The four models each show two parallel lines cut by a transversal and some angle measures formed by the
intersection of the lines.
What are the values of angle measures a and b in Model 4?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.
19° 71° 90° 109° 180° 119°
The value of a is ____, and the value of b is ____.
The value of a is 71°, and the value of b is 109°.
What is a parallel line?A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.
When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;
Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles and Consecutive Interior Angles.From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.
That is 180 - 71 = 109°
Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.
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What’s the solution set of 2x+8>-4x+5
Answer:
x > –1/2
or x > –0.5
Step-by-step explanation:
2x + 8 > – 4x + 5
2x + 4x > 5 – 8
6x > –3
x > –3/6
x > –1/2
or x > –0.5
Inequalities in the real world
Pls help
The number line which describes the the measure of third side of the triangle must be greater than 10 cm is the second figure.
What is Number line?Number line is a straight horizontal line on which numbers are written in a certain intervals.
We can use number line for basic mathematical operations like addition, subtraction, division and multiplication.
Here the situation described is that measure of the third side of the triangle must be greater than 10 cm.
The inequality sign is '> 10'.
Since the inequality sign does not contain the equal to (≥) sign, the point 10 does not belong to this set.
So we will mark an open circle at the point 10 and draw a line afterwards.
Hence the second number line describes the situation that the third side of the triangle must be greater than 10 cm.
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2 1/2 + x = 5 1/3
Help is very much appreciated!
20 pts!!
Answer: hope it helps
Step-by-step explanation:
2 1/2 + x = 5 1/3
(2 + 1/2) + x = (5 + 1/3)
6x = 17
x = 17/
6
= 2.83333333
x = 17/
6
≈ 2.833333
[tex] \huge \underline{ \boxed{ \tt Solution: }}[/tex]
[tex] \tt \pink{\large\dagger} \: \: \: \: \: \: 2\dfrac{1}{2} + x = 5\dfrac{1}{3} \\ \tt : \implies \dfrac{5}{2} + x = \dfrac{16}{3} \\ \tt : \implies x = \dfrac{16}{3} - \dfrac{5}{2} \\ \tt : \implies x = \dfrac{16 \times 2}{3 \times 2} - \dfrac{5 \times 3}{2 \times 3} \\ \tt : \implies x = \dfrac{32}{6} - \dfrac{15}{6} \\ \tt : \implies x = \dfrac{32 - 15}{6} \\ \tt : \implies x = \dfrac{17}{6} [/tex]
[tex] \tt \pink{ \star \: Hence \: the \: answer \: is \: \dfrac{17}{6}.}[/tex]
What are the restrictions on the domain for the following rational expression?
Answer:
x <> -3, 8
Step-by-step explanation:
x² - 5x - 24 (the denominator of the fraction) must not be 0, because n/0 is not defined for any n.
since this is a quadratic equation, it must have 2 solutions.
therefore, the second answer must be right.
let's check.
a quadratic equation
ax² + bx + c = 0
has the solutions
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (5 ± sqrt((-5)² - 4×1×-24))/(2×1) =
= (5 ± sqrt(25 + 96))/2 = (5 ± sqrt(121))/2 =
= (5 ± 11)/2
x1 = (5 + 11)/2 = 16/2 = 8
x2 = (5 - 11)/2 = -6/2 = -3
correct.
The store clerk created a display of R rows of cereal boxes. Each row contained 16 boxes. Choose the expression that shows the total number of cereal boxes on display.
Answer:
16R = T or T = 16R
Step-by-step explanation:
R represents the unknown amount of rows and we know there are 16 boxes in each row.
This means to find the total number of boxes on display, you will have to times the number of rows by 16 as the clerk puts 16 boxes of cereal in each row
e.g, if there are 3 rows, then to find the total amount of cereal boxes, you would do 3 × 16 = 48
Since it's an expression, you need something to represent the total number so that can be represented by any letter ( I chose T ) — in most cases you can probably represent the total as x
Hence the expression should be 16R = T or T = 16R
...at least I think so
Kyle invests in an account earning 4.5% interest compounded continuously. How long will it take to double his investment?
Doubling time in years =
let's take from the basic of one dolla!!! how long for a buck to turn into two bucks at 4.5%?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years \end{cases} \\\\\\ 2=1e^{0.045\cdot t} \implies \log_e(2)=\log_e(e^{0.045t})\implies \log_e(2)=0.045t \\\\\\ \ln(2)=0.045t\implies \cfrac{\ln(2)}{0.045}=t\implies 15.4\approx t\qquad \textit{about 15 years and 146 days}[/tex]
Using Function Notation
State if the following are functions or not.
The following given table with input and output is a function.
What is function?A relation between a domain and range is called a function when each value in the domain only has one value in the range. This notion is violated by relations that are not functions. They have at least one domain value that corresponds to two or more range values.
Write names of type of functions.Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.
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The following given table with input and output is a function.
What is function?
A function is a self-contained block of code that performs a specific task. It is a logical grouping of instructions and operations that can be used multiple times throughout a program. Functions help to keep code organized and modular, making it easier to debug and maintain. They also allow for code reuse, which can result in faster development times and greater efficiency. Furthermore, functions can be used to pass data between different parts of a program, making it easier to share information and reduce the need for redundant code.
Write names of type of functions.
Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.
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b. 2/(x-2)(x-3)+2/(x-1)(3-x)+1/(1-x)(2-x)
After using the quadratic equation the answer is [tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]
What is quadratic equation ?
Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).
[tex]\frac{2}{x-2} (x-3) = \frac{2(x-3)}{x-2} \\\\ \frac{2}{x-1} (3-x) = \frac{2(3-x)}{x-1} \\\\\frac{1}{1-x} (2-x) = \frac{2-x}{1-x} \\\\[/tex]
[tex]\frac{2\left(x-3\right)}{x-2}+\frac{2\left(3-x\right)}{x-1}+\frac{2-x}{1-x}[/tex]
[tex]\frac{2(3-x)}{x-1} + \frac{2-x}{1-x}[/tex]
[tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]
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Help please!!!!!! Which table represents a linear equation that has a y-intercept of -3?
Answer: A
Step-by-step explanation:
A y-intercept is a point where a function (i.e a line) intercepts the y-axis.
Every point on the y-axis has a x value of 0.
The ordered pair will look like this (0,y)
In answer a, you have an x value of 0 with a corresponding y value of 3.
This point is (0,3).
You could also graph the points and look for where the function crosses the y-axis.
determine the range of the following graph
The required range of the given function is -4 < y < 6.
What is the range?Range, it is the set of values that come out to an outcome for certain mathematical operations.
Here,
A graph of a function is shown,
From the graph, it has been determined that,
The function is defined for domain -11 < x < -3.
As every value on the y- axis for the respective domain represents the element of range so,
The respective domain range of the function on the graph is -4 < y < 6.
Thus, the required range of the given function is -4 < y < 6.
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A truck can be rented from Company A for $150 a day plus $0.50 per mile. Company B charges $60 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
At 300 miles the rental costs for Company A and Company B are the same.
What is meant by an equation?An assertion that two expressions containing variables or numerical values are equivalent is known as an equation. The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the unknown values that satisfy the equality are referred to as the equation's solutions.
Given :
Vehicle A: 150 + 0.5m = Cost A
Cost B = 60 + 0.8m for truck B.
Given that a one-day scenario was required by the challenge, the two equations are as follows:
Price B =60+0.8m Price A =150+0.5m
By combining the two equations, we get
150 + 0.5m = 60 + 0.8m.
150-60=0.8m-0.5m
90=0.3m
m=90/0.3
m=300 miles
Consequently, there are 300 miles in a day.
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This question is based on a time when people needed to log in to email servers to write emails. Assume that Adam logs in to an email server at time zero. He then spends his time exclusively on writing emails. The times that his emails are sent can be modeled by a Poisson process with a rate
λ A
/
hour. His friend Brianna also logs in to the server at time 1 (which means 1 hour later) and starts typing emails independently of Adam. The time that her emails are sent also can be modeled by a Poisson process with a rate
λ B
/
hour. (a) (6 points) Let
Y 1
, and
Y 2
be the times at which Adam's first and second emails were sent. Find
E[Y 2
∣Y 1
]
(b) (8 points) Similar to the last question, let
Y 1
and
Y 2
be the times at which Adam's first and second emails were sent. When Brianna logs in to the server, you are told that Adam has sent exactly one email so far. (b.1) (4 points) What is the conditional expectation of
Y 1
given this information? (b.2) (4 points) What is the conditional expectation of
Y 2
given this information? (c) (8 points) Find out the PMF of the total number of emails sent by two of them together during the interval of
[0,2]
(which means in the first two hours). (d) (8 points) Given that a total of 10 emails were sent during the period of
[0,2]
(the first two hours), what is the probability that exactly four emails were sent by Adam? (e) (10 points) Suppose that
λ A
=4
. Use Chebyshev's (4 points) and Markov's (4 points) inequality to find upper bounds on the probability that Adam sent at least five emails during the time interval [0, 1 ]. Which one provides a better bound ( 2 points)?
The upper bounds on the probability that Adam sent at least five emails during the time interval is [0, 1].
in math upper bound refers a number that is greater than or equal to any number in a set
Here we have given that, Adam logs in to an email server at time zero. He then spends his time exclusively on writing emails. His friend Brianna also logs in to the server at time 1 (which means 1 hour later) and starts typing emails independently of Adam.
And we need to find the upper bounds on the probability that Adam sent at least five emails during the time interval.
While we looking into the given question, we have identified that Adam Poisson process with a rate λ A/hour and Brianna Poisson process with a rate λ B/hour.
Here let us consider that Y1 and Y2 be the times at which Adam's first and second emails were sent.
Here we know that the Brianna logs in to the server, you are told that Adam has sent exactly one email so far.
So, here the upper limit while logging is 1. So, the lower limit is 0.
Because these is the real life scenario so the negative value is not applicable.
Therefore, the resulting interval is [0, 1].
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Salaries of 40 college graduates who took a statistics course in college have a mean x of $60.600. Assuming a standard deviation of $13,553 construct a 90% confidence level for estimating the population mean u
The confidence level is 60600<μ<3,524.786, assuming a standard deviation of $13,553 and the confidence level for estimating the population mean is 90%.
What do you mean by confidence level?
A confidence interval is a range of values that can contain the true value of the parameter being studied in statistics. It is created using observed data and calculated at a desired level of confidence.
The confidence level—for instance, a 95% confidence level—relates to the accuracy of the estimation process, not to the degree to which it is certain that the computed confidence interval contains the actual value of the parameter under investigation.
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What is the exact value of tan 75°?
A.
OB.
O c.
D.
1-
1+
3
1+
1-4
1+√3
1-v3
1+√3
The exact value of the tan(75°), found using trigonometric identities for the tangent of the sum of two angles, indicates that the exact value of tan(75°) is (1+√3/3)/(1 - √3/3))
What are trigonometric identities?Trigonometric identities are equalities of expressions that includes trigonometric functions which are valid for all values of the argument, or the domain of the function.
The exact value of tan(75°) can be found from the formula for the tangent of the sum of two angles as follows;
tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)•tan(B))
tan(75°) = tan(45° + 30°)
tan(45° + 30°) = (tan(45°) + tan(30°))/(1 - tan(45°)•tan(30°))
tan(30°) = √3/3
tan(45°) = 1
tan(45° + 30°) = (1 + √3/3)/(1 - √3/3)
tan(75°) = (1 + √3/3)/(1 - √3/3)
The correct option is therefore option B
[tex]tan(75 ^{ \circ } ) = \dfrac{1 + \frac{ \sqrt{3} }{3} }{1 - \frac{ \sqrt{3} }{3} } [/tex]
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how to solve 4 divided by 3
Answer:
1.33333 , it just keeps going
Step-by-step explanation:
divide 4/3 you can use a long division or a calculator.
Hope this helps!!
(b) 2(w 2 5 z)+3(2 x -2 -6)=4(4 7 y 3)
From the given matrices, the values w,x,x and z are 5,-8,4 and -3 respectively.
How to solve matrix equations?Matrices is the rectangular arrangement of numbers and letters in rows and columns
An equation is defined as a mathematical expression showing the equality of two sides of the statement
The given matrices are;
[tex]2\left[\begin{array}{ccc}w&2&\\5&z&\/\end{array}\right] -3\left[\begin{array}{ccc}2&x&\\-2&-6&\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]
Opening the brackets in the matrices
[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] -\left[\begin{array}{ccc}6&3x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]
Adding the Left hand side
[tex]\left[\begin{array}{ccc}2w-6&4-3x\\16&2x+18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y12&6\\\end{array}\right][/tex]
Equate Left hand side with Right hand side to form linear equations
2w-6=16
2w=10
w=5
4-3x=28
-3x=28-4
-3x=24
x=-8
16=4x
4=x
2z+18=12
2x=12-18
2x=-6
x=-3
These are how the various values are gotten
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What is 11.661903 rounded to the nearest hundreth?
Answer:
The number 11.661903 rounded to the nearest hundredth is 11.66.
Step-by-step explanation:
We have the following number:
11.661903And we need to round this number to the nearest hundredth.
To determine that, we can proceed as follows:
1. Round a number to the nearest hundred is equivalent to rounding the number to two decimal places.
2. Now, we can see that the number in the third decimal position or thousandth place is 1:
3. If this number were 5 or greater than 5, we would need to round up that number to the next following number, that is, 7. However, this is not the case.
4. Therefore, if we have to round that number to the nearest hundredth, then the number is 11.66.
Hence, in summary, the number 11.661903 rounded to the nearest hundredth is 11.66.
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
if grocery price increases 1% per month for a whole year, how much would groceries that cost $100 at the beginning of the year cost at the end of the year
Answer: it's still $100 because the beginning of the year hasn't started yet so you need to wait for the year to end so the 1 percent can be added
Step-by-step explanation:
what is capacity . please explain
Answer:
Step-by-step explanation:
the ability to hold, receive, store, or accommodate. : a measure of content : the measured ability to contain : volume. a beaker with a capacity of one liter.
Answer:
Capacity is the maximum amount that something can contain; Volume, or the amount that something can produce.
Capacity is a noun
Hope this helps
If 2x-4 = 6, what is the value of 3x + 2?
When 2x-4 = 6, the value of 3x + 2 is 17.
What is the value of 3x + 2?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
When 2x - 4 = 6, the value of x will be:
2x - 4 = 6
2x = 6 + 4
2x = 10
Divide
x = 5
Therefore, 3x + 2 will be:
3x + 2 = 3(5) + 2
= 15 + 2
= 17
The value is 17.
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A water tank initially contained 105 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute How many minutes have passed, m. when the tank contains 181 liters? Round to the nearest hundredth
Answer:
8.44 minutes
Step-by-step explanation:
The tank initially contained 105 liters so the amount of water needed is 181 - 105 = 76 litters
if the rate is 9 L/min then the number of minutes is
76/9 = 8.44 minutes
You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary? (round to the nearest tenth, if needed)
The percent change in your salary is = 6%
Initial earning per hour = $12.50
New earning per hour after the raise = $13.25
The formula that we will be using to solve this question is -
= %change = [final value - initial value] ÷ [initial value] × 100
First, find the difference between the initial value and the final value
= $13.25 - $12.50
= $0.75
Divide the difference by the initial ( $12.50) value
= $0.75 ÷ $12.50
= 0.06
Convert the quotient into a percentage
= 0.06 x 100
= 6%
Therefore, the percentage change in your salary is = 6%
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For the job paying $12.50 per hour, the percent change in your salary after the raise is 6%.
What is the percent change in your salary after a raise?Given data:
Hourly salary after the raise = $13.25Hourly salary before the raise = $12.50Hourly increase:
= Hourly salary after the raise - Hourly salary before the raise
= $13.25 - $12.50
= $0.75
The percent increase is:
= (Hourly increase / Hourly salary before the raise) * 100
= ($0.75 / $12.50) * 100
≈ 6%.
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Write an equation of the line that goes through (-2,7) and (4,7)
Answer:
y=7
Step-by-step explanation:
y is always the same and it is 7
Write an equation to show that 68 is 8 times an many as 6.
8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.
What is meant by an equation?An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.
Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.
8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.
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sin 0 = 5/13 find tan 0 A 13/12 B 12/5 C 5/12 D 12/13
Answer: C.5/12
Step-by-step explanation:
Need an answer please will give Brainliest
The quotient will be = 2m^2 + 6m - 9m
The remainder will be = 0
Long division algorithm is below:
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Put the steps up above in order.
Answer:
1. Given
2. Vertical Angles Theorem (1st Occurrence)
3. Vertical Angles Theorem (1st Occurrence)
4. Transitive Property of Congruence
5. Converse of the Alternate Interior Angles Theorem
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Transitive Property of Congruence
If one pair of angles is congruent to a third angle, then the first angle is congruent to the third angle.
Converse of the Alternate Interior Angles Theorem
If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.
[tex]\begin{array}{l|l}\vphantom{\dfrac12} \sf Statements & \sf Reasons \\\cline{1-2}\\1. \; \angle 2 \cong \angle 7 & 1.\; \sf Given\\\\2. \; \angle 2 \cong \angle 3 & 2.\; \sf Vertical\;Angles\;Theorem\;(1st\;Occurrence)\\\\3. \; \angle 6 \cong \angle 7 & 3.\;\sf Vertical\;Angles\;Theorem\;(2nd\;Occurrence)\\\\4. \; \angle 3 \cong \angle 6 & 4.\;\sf Transitive\;Property\;of\;Congruence\\\\5. \; a \parallel b & 5.\;\sf Converse\;of\;the\;Alternate\;Interior\;Angles\;Theorem\\\\ \end{array}[/tex]
From inspection of the given diagram, we can see that angles 2 and 3 are vertical angles, similarly angles 6 and 7 are vertical angles. Therefore, the Vertical Angles Theorem applies.
According to the Transitive Property of Congruence, if ∠2 ≅ ∠7 and ∠2 ≅ ∠3 and ∠6 ≅ ∠7 then ∠3 ≅ ∠6.
The two lines a and b are intersected by transversal [tex]\ell[/tex] so that the alternative interior angles 3 and 6 area congruent, then the lines a and b are parallel. This is the Converse of the Alternate Interior Angles Theorem.
Let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) = integral^x_1, (t) dt. Find the values of g(2) and g(-2). For each of g'(-3) and g"(-3), find the value or state that it docs not exist. Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. For -4 < x < 3, find all values of v for which the graph of g has a point of inflection. Explain your reasoning.
a) The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2
b) The value of g'(x) = 2 The value of g''(x) =1
c) g has neither a relative maximum nor a relative minimum at x= 1
d) the graph of g has a point of inflection at each of x=-2 , x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
There are several types of functions in maths. Some important types are:
Injective function or One-to-one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
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Simplify the expression (-3r^2+13)+2r(r-6)-4r
Answer:
A potential energy function is given by U(x) = (3.6)x + (1.2)x3. What is the force function F(x) that is associated with this potential energy function
Step-by-step explanation: