 10 ft 7 8 ft What is the total surface area of the pyramid in square feet?
The surface area of the given pyramid is 336 square feet. the correct answer would be an option (F) 336 ft².
What is the total surface area of the pyramid?A square pyramid's total surface area is the total area covered by its four triangular sides and square base. The formula may be used to calculate the total surface area of a square pyramid with slant height.
The surface area of a square pyramid = a² + 2al
The figure of the square pyramid is given in the question, as shown
The surface area of the pyramid = a² + 2al
Here a = 12 ft and l = 8 ft
Substitute the values of a = 12 ft and l = 8 ft in the formula,
The surface area of the pyramid = 12² + 2 × 12 × 8
The surface area of the pyramid = 336 square feet
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The question seems incomplete, the correct question would be as:
Find the value of sin S rounded to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
sin angle S = [tex]\frac{opposite}{hypotenuse}[/tex]
sin S = [tex]\frac{30}{hypotenuse}[/tex]
To complete the ratio we need to find the hypotenuse:
a² + b² = c²
16² + 30² = c²
256 + 900 = c²
1156 = c²
√1156 = √c²
34 = c
Now substitute 34 in the sin ratio:
[tex]\frac{30}{34}[/tex] = .8824
nearest hundredth = .88
what is errors in calculations?
Errors in calculations are mistakes or inaccuracies that occur when performing mathematical calculations. They can be caused by a variety of factors, including human error, equipment malfunction, incorrect assumptions or data, and flawed methodology.
There are several types of errors that can occur in calculations, including:
Transcription errors: These occur when a number or a calculation is copied down incorrectly from one place to another, such as from a calculator to a piece of paper.
Calculation errors: These occur when the wrong calculation is used, or when a mistake is made in performing a calculation, such as forgetting to carry a digit when doing long division.
Rounding errors: These occur when numbers are rounded to a certain number of decimal places, and the resulting calculation is not as precise as it could be.
Measurement errors: These occur when the instruments used to measure quantities are not accurate, or when the measurements are not taken correctly.
Conceptual errors: These occur when the underlying concepts or principles of the problem are not fully understood, leading to incorrect calculations.
It is important to identify and correct errors in calculations to ensure the accuracy and validity of the results. Checking calculations multiple times and using multiple methods of verification can help to reduce the risk of errors.
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4^3/4^6 times 4^17 as an exponent
The value of the exponent is 4¹⁴
What area index forms?Index forms are defined as mathematical models of writing numbers that are large or small in more convenient forms.
The other names are scientific notations and standard forms.
The rules of index forms;
Add the exponents of forms with the same bases and multiplying one anotherSubtract the exponents of forms with same bases and dividing each other.From the information given, we have;
4^3/4^6 times 4^17
subtract the bases
4 ³⁻⁶ ⁺¹⁷
Add the values
4¹⁴
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Solve the system of equations using the substitution method. y = 7x – 16, y = 2(2x – 5) What is the solution?
Answer:Y = 7x – 16,
y = 2(2x – 5)
Step-by-step explanation:
he answer to the system of equations is (2,-2)
First, we can substitute in for y in the other equation
This will give us
Next, we distribute the 2 throughout the parenthesis
Now we can solve for x. Begin by adding 16 to each side
Now we can subtract 4x from each side
Lastly, we can divide each side by 3
Now, we need to substitute in the value that we got for x into one of the equations to find the y value.
This becomes
So
This means that the solution to the system of equations is (2,-2)
A sensor on a boat notices buried treasure 200 meters away diagonally with an angle of depression of 25 degrees. How deep is the treasure beneath the water rounded to the nearest tenth of a meter?
Answer: To solve this problem, we can use the Pythagorean theorem. Let's call the depth of the treasure "d".
We can create a right triangle with the following sides:
The sensor on the boat is at the top of the triangle and is 200 meters away from the treasure diagonally.
The line from the sensor to the treasure, which we can call "x", is at a 25-degree angle from the surface of the water.
The line from the treasure to the ocean floor, which we can call "d", is perpendicular to the surface of the water.
Since we know that the angle of depression is 25 degrees, we can use tangent to find the length of x.
tan(25) = x/d
x = d * tan(25)
Now, we have two sides of a right triangle and can use the Pythagorean theorem to find d:
x^2 + d^2 = 200^2
d^2 = 200^2 - x^2
d^2 = 200^2 - (d * tan(25))^2
Solving for d, we find that d = 174.59 meters. Rounding to the nearest tenth of a meter, we get d = 174.6 meters.
Step-by-step explanation:
what is 73kg to lbs?
73 kg is equivalent to approximately 160.937 pound (lbs).
Kilogram (kg) and pound (lb) are both units of mass commonly used in different parts of the world. Kilogram is the base unit of mass in the International System of Units (SI) and is defined as the mass of the International Prototype of the Kilogram, which is a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France.
Pound, on the other hand, is a unit of mass commonly used in the United States, the United Kingdom, and other countries, which is defined as exactly 0.45359237 kilograms. This value is based on the international avoirdupois pound, which is defined as exactly 0.45359237 kg.
To convert kilograms to pounds, you can use the conversion factor of 2.20462 lbs/kg. To convert pounds to kilograms, you can use the conversion factor of 0.45359237 kg/lb.
To convert 73 kilograms (kg) to pounds (lbs), you can use the conversion factor of 2.20462.
So,
73 kg * 2.20462 lbs/kg = 160.937 lbs (rounded to three decimal places)
Therefore, 73 kg is equivalent to approximately 160.937 lbs.
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In the diagram, segment AD bisects angle BAC.
Given the following segment lengths, find the value of x.
Round to the nearest tenth.
AB = 23
AC = 18
The value of x is 77.5. In order to solve for x, we need to use the Triangle Angle Sum Theorem.
What is value?Value is a subjective concept that referred to the word of importance that an individual group of people places on something it is often associated with principal beliefs and standard that are accepted by society when you can be seen as a measure of how important something is true person of organization it is often seen as a reflection of ones worldview and can help to save attitudes decision and behaviors believe is not an absolute and very depending on the context of the looks like commands.
In order to solve for x, we need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180°. Since angle BAC is bisected by segment AD, the two angles must be equal. Therefore, we can set up the following equation to solve for x:
180° = angle BAC = (x + 7) + (x + 18)
We can solve this equation by combining like terms and isolating the variable x.
180° = 2x + 25
2x = 155
x = 77.5
Therefore, the value of x is 77.5.
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3 pounds of apples cost 5.52 how much for 10 pounds?
Answer:
OUT OF BUSINESS
Step-by-step explanation:
you cant afford it on food stamps my guy
5. Name the angle that is supplementary to COD.
A
F
OZCOA
O ZBOC
OLCOB
O ZBOA
B
O
۶,
D
(1 point)
Answer:
Example 2:
Find m∠P and m∠Q
if ∠P and ∠Q
are supplementary, m∠P=2x+15
, and m∠Q=5x−38
.
The sum of the measures of two supplementary angles is 180°
.
So, m∠P+m∠Q=180°
Substitute 2x+15
for m∠P
and 5x−38
for m∠Q
.
2x+15+5x−38=180°
Combine the like terms. We get:
7x−23=180°
Add 23
to both the sides. We get:
7x=203°
Divide both the sides by 7
.
7x7=203°7
Simplify.
x=29°
To find m∠P
, substitute 29
for x
in 2x+15
.
2(29)+15=58+15
Simplify.
58+15=73
So, m∠P=73°
.
To find m∠Q
, substitute 29
for x
in 5x−38
.
5(29)−38=145−38
Simplify.
145−38=107
So, m∠Q=107°
.Example 2:
Find m∠P and m∠Q
if ∠P and ∠Q
are supplementary, m∠P=2x+15
, and m∠Q=5x−38
.
The sum of the measures of two supplementary angles is 180°
.
So, m∠P+m∠Q=180°
Substitute 2x+15
for m∠P
and 5x−38
for m∠Q
.
2x+15+5x−38=180°
Combine the like terms. We get:
7x−23=180°
Add 23
to both the sides. We get:
7x=203°
Divide both the sides by 7
.
7x7=203°7
Simplify.
x=29°
To find m∠P
, substitute 29
for x
in 2x+15
.
2(29)+15=58+15
Simplify.
58+15=73
So, m∠P=73°
.
To find m∠Q
, substitute 29
for x
in 5x−38
.
5(29)−38=145−38
Simplify.
145−38=107
So, m∠Q=107°
.
X, Y, Z Axis. What do they stand for?
The X, Y, and Z axes define a three-dimensional coordinate system, which is commonly used to represent physical objects or mathematical functions in space.
The X, Y, and Z axes are terms commonly used in mathematics, physics, engineering, and computer graphics to refer to the three dimensions in a three-dimensional coordinate system.
The X-axis is the horizontal axis and is used to represent values along the horizontal plane. It is often called the "abscissa" and is typically drawn as a horizontal line that intersects with the Y-axis at the point where they meet, which is called the origin.
The Y-axis is the vertical axis and is used to represent values along the vertical plane. It is often called the "ordinate" and is typically drawn as a vertical line that intersects with the X-axis at the origin
.The Z-axis is the third axis and is used to represent values along the depth or height plane. It is often called the "applicate" and is typically drawn as a line that is perpendicular to both the X and Y axes, intersecting with both at the origin.
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