Answers
For h(x), to find out the maximum, you would need to use this formula: [tex]c-(\frac{b^{2} }{4a} )[/tex]
We are given the equation: [tex]h(x)=-x^{2}+4x-2[/tex].
So, a = -1, b = 4, and c = -2. Then, substitute the numbers into the formula:
h(x)'s maximum = [tex]c-(\frac{b^{2} }{4a} )[/tex]
= [tex](-2)-(\frac{(4)^{2} }{4(-1)} )[/tex]
= [tex](-2)-(\frac{16 }{-4} )[/tex]
= [tex](-2)-(-4)[/tex]
= [tex]2[/tex]
For g(x), to find out the maximum, just look at the highest point of y on the graph of the function, which is 2.
Thus, the answer you have chosen is the correct answer, which is choice 3: functions g and h have the same maximum of 2. Hope this helps :)
Related Questions
What does it mean when a set is closed under addition?
Answers
Answer: I don't know
Step-by-step explanation:
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 9 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.
Answers
An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]
Given that,
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.
Define Parabola:A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The pipe is located 9 inches from the vertex of the mirror.
The parabola is open upwards . the vertex of the parabola is (0,0)
and pipe is located 9 inches from the vertex (0,0)
9 inches is the focus of the mirror
The distance between the vertex and the focus = 9
Since parabola is upwards and vertex is (0,0) we use formula,
[tex]4py = x^{2}[/tex]
Where,
p is the distance between the vertex and focus p = 9
Now,
[tex]4*9*y = x^{2}[/tex]
[tex]36y =x^{2}[/tex]
Now isolate y by dividing 36 on both sides, we get
y = [tex]\frac{x^{2} }{36}[/tex]
Therefore,
An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]
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What are all of the solutions to the equation 2x2 = 100?
O +5√2
O +10
O +50
O +√2
Answers
The solutions to the equation 2x^2 = 100 is [tex]x=\pm 5 \sqrt{2}[/tex].
How do you find all solutions of a quadratic equation?
The solutions of a quadratic equation ax2 + bx + c = 0 are given by the quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula, just get the equation into standard form ax2 + bx + c = 0, and apply the quadratic formula.
[tex]$$2 x^2=100$$[/tex]
Divide both sides by 2
[tex]\frac{2 x^2}{2}=\frac{100}{2}$$[/tex]
Simplify
[tex]x^2=50$$[/tex]
For [tex]$x^2=f(a)$[/tex] the solutions are [tex]$x=\sqrt{f(a)},-\sqrt{f(a)}$[/tex]
[tex]$$x=\sqrt{50}, x=-\sqrt{50}$$[/tex]
[tex]$$\begin{aligned}& \sqrt{50}=5 \sqrt{2} \\& -\sqrt{50}=-5 \sqrt{2} \\& x=5 \sqrt{2}, x=-5 \sqrt{2}\end{aligned}$$[/tex]
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6. A shop keeper has 56 pens. He
soid them for 280 dollars. How
much did the shopkeeper charge
for each pen?
Answers
The cost of each pen would be 5 dollars.
What is a unit value?
When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. Context: The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities
The shopkeeper has 56 pens. and he sold them for 280 dollars
Cost of each pen = total amount/ number of pens
= 280/56
=10/2
= 5
Hence, the cost of each pen would be 5 dollars.
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What is the nature of the roots 5x² 3x 2 0?
Answers
The Nature of roots of the quadratic equation "5x² -3x +2 = 0" is imaginary and conjugate .
To find the Nature Of Roots of the Quadratic Equation ax² + bx + c = 0 , we find the discriminant(D) by the formula ; D = b² - 4ac .
the quadratic equation is given as 5x² -3x +2 = 0 ;
On comparing , we get , a = 5 , b = -3 and c = 2 .
Substituting the values in the Discriminant formula mentioned above , we get
D = (-3)² - 4×5×2
= 9 - 40
= -36 .
Since the value of the discriminant is less than 0 ,
Therefore , the roots will be imaginary and conjugate .
The given question is incomplete , the complete question is
What is the nature of the roots of the equation 5x² -3x +2 = 0 ?
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What is the formula for 3 consecutive integers?
Answers
The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let us find three consecutive integers whose sum is 399. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 399. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 399
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 399
3X + 3 = 399
3X + 3 - 3 = 399 - 3
3X = 396
3X/3 = 396/3
X = 132
Which means that the first number is 132, the second number is 132 + 1 and the third number is 132 + 2. Therefore, three consecutive integers that add up to 399 are 132, 133, and 134.
Hence , The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.
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Write the inequality that represents the scenerio :
Vanessa has at most $100 in her savings account
Answers
Answer: I am bad at math, but I'd say _> is the sign...
Step-by-step explanation:
elloooo
Why is 2 a prime number?
Answers
2 is a prime number because it has only two factors (1 x 2).
What are prime number?A natural number greater than one that is not the product of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than 1 that is not prime.
Numerical tables, which were typically printed before calculators and computers, were used to record all primes or prime factorizations up to a certain limit. The Sieve of Eratosthenes is the most well-known method for making a list of prime numbers.
Given why 2 is prime,
The natural numbers greater than 1 with exactly two factors, i.e. 1, and the number itself, are known as prime numbers.
so 2 has only two multiple
1 and 2,
Hence 2 is a prime number.
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What are the 3 steps when finding vertical asymptote?
Answers
Identify the denominator of the function and set it equal to zero. Solve the equation to find the x-values of the asymptote. Substitute the x-values found in step two into the original equation to determine if the vertical asymptote is a true asymptote.
The first step when finding vertical asymptotes is to identify the
denominator of the function and set it equal to zero. This creates an equation which can then be solved to find the x-values of the asymptote. The second step is to solve the equation, using methods such as factoring or completing the square, to find the x-values of the asymptote. The final step is to substitute the x-values found in step two into the original equation and determine if the vertical asymptote is a true asymptote. If the limit of the function as x approaches the x-value found in step two is either positive or negative infinity, then the vertical asymptote is a true asymptote. If, however, the limit of the function as x approaches the x-value found in step two is not infinity, then the vertical asymptote is not a true asymptote. This process of finding vertical asymptotes can be used to find the vertical asymptotes of any function.
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What is the value of polynomial 5 x minus 4 x square 3 at x is equal to zero?
Answers
The value of polynomial 5x - 4x² + 3 at x=0 is equal to 3
Given that,
The polynomial is 5x - 4x² + 3
To find : The value of polynomial 5x - 4x² + 3 at x=0
A combination of more than two algebraic expressions, particularly when they each contain a distinct power of the same variable (s).Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.
Given : x = 0
→ 5x - 4x² + 3
→ 5 ( 0 ) - 4 ( 0) ² + 3
→ 0 - 0 + 3 ( ∵ here + 0 - 0 cancels )
→ 3
Therefore, The value of polynomial 5x - 4x² + 3 at x=0 is 3.
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A movie theater lets you serve yourself candy for $0.79 per ounce. At that price, how much would you pay for 5.27 ounces of candy? Round your answers to the nearest cent.
Answers
So 4.2 is the answer
Who find the sum of integers from 1 to 100?
Answers
The sum of the integers from 1 to 100 is 5050. You can find this sum by adding all of the integers together or by using the formula for the sum of an arithmetic series.
sum = (number of terms) * (average of the first and last term)In this case, there are 100 terms, and the average of the first and last term is (1 + 100) / 2 = 50.5, so the sum is 100 * 50.5 = 5050.
Another way to find the sum is To find the sum of the integers from 1 to 100, we can add all of the integers together. This can be done by starting with 1 and repeatedly adding 1 to get the next integer, or by using a calculator or computer program to do the calculations for us.
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What is the inverse of X²?
Answers
Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].
Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].
What is Inverse ?To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.
A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex] .
Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].
Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].
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Figure P is the result of a transformation on Figure O Which transformation would accomplish this?
Answers
Figure P is the result transformation figure O by the rule (x + 1, y-4). In other words, figure O shifted 1 unit left and 4 units downward direction.
What is meaning transformation?
An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.
The coordinate of vertices of figure O are (2,4), (3,5), and (4,2).
The coordinate of vertices of figure P are (3, 0), (4,1), and (5, -2).
The difference between x-coordinates is (3 - 2) = (4 - 3) = (5 - 4) = 1.
The difference between y-coordinates is (0 - 4) = (1 - 5) = ( -2 - 2) = -4.
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The boeing 747-8 intercontinental jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel. use a linear model to predict the amount of jet fuel that is present on the jet after it has been in flight for 18 hours without stopping to refuel. in two or more complete sentences, explain your answer.
Answers
The initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours of flight.
The linear model that can be used to predict the amount of jet fuel present on the Boeing 747-8 Intercontinental jet after 18 hours of flight without refueling is given by the equation
F = 63,500 - (800 x 18),
where F is the amount of jet fuel in gallons and 18 is the number of hours of flight. This equation indicates that after 18 hours of flight, the jet would have an estimated amount of jet fuel of 42,400 gallons remaining. This amount is significantly lower than the initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours of flight.
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A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 10,000 3% 10,001 - 50,000 5% 50,001 - 100,000 5.5% Calculate the state income tax owed on a $40,000 per year salary. tax = $[?] Round your answer to the nearest whole dollar amount. Enter
Answers
The state income tax owed on the $40,000 salary should be $1,800.
What is Income Tax?An income tax is a tax levied on persons or companies based on their earnings or profits. In most cases, income tax is calculated as the result of a tax rate multiplied by the taxable income. Taxation rates may differ depending on the taxpayer's attributes and the source of income.
Given:
Income Progressive Range ($) Tax Rate
0- 10,000 3%
10-001- 50000 5 %
50001- 100000 5.5%
The calculation of the state income tax owed on $40,000 salary
= 3% of $10,000 + 5% of $30,000
= $300 + $1,500
= $1,800
Hence, the state income tax owed is $1,800.
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3kx + 24 = 9kx solve for X
A: -2/k B: 4/k C: -4/k D:2/k
Answers
Answer: x= 4/k
Step-by-step explanation:
Answer:
B.) [tex]\frac{4}{k}[/tex]
Step-by-step explanation:
[tex]3kx+24=9kx\\3(kx+8)=9kx\\\frac{3(kx+8)}{3}=\frac{9kx}{3}\\kx+8=3kx\\(kx+8)-kx=(3kx)-kx\\8=2kx\\\frac{8}{2k}=\frac{2kx}{2k}\\\frac{4}{k}=x[/tex]
What's the most common number of siblings students in this class have?
Answers
Answer:
Three and four and five and zero.
Step-by-step explanation:
Answer:
3 and 4
Step-by-step explanation:
The question is in the picture below :)
Answers
Answer:
Number of international passengers increased then decreased whereas the number of domestic passengers constantly increased
Step-by-step explanation:
Nancy is making accessories for the soccer team. She uses 866.18 inches of fabric on headbands for 43 players and 3 coaches. She also uses 378.83 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answers
The amount of fabric used on the headband and wristband for each player is 27.64 inches.
Mathematical Operations:
The operations that we use in particular actions like adding and taking away things or adding multiple times, diving things, etc.
The four basic Mathematical operations are addition, subtraction, multiplication, and division.
Here in this problem, we use divisions to solve the problem,
Given that,
Nancy uses 866.18 inches of fabric on headbands for 43 players and 3 coaches. 378.83 inches of fabric used on wristbands for the players only.
Number of headbands made with 866.18 inches
= 43 (player's) + 3 (coach's)
= 46 headbands
The amount of fabric used for 1 head band = (866.18)/46 = 18.83 in
378.83 inches of fabric used on wristbands for the players only.
The amount of fabric used for each wristband = 378.83/43 = 8.81 in
Amount of fabric used on headband and wristband = 18.83 + 8.81
= 27.64 inches
Therefore,
The amount of fabric used on the headband and wristband for each player is 27.64 inches.
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What is the answer to -( 7 4x )= 9?
Answers
The answer to the expression -( 7 4x )= 9 is -7, since subtracting 7 from both sides of the equation leaves us with 4x = 2, and then dividing both sides of the equation by 4 gives us x = -7.
The expression -( 7 4x ) = 9 can be solved by using basic algebraic operations. First, we subtract 7 from both sides of the equation to obtain -4x = 2. This is because when subtracting a number from both sides of an equation, we are essentially adding the opposite of that number to both sides. Then, we divide both sides of the equation by 4 to obtain x = -7. This is because when dividing both sides of the equation by a number, we are essentially multiplying both sides by the inverse of that number. Therefore, the answer to the expression is -7.
-(7 4x ) = 9
-7 - 4x = 9
-4x = 2
x = -7
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What is the mode of 1 2 3 4 5 6 7 8 9 10?
Answers
The mode of a set of numbers is the number that appears most often in the set. In the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there is no number that appears more often than any other, so the mode of this set is not defined.
How does math work out the mode?The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group. The mode is the one that is most prevalent.
With an example, what is the mode formula?The value that appears most frequently in a set of values is referred to as the mode. It is the value that shows up the most frequently. Example: Since the number 5 appears twice in the provided data set of 2, 4, 5, 6, and 7, it is the mode of the data set. 2
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Which polynomial function could be represented by the graph below?
Answers
The polynomial function that could be represented by the graph is; f(x) = x³ + x² - 6x
What is the equation of the Polynomial?Let us find the zeros of the polynomial from the graph. The zeros of the polynomial will be the points where the graph crosses the x-axis.
Thus, we see that the graph crosses the x-axis at x = -3, 0 and 2. Thus, the factors of the polynomial are;
(x - 0), (x + 3) and (x - 2)
Therefore, the equation of the polynomial is;
f(x) = x(x - 2)(x + 3)
Expanding this gives us;
f(x) = x(x² + x - 6)
f(x) = x³ + x² - 6x
We conclude that is the equation of the polynomial represented by the graph.
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Latanya had math and reading homework tonight. Latanya can solve each math problem in 1.5 minutes she can read each page in two minutes. The number of math problems Latanya had is 4 more than the number of pages she read and it took her 48 minutes to complete all of her homework. graphically solve a system of equations in order to determine the number of math problems Latanya solved, X, and the number of pages she read, y.
Answers
The system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.
What exactly is a math equation?equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, the search for a way to respond to them has spurred the development of mathematics.
Here,
Given data:
Time taken by Latanya to solve a problem = 1.5 minute.
Time to read one page = 2 minutes.
Number of problems completed = x problems.
Total time used for reading = y minutes.
Using the data to consider:
Let x be the the number of math problems that Latanya solved.
Let y be the number of pages that Latanya read.
thus,
1.5x +2 y = 48
and
x = 4 + y
Thus, we can conclude the the system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.
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Why is 3.14 called pi?
Answers
It was first called "pi" in 1706 by William Jones, because pi is the first letter in the Greek word perimitros, which means "perimeter."
question 21 options: suppose the american kennel club estimates that 38% of households in u.s. have a pembroke welsh corgi. a random sample of 400 households is taken. round probability answers to 4 decimal places, i.e. .xxxx do not include leading or ending zeros. what is the probability the sample proportion is more than 40%?
Answers
The probability that the sample proportion is more than 40% is approximately .0001.
What is Probability?
Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.
To find the probability that the sample proportion is more than 40%, we need to use the normal distribution and the central limit theorem.
The central limit theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
To find the probability that the sample proportion is more than 40%, we need to first calculate the mean and standard deviation of the sample proportion. The mean of the sample proportion is equal to the population proportion (38%), and the standard deviation of the sample proportion is equal to:
[tex]standard\ deviation = sqrt((population\ proportion * (1 - population\ proportion)) / sample\ size)\\\\= \sqrt{((.38 * .62) / 400)}\\\\= .048[/tex]
Next, we need to standardize the sample proportion of 40% by subtracting the mean and dividing by the standard deviation:
z = (40% - 38%) / .048 = 4.17
The probability that it is less than or equal to 40% is approximately .9999.
The probability that the sample proportion is more than 40% is then equal to 1 - .9999 = .0001.
So, The probability that the sample proportion is more than 40% is approximately .0001.
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What is the domain of F x all real numbers?
Answers
On solving the provided question we can say that - The answer to the question is that all real numbers or domain (−∞,∞)
What is Domain?The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.
The answer to the question is that all real numbers or (−∞,∞)
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A business recently upgraded a conference TV they had in their conference room. Originally the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches. The new TV is 66 inches across the diagonal. Since the new TV will be recessed in the wall, it will need trim put on the border. What is the perimeter of the new TV? Round your answer to two decimal places.
Answers
The perimeter of the new TV will be 179.77 inches.
How to calculate the perimeter?From the information, the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches and the new TV is 66 inches across the diagonal.
It should be noted that the perimeter simply means the total length of the boundary of the object. This will be calculated thus:
= (66 × 87.16) / 32
= 5752.56 / 32
= 179.77 inches.
In conclusion, the perimeter is 179.77 inches.
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3200 people attended a football game. If 10% of the people who attended were teenagers, how many teenagers attended the game?
Answers
Answer:
320 teenagers
Step-by-step explanation:
10% = 0.1
Take 3200 times 0.1 = 320
So, there are 320 teenagers attended the football game.
During which phase of the systems life cycle are users trained to use the new system?
Answers
Answer:
Step-by-step explanation:
The phase of the systems life cycle during which users are trained to use the new system is called the implementation phase. In this phase, the new system is installed and made operational, and users are trained on how to use it effectively. This phase typically follows the design and development phases and precedes the maintenance phase.
What is the main focus of the implementation phase in the systems life cycle?
The main focus of the implementation phase is training users to use the new system effectively. This includes installing the system and making it operational, as well as providing necessary support and training to ensure users are able to utilize the system efficiently.
The phase of the systems life cycle during which users are trained to use the new system is the implementation phase. This is the phase where the new system is actually implemented and made available for use by the users. It is important to provide training to users during this phase so that they are able to effectively use the new system and understand its functionality.
Therefore, users are trained to use the new system during the implementation phase.
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The implementation phase of the systems life cycle is the time when users are taught how to utilize the new system.
The new system is installed, made operational, and users are instructed on how to utilize it efficiently during the implementation phase. In most cases, this phase comes after the design and development phases and comes before the maintenance period.
Why is user training important during the implementation phase of the systems life cycle?
User training is important during the implementation phase of the systems life cycle because it ensures that users are able to effectively use the new system and understand how it works. This is essential for the successful adoption and utilization of the system by the organization. Without proper training, users may struggle to use the system effectively, leading to reduced productivity and potentially even causing issues with data accuracy and integrity. By providing thorough user training, organizations can ensure that their employees are able to use the new system efficiently and effectively, leading to a successful implementation.
The implementation phase of the systems life cycle is the time when users are taught how to utilise the new system. In this stage, the new system is really put into use and made accessible to users. During this stage, it's crucial to give users training so they can utilize the new system correctly and comprehend its functions.
Therefore, during the implementation phase, users are instructed on how to utilize the new system.
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