Therefore , the solution of the given problem of slope comes out to be
y = (-1/2)x + 8.
Define slope.The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line's slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the formula y = 3x - 7.
Here,
Locate the slope first.
These two positions (0, 8) and are in the line, therefore we know that (6,5)
Slope: (y2-y1)/(x2 - x1)
Slope = 8-5 / 0-6
Slope = 3/-6 => Slope = -1/2
The gradient is -1/2. When x = 0, you can find the y-intercept. We also know that the line passes through the point (0,8), and since x = 0, the y-intercept is equal to 8.
using the slope-intercept form, which is
Using the equation y = mx + b, where m denotes the slope and b the y-intercept, we get:
y = (-1/2)x + 8
Therefore , the solution of the given problem of slope comes out to be
y = (-1/2)x + 8.
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Select the equation in standard form for the line that passes through (-9, 8) and (1, -12).
A) x + 2y = -20
B) 2x + y = -13
C) 2x+y = 7
D) 2x+y = -10
E) x + 2y = 20
Answer: D
Step-by-step explanation:
Since we are given 2 points, we can use that to find slope, convert to slope-intercept form, and then manipulate it to be standard form. Standard form is ax+by=c.
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-12-8}{1-(-9)} =\frac{-20}{10} =-2[/tex]
With m=-2, we can plug it into slope-intercept form to find the y-intercept.
[tex]y=-2x+b[/tex] [plug in point]
[tex]8=-2(-9)+b[/tex] [multiply]
[tex]8=18+b[/tex] [subtract both sides by 18]
[tex]b=-10[/tex]
With m and b, we can plug in the equation.
[tex]y=-2x-10[/tex] [add both sides by 2x]
[tex]2x+y=-10[/tex]
This gives D as the answer.
Find the volume of the given solid.
Bounded by the coordinate planes and the plane
6x + 7y + z = 42
The volume of the given solid is equal to the triple integral of 1 over the region bounded by the coordinate planes and the plane 6x + 7y + z = 42. This can be written as:
[tex]$\iiint 1\, dV = \iiint 1\, dx\, dy\, dz$[/tex]
The region of integration is bounded by the coordinate planes x = 0, y = 0, and z = 0, and the plane 6x + 7y + z = 42. This is a right triangular prism with vertices (0,0,0), (6,0,0), and (0,6,42). To calculate the volume, we will use the triple integral in cylindrical coordinates, which can be written as:
[tex]$\iiint 1\, dV = \int0^{2\pi}\int0^6\int_0^{42/7} r\, dz\, dr\, d\theta$[/tex]
The volume of the given solid is given by:
[tex]$\frac{504\pi}{7}$[/tex]
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A cylinder's height equals the diameter of its base. What fraction of the total surface area of the cylinder is the total area of the two bases
If the Cylinder's height equals to the diameter of its base , then the fraction of the total surface area of the cylinder to the total surface area of the two bases is 1/3 .
The curved surface area of the cylinder with height "h" and radius "r" is written as ⇒ [tex]2\pi rh[/tex] ;
the area of the top and bottom of the cylinder is ⇒ [tex]\pi r^{2} + \pi r^{2}[/tex] = [tex]2\pi r^{2}[/tex] ;
the total surface area of the cylinder will be ⇒ [tex]2\pi rh[/tex] [tex]+2\pi r^{2}[/tex] ....equation(1)
it is given that the height of cylinder is equal to the diameter of the base ,
that means ; [tex]h = 2r[/tex]
Substituting the value [tex]h = 2r[/tex] in the equation(1) ,
we get ,
total surface area of cylinder = [tex]4\pi r^{2} +2\pi r^{2}[/tex] = [tex]6\pi r^{2}[/tex]
So , the required fraction is = [tex]\frac{2\pi r^{2} }{6\pi r^{2} }[/tex] ,
On simplifying ,
we get ,
= [tex]\frac{1}{3}[/tex] .
Therefore , the fraction of two bases to the total surface area is [tex]\frac{1}{3}[/tex] .
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what is the rate of decay f(x)=(.8)^x
9th grade AP algebra
The provided function, f(x)=(.8)^x, has a 20% rate of decay.
What is the Rate of decay or growth?
A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.
given, a function f(x)=(.8)^x. To calculate the decay rate of this function.
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a (1 - r)x is the general form.
Where
a = the initial amount
1-r is the decay factor
x = time span
from the given expression,
Decay factor = 0.8
That is also equal to 1 - r
1 - r = 0.8
r =0.2
Thus, rate of decay = r * 100%
rate of decay = 0.2 * 100 = 20%
therefore, The rate of the of the given function f(x)=(.8)^x is 20%.
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The basketball team averaged 68 points per game last season and average 77 points per game this season. What is the approximate percent of the increase
According to question we can say that the approximate percentage of the increase is 13.2352%.
What is percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on a test (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.
Based on the given conditions, formulate: (77 —68)/ 68
e sum or difference:9/68 = 0.132352
0.132352 x100/100
=13.2352%
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At Clara's Beading Boutique, 9 out of the 18 beads on clearance are plastic. What percentage of beads on clearance are plastic?
The percentage of beads on clearance are plastic is 50%.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Total number of beads = 18
Number of beads which are plastic on clearance = 9
Percentage of beads which are plastic on clearance = (9 / 18) × 100
= (1/2) × 100
= 0.5 × 100
= 50%
Hence 50% of beads on clearance are plastic.
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You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each
Therefore, 60 different combinations can be made wearing one of each type
What is Fundamental Counting Principle? If an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m × n.This video uses manipulatives to review the five counting principles including stable order, correspondence, cardinality, abstraction, and order irrelevance. When students master the verbal counting sequence they display an understanding of the stable order of numbers.Fundamental Principle of Counting helps to determine how selection is done on the basis of available choices. Fundamental Principle of Counting simplifies the approach of selection considering all the possible choices and their combinations for calculating the ProbabilityThe fundamental counting principle states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things. Example 1: Suppose you have 3 shirts (call them A , B , and C ), and 4 pairs of pants (call them w , x , y , and z ). Then you have. 3×4=12.To learn more about Fundamental Counting Principle refers to:
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The table shows pairs of values for the linear function f(x) = 3x
f(x)
-2
1
4
7
10
X
0
1
2
3
4
Which conjecture about linear functions in general is best supported by the
table?
Equal changes in the value of x
result in equal changes in the value
of y.
B. The difference between the x- ar
y-values in each ordered pair (x,
is a constant.
Answer:
the answer is. The answer is
57
Step-by-step explanation:
Big Ideas Math:
Q1. The graph of which of the following functions does not belong with the other three?
Answer: f(x) = 3x^2 + 24x - 6
Q2. This is the only function that does not have x-intercepts at x= Response and x= Response and a vertex at (Response, Response).
Function 3x²+24x-6 does not belong with the other three
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the option we have to simplify each function
a. f(x)=3x²+6x-24
b. f(x)=3x²+24x-6
c. f(x)=3(x-2)(x+4)
=3(x²+4x-2x-8)
=3x²+6x-24
d. f(x)=3(x+1)²-27
3(x²+1+2x)-27
3x²+3+6x-27
3x²+6x-24
So function 3x²+24x-6 does not belong with the other three
Hence, function 3x²+24x-6 does not belong with the other three
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What do you get when you subtract 3xy from 5 by?
When we subtract 3xy from 5 we will get 3xy - 5.Both are different 3xy is a polynomial in xy and 5 is a constant we can not simplify further.
First, let's try to learn subtraction in the case of polynomials.
3xy is a polynomial.
5 is a constant.
Polynomials can be subtracted using a method that involves changing the signs to the opposite sign. The process resembles adding polynomials. Depending on the specific equation, we transform the sign while subtracting polynomials to either positive or negative. Learn more about subtracting polynomials, their techniques, procedures, and examples by reading on.
For instance, subtract 5x + 8y - 20z from 4x - 10y + 15z.
The polynomials should first be arranged in standard form. In this illustration, it has already been set up.
Place them horizontally in step two.
(4x - 10y + 15z) - (5x + 8y - 20z)
Step 3: By using parenthesis, modify the second polynomial's sign.
4x-10y-15z, and 5x+8y 20z
Step 4: Group terms that are similar together.
4x - 5x - 10y - 8y + 15z + 20z
Step 5: Resolve the problem
-x - 18y + 35z
As a result, we get -x - 18y + 35z when we subtract 4x - 10y + 15z from 5x + 8y - 20z.
In the same way, if we subtract 3xy from 5 we will get 3xy - 5.
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What is 3 8 equivalent to as a fraction?
Answer:
6/16
Step-by-step explanation:
Answer:
Step-by-step explanation:
15/40 i think
Evie practices her violin for exactly
310 minutes each week. On Monday, she
practices twice as long as she does on
Tuesday. On Thursday, she practices the
same number of minutes as Tuesday. On
Saturday, she practices 5 fewer minutes
than three times her Tuesday practice.
How many minutes does Evie practice on
Monday?
On Monday, Evie practices 2T = 2*45 = 90 minutes.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Let's call the amount of time Evie practices on Tuesday T.
On Monday, she practices twice as long as she does on Tuesday, so she practices 2T minutes.
On Thursday, she practices the same number of minutes as Tuesday, so she practices T minutes.
On Saturday, she practices 5 fewer minutes than three times her Tuesday practice, so she practices 3T-5 minutes.
We know that Evie practices 310 minutes in total in a week.
So we can set up an equation:
T + 2T + T + 3T-5 = 310
7T-5 = 310
7T = 315
T = 45
On Monday, Evie practices 2T = 2*45 = 90 minutes.
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1/4(12x-20)+3(3x+5) I'm extremally confused I'm supposed to simplify
Answer:
12X+10
Step-by-step explanation:
THAT IS THE SIMPLFY 1-4 x (12x-20)+3(3x+5) Facout our 4 from the expression 1-4 x4 (3x-5)+3(3x+5) Simply the expression cancel out the greatest common factor 4 remove unncessary parntheses if so collect the terms 3x 9x 12x and the solutin is 12x+10
an elargemnet or expansion occurs when the absolute value of the scale factor is less than one true or false
Yes the statement is true.
What are scale factors in Dilation?An object is enlarged if the scale factor is greater than 1. An object is reduced if the scale factor is a fraction, less than 1. A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.
Given here Absolute value of the scale factor is greater than 1
∴ The object is enlarged if the scale factor is greater than 1.
Hence, Yes the statement is true.
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What property of multiplication is 5x1 5 1x5 5?
The property used in this is the commutative law of multiplication.
What is the commutative law of multiplication?
In mathematics, commutative law refers to either of two rules relating to the addition and multiplication of numbers that are expressed symbolically as a + b = b + a and ab = ba. These principles imply that rearranging the terms or factors of any finite sum or product has no effect on it.
Here, we have
Given: 5x1 = 5 = 1x5
We have to find which property of multiplication is applied here.
5x1 = 5
1x5 = 5
We concluded from the given statement that the commutative law of multiplication is applied here.
commutative law of multiplication: ab = ba
Hence, the property used in this is the commutative law of multiplication.
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A hurricane blows onto the East Coast of the United States on September 16, 2017. The maximum sustained wind speed is 176 kilometers (109 miles) per hour and the sea level height is pushed 2.3 meters (7.5 feet) above normal. What category is this hurricane
This hurricane would be classified as a Category 2 hurricane on the Saffir-Simpson Hurricane Wind Scale.
What hurricane classification is this?This hurricane would be classified as a Category 3 hurricane. The Saffir-Simpson Hurricane Wind Scale is used to classify hurricanes based on their maximum sustained wind speeds.Category 3 hurricanes have wind speeds between 178 and 209 kilometers (111 and 130 miles) per hour.The maximum sustained wind speed of this hurricane is 176 kilometers (109 miles) per hour, which is below the threshold for Category 4 hurricanes, but still within the range of Category 3 hurricanes. The storm surge is also a major factor in the classification of hurricanes. Storm surges are caused by the winds of a hurricane pushing the water of the ocean up onto the coast.This hurricane has a storm surge of 2.3 meters (7.5 feet).The Saffir-Simpson Hurricane Wind Scale does not take into account the height of storm surges. Therefore, this hurricane would be classified as a Category 3 hurricane due to its maximum sustained wind speed of 176 kilometers (109 miles) per hour and the storm surge of 2.3 meters (7.5 feet).The Saffir-Simpson Hurricane Wind Scale is a useful tool for measuring the severity of a hurricane and can help to prepare people in its path.To learn more about the Saffir-Simpson Hurricane Wind Scale refer to:
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What is the Value of P? 9=p÷9
Answer:
p = 81
Step-by-step explanation:
9 = [tex]\frac{p}{9}[/tex] Multiply both sides by 9
9(9) = [tex]\frac{p}{9}[/tex][tex](\frac{9}{1})[/tex] another name for 9 is [tex]\frac{9}{1}[/tex]
81 = p
Exponential from Two Points (Level 1)
Write an exponential function in the form y = ab* that goes through points (0, 13)
and (2, 325).
a = 13. b^0 = 1, y=a(1), 13 = a 325 = 13(b)^2 b^2 = 325/13 = 25
b = sqr25 = 5 y=13(5)^x is the exponential equation going through the two given points
What is Exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.The graphs of all exponential functions have these characteristics. They all contain the point (0, 1), because a0 = 1. The x-axis is always an asymptote. They are decreasing if 0 < a < 1, and increasing if 1 < a. If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variableTo learn more about Exponential function refers to:
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Kayden has 50 m of railing.
How much more railing does Kayden need
so that he can put railing all the way around
the roof garden?
12 m
3 m
7m
10 m
20 m
10 m
Not drawn accurately
Answer: Kayden needs 12 more meters of railing.
Step-by-step explanation:
To find the perimeter of the roof garden I added up all the numbers you listed (12m+3m+7m+10m+20m+10m) to get a total perimeter of 62 meters.
Since Kayden already has 50 meters of railing we can subtract that from the total he needs to get the remaining amount needed.
62m - 50m = 12 meters of railing remaining.
1. Find the radian measures that correspond to the degree measures 330° and 135°
Answer:
Converting from degrees to radians is actually very simple, it is a one step unit conversion.All we need to know to solve this is that (π)radians=(180)degrees Therefore 135degrees⋅(π)radians180degrees=(135180)π radians =3π4 radians
Step-by-step explanation:
hope this helps
How do you check if a function has an inverse function?
We can check if a function has an inverse function using horizontal Line Test.
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connect
horizontal Line Test
Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F does have an inverse if there are no horizontal lines that cross the graph of f more than once.
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The cost of a certain cell phone plan can be modeled by C(m) = 2m + 15, where C(m) is the total cost for m minutes of cell phone usage. State the meaning of the slope with respect to the cost associated with the cell phone plan.
The interpretation of the slope is that the cost per minute is $2
How to determine the interpretation of the slope?From the question, we have the following parameters that can be used in our computation:
C(m) = 2m + 15
Where
m = number of minutes
C(m) = cost function
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 2
This means that the slope is 2
And it means that the cost per minute is $2
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A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 6cm. If a box contains 15 pieces of candy, how much chocolate does the box contain? Use 3. 14 for π, and do not round your answer
The total amount of solid sphere chocolate in the box is 1695.6 cubic centimeters.
What is volume?The space occupied within an object's borders in three dimensions is referred to as its volume.
What is the volume of sphere?The volume or the space inside the borders of the sphere is given by the formula:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Given that the diameter is 6cm, the radius r = 3cm.
Substituting the value of radius in volume we have:
[tex]V = \frac{4 (3.14)(3)^3}{3}[/tex]
[tex]V= 113.04[/tex]
The box contains 15 candies hence the total volume will be:
V = 15 * 113.04
V = 1695.6 cubic centimeters.
Hence the total amount of chocolate in the box is 1695.6 [tex]cm^3[/tex].
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What is the value of the discriminant of the given equation 2x^2 4x 3?
The discriminant of the given quadratic equation 2x² - 4x + 3 = 0 is -8.
The standard form of quadratic equation is ax² + bx + c = 0
Compare the given equation with its standard form
a = 2, b = -4, c = 3
We know that
D = b² - 4ac
Substitute the values in the formula
D = (-4)² - 4(2)(3)
⇒ D = 16 - 24
⇒ D = -8
Since D < 0
Therefore, the given equation has no real roots.
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a car travels at a constant speed.what does the gradient of a distance-time graph of the car's journey represent?distance the car travelled, the area under the graph,the speed of the car, the acceleration of the car
the speed of the car
=========================================================
Reason:
The term "gradient" is the same as "slope".
Recall that slope = rise/run = (change in y)/(change in x).
The change in y represents how far you travel, as the distance is along the vertical axis. The change in x is the time duration.
Then,
speed = distance/time
which helps show the slope of this distance-time graph is the speed of the car. The steeper the slope, the faster the car.
-------------
An example:
The equation y = 50x has slope 50. The x is the time and y is the distance traveled.
At time x = 0 hours, you have traveled y = 0 miles.
At time x = 1 hour, you have traveled y = 50 miles.
The two points (0,0) and (1,50) are on this line. Use the slope formula to get a slope of 50, which represents the speed of the car in miles per hour (mph). Or note that y = 50x is in the form y = mx+b
m = slope = 50
b = y intercept = 0
Find the measure of the indicated angle to the nearest degree.
Answer:
57⁰
Step-by-step explanation:
To get the indicated angle we need to use the knowledge of trigonometry.
Since the required angle has both opposite and adjacent sides we use Tangent
Tan ? = opposite/adjacent
= 37/24
= 1.5412
To get the angle we now need to to find the tan inverse of the value we found
Tan inverse of 1.5412
= 57.03⁰
to the nearest degree it will be 57⁰
Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
The triangles can be proved congruent by SAS theorem.
Properties of congruent triangles.Two or more triangles are said to be congruent if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.
To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.
Therefore in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;
Opposite sides of a parallelogram are equal in length. Thus, it can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.
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In triangle JKL, tan(bº) = 3/4
and sin(bº) = 3/5. If triangle JKL is dilated by a scale factor of 3, what is cos(bº)?
bº
If triangle JKL is dilated by a scale factor of 3,cos(bº)=4/5.
Define trigonometric ratio.Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
Why trigonometric identities are used?If you know the lengths of two of the triangle's sides, you can use trigonometric ratios to get the measurements of one (or both) of the acute angles.
tan(b)=P/B=3/4
sin(b)=P/H=3/5
cos(b)=B/H= To find
B=4, H=5
cos(b)=4/5
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What does 2 equivalents mean in chemistry?
An equivalent is the amount of a substance that reacts with an arbitrary amount of another substance in a given chemical reaction.
Arbitrary
It is a relative unit of measurement to show the ratio of amount of substance, intensity, or other quantities, to a predetermined reference measurement.
chemical reaction
chemical reaction is a process in which one or more substances, the reactants, are converted to one or more different substances, the products. Substances are either chemical elements or compounds.
Examples of chemical changes include baking soda and vinegar creating carbon dioxide, iron rusting, and wood burning.
There are five types of general chemical reactions: Combination or synthesis, decomposition, single displacement, double displacement, and combustion.
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How do you tell if a graph is a function and inverse is a function?
If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).
What is a function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The function f has an inverse if and only if the result of reflecting a function's graph about the line y = x is the function's graph (passes the vertical line test).
Therefore, if and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f has an inverse (passes the vertical line test).
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