Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary when calculated using discriminant.
Define root.In mathematics, the number that results in the original number when it is multiplied by itself is called the root.
How we can find nature of roots?We can find nature of root using discriminant.
B² - 4AC = 0 ----> Roots are equal ,real & rational
B² - 4AC > 0 , and also a perfect square --> Roots are real , distinct & rational
B² - 4AC >0 ,but not a perfect square -----> Roots are real, distinct & irrational
B² - 4AC <0 , ---> Roots are imaginary
B² - 4AC >= 0 ---> Roots are real
Given 2x² - 4x + 3 = 0
Now, Calculate Discriminant,
Here
B = -4
A = 2
C = 3
==> B² - 4AC
= (-4)² - 4 * 2 * 3
= 16 - 24
= -8 < 0
Discriminant is negative
Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary .
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What is the quotient x3 3x2 5x 3 )/( x 1?
The quotient (x3 - 3x2 + 5x - 3) ÷ (x - 1) is x2 - 2x + 3 and remainder becomes zero
What means quotient in math?
Definition of Quotient
The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.
x^3 - 3x^2 +5x -3 / x-1 = x^2 -2x +3
x^3 -+ x^2
------------
0 2x^2 +5x
2x^2 +2x
----------------
0 3x +3
3x +3
---------
0 0
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The table shows three unique, discrete functions.
Which statements can be used to accurately compare the functions? Select two options.
g(x) has the lowest minimum.
f(x) has the greatest maximum.
All three functions have a y-intercept.
All three functions have an x-intercept.
The domain of all three functions is the s
We are aware that a discrete function is one that satisfies the criteria for a function and has a countable domain (represented as a collection of disconnected points) (each input has at most one output). Many inputs in discrete functions won't have any outputs.
According to the inquiry,
All three of the functions have a y-intercept and, given the facts in the question, f(x) is the highest maximum.
The largest maximum of the three functions—g(x), f(x), and f(y)—has an x-intercept.
Three distinct discrete functions are displayed in the table.
f(x)minimum: 1 g(x)minimum; -4 12 h(x)minimum-5; as a result, f(x)maximum: 10 g(x)maximum; 3 12 h(x)maximum; 12 f(x)domain; (0, 2) g(x)domain; (-2, 2) h(x)domain; (0, 1) g(x)y-inter (0, -5)
Using the procedures above, we may conclude that f(x) has no x.
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solve the simultaneous equation:
6x+y=29
3x-y=7
Answer:
x=4
y= 5
Step-by-step explanation:
6x+y=29
3x-y=7
Let's add them together
9x = 36
x= 4
Then put 4 back in the equation for x
6(4) + y =29
24 + y = 29
y= 5
find the exact length of the curve. y = ln 1 − x2 , 0 ≤ x ≤ 1 9
The exact length of the curve for the function y = ln(1 - x²) is log(5/4) - 1/9
The general formula for the arc length of the curve y on the interval [a, b] is written as,
[tex]s=\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx[/tex]
Here we have given that the function is y = ln(1 - x²)
And the limit is 0 ≤ x ≤ 1/9
When we differentiate the function, then we get the value of y' as,
y' = 1/(1 - x²) × (-2x) = -2x/(1 - x²)
Now, we have to apply the values on the arc length formula, then we get,
[tex]s=\int\limits^{1/9}_0 {\sqrt{1+(\frac{-2x}{1-x^2} )^2 } } \, dx[/tex]
When we simplify this one then we get,
[tex]s=\int\limits^{1/9}_0 {\sqrt{\frac{1+x^4-2x^2+4x^2}{(1-x^2)^2} } } \, dx[/tex]
Now, we have to divide numerator by denominator and expressing using
the rule Dividend/Divisor = Quotient + (Remainder/Divisor)
Then we get the resulting equation as,
[tex]s=\int\limits^{1/9}_0 {-1 + \frac{2}{1-x^2} } \, dx[/tex]
When we apply the limit value, then we get
s = −1/9 + log∣10/8∣−log(1)
When we simplify this one then we get,
s = log(5/4) - 1/9
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What are actual roots of FX according to the rational root theorem The following are potential roots of FX 2x 2 2x 24 4 3 2 3 4?
All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.
We have the given polynomial:
f(x) = 20x4 + x3 + 8x2 + x - 12
All potential polynomial roots are represented by rational numbers, according to the Rational Root Theorem:
x = a/b
Where a is a factor of a constant term
b is the factor of coefficient of leading term
From the given polynomial:
-12 is the constant term and 20 is the coefficient of leading term
The possible factors of -12 are ±1, ±2, ±3, ±4, ±6, ±12
The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20
So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)
Solve for x when the given function is equal to zero
20x4 + x3 + 8x2 + x - 12 = 0
(4x - 3)(5x + 4)(x2 + 1) = 0
So we get:
4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0
x = 3/4, x = -4/5, x =1, x = -1
Hence, the rational roots are x = 3/4, x = -4/5.
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We have the given polynomial:
f(x) = 20x4 + x3 + 8x2 + x - 12
x = a/b
b is the factor of coefficient of leading term
-12 is the constant term and 20 is the coefficient of leading term
The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20
So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)
Solve for x when the given function is equal to zero
20x4 + x3 + 8x2 + x - 12 = 0
(4x - 3)(5x + 4)(x2 + 1) = 0
4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0
x = 3/4, x = -4/5, x =1, x = -1
Yesterday at a museum there was a total of 30
adult and children tickets bought. Children
tickets cost 5$ and adult tickets cost 8$. In total
40$ was spent yesterday. What is the total
amount of children tickets bought?
Thus, total amount of children tickets bought =30 tickets
What is equation ?equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.
Here,
The total adults and children ticket bought = 50
The cost of one children ticket= 10$
The cost of one adult ticket= 20$
The total spent amount = 700$
let adult be y and children be x
Thus,
equation => x+y=50 and 10x+20y=700
=>x=50-y
=>10(50-y)+20y=700
=>500 -10y +20y =700
=>500+10y =700
=>10y=500-700
=>y=200/10
=>y=20
=>x=50-20=30
=>x=30
Thus, total amount of children tickets bought =30 tickets
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eliminate the parameter t to find a Cartesian equation for: x=t2 y=2+3t x=Ay2+By+C Where A=________ B=__________ and C=________ If you can give step by step help that is GREATLYappreciated!!!
The cartesian equation for x = t² and y = 2 + 3t is x = (1/9)y² - (4/9)y + (4/9).
Where the value of A, B, and C are 1/9, - 4/9, and 4/9.
The parameter t that we have
y = 2 + 3tThe cartesian equation x = (1/9)y² - (4/9)y + (4/9)
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pls help me and explain how to do this TwT
Answer:
7
Step-by-step explanation:
index of root = 2
exponent = 2
divide both by 2
2:2 = 1 (the root expires)
2:2 = 1 (the exponent expires)
7
What is the solution of the system of equations 6x 2y 4 9x 3y 12?
The solution of the given system of equations 6x + 2y = 4 , 9x -3 y = 12 is equal to x =1 and y = -1.
As given in the question,
Given system of equations are :
6x + 2y = 4 ____(1)
9x -3 y = 12 _____(2)
Multiply (1) by 3 and (2) by 2 and add equation (1) and (2) to eliminate y variable and get the value of variable x ,
18x + 6y = 12
18x - 6y = 24
36x = 36
⇒x = 36 / 36
⇒ x = 1
Substitute value of x = 1 in the given equation (1) to get the value of variable y,
6(1) + 2y = 4
⇒ 6 + 2y = 4
⇒ 2y = 4 - 6
⇒ y = -1
Therefore, given system of equations 6x + 2y = 4 , 9x -3 y = 12 solution is equal to x = 1 and y = - 1.
The above question is incomplete, the complete question is:
What is the solution of the system of equations 6x + 2y = 4 , 9x -3 y = 12?
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What us the third step in sketching the graph of a rational function
The third step in sketching the graph of a rational function is "Finding the function's zeros and vertical asymptotes and plotting them on a number line".
What is vertical asymptotes?
A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as the inputs get closer to the value of a. A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph approaches the line as the inputs go closer to ∞ or –∞.
The steps to sketch a graph of rational function:
1. Ensure that the function's denominator and numerator are listed in decreasing order of power.
2. Discover the domain
3. Completely factor the numerator and denominator. Any shared factors between the numerator and denominator should be eliminated. (Once factors have been cancelled, the reduced function is what remains. For all subsequent actions, employ the reduced function.) Skip Step 4 if there are no common factors.
4. Look for any holes
5. Search for any vertical asymptotes.
6. Find the Horizontal Asymptote.
7. Look for any x- and y-intercepts.
8. Locate test points
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What is the median of the number 445 767 712 and 3?
The Median for the following data 3 445 712 767 will be 578.5.
One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.
When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:
sorting of the sample data in ascending or descending order.
If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.
The average of the top two observations is the same as the median of the data given (as determined in step 2).
Here n = 4, So [4/2 + (4/2)+1}/2, So the median will be 578.5.
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A 5 1/2 inch candle burns down in 11 hours. how far has it burned after 6 1/2 hours?
The candle has burned down [tex]3 \frac{3}{4}[/tex] inches after 6.5 hours.
To calculate this, we first need to determine the rate at which the candle burns by dividing the total burn time (11 hours) by the total length of the candle ( [tex]5 \frac{1}{2}[/tex] inches). This gives us a burn rate of 2 hours per inch.
Next, we can multiply the burn rate by the time the candle has been burning (6.5 hours) to determine how far the candle has burned. This gives us a result of 13 inches, which is equal to [tex]3 \frac{3}{4}[/tex] inches in standard units. Therefore, the candle has burned down [tex]3 \frac{3}{4}[/tex] inches after 6.5 hours.
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How do you arrange the angles of a triangle from smallest to largest?
If you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.
What are angles?Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned.
Angles are also produced when two planes intersect.
These are what are known as dihedral angles.
Consequently, if you have three side lengths, you should discover the lowest angle by finding the angle that is opposite the smallest side, the medium-sized angle by finding the angle that is opposite the medium-sized side, and the greatest angle by finding the angle that is opposite the largest side.
Therefore, if you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.
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Which out of the following are expressions with numbers only?
(a) y + 3
(b) (7 × 20) – 8z
(c) 5 (21 – 7) + 7 × 2
(d) 5
(e) 3x
(f) 5 – 5n
(g) (7 × 20) – (5 × 10) – 45 + p
5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.
What equation contains an expression?
The equal to sign (=) is the best indicator of whether a given problem is an equation or an expression because it indicates that the problem is an equation.
It is only an expression if there isn't an equal to (=) sign present. It contains data that is used to demonstrate value, such as numbers, variables, and operators.
5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.
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What is the mean of the data 6 7 10 12 13 4 8 12?
The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms. Hence, we can say;
Mean = Sum of the Given Data/Total number of Data
Mean= 6 +7+ 10+ 12+ 13+ 4+ 8 +12 / 8 = 72/8 = 9
Hence, The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.
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Which inequality is true?
A. 2 pi/ 2 < 3
B. 4 pi > 12
C. pi + 6 < 9
D. 3 pi - 1 < 8
The true inequality is 4π > 12.
How to solve inequality?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. Therefore, let's solve the inequalities that is true.
Hence,
[tex]\frac{2\pi }{2} < 3[/tex]
π < 3 (This is false because 3.14 is greater than 3)
4π > 12
divide both sides by 4
π > 3 (This is true.)
π + 6 < 9
subtract 6 form both sides
π < 3 (This is false)
3π - 1 < 8
3π < 9
π < 3 (This is false)
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find the range of the function f(x) = x^2 - 6x if the domain is (-7, -2, 1)
The range of the function f(x) = x² - 6x with domain of (-7, -2, 1) is calculated to be (91, 16, -5)
How to find the range for the given domainsThe domain is controlled by the input values. considering the points (-7, -2, 1)
The range is solved using the given function
f(x) = x^2 - 6x
substituting for x in the function
for x = 7
= 7² - 6 * -7 = 91
for x = -2
= -2² - 6 * -2 = 16
for x = 1
= 1² - 6 * 1 = -5
The range is (91, 16, -5)
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Select each pair of equivalent numbers.
Answer:
B, D
Step-by-step explanation:
To change a fraction to a decimal, divide the numerator (number on top) by the denominator (number on the bottom).
To change a decimal number to a percent, multiply the number by 100%.
A. 40/1000 = 0.04 = 4%
No
B. 6/5 = 1.2 = 120%
Yes
C. 50/33 = 1.5151... = 151.51...%
No
D. 1/8 = 0.125 = 12.5%
Yes
E. 1/3 = 0.333... = 33.333...%
No
Answer: B, D
Create a proportional ratio to the given ratio.
14
17
(well i'll give it my best shot)
14:17
⬇️
let's add 14 and 17 together.
***************
14 + 17 = 31
14 = 14/31 (*fraction*)
17 = 17/31 (*fraction*)
I hope this helps in any way possible.
Merry Christmas (Eve), Happy New Year, and Happy Holidays!
In 2010, the population of a city was 193,000. From 2010 to 2015, the population grew by 6%. From 2015 to 2020, it fell by 3%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
Answer:
6138
Step-by-step explanation:
First, we have to find the population of the city in 2015
6% = 0.06
193,000 times 0.06 = 11580 people increase
We know it is increasing, so we have to add them
193,000 + 11580 = 204580 people in 2015
Now let's find the 3% decrease
3% = 0.03
204580 times 0.03 = 6137.4
So, about 6138 people decrease from 2015 to 2020
Kathleen likes to make desserts for bake sales. Last month, she made 1 batch of brownies
and 1 batch of cookies, which called for 7 eggs total. The month before, she baked 1 batch of
brownies and 2 batches of cookies, which required a total of 11 eggs. How many eggs did
Kathleen use for a batch of each dessert?
eggs to make a batch of brownies and
Kathleen uses
of cookies.
Submit
eggs to make a batch
You h
Jay
Sales is a term used to describe the activities that lead to the selling of goods or services.
What is sales explain with an example?A sale is a transaction between two or more parties in which goods or services are exchanged for money or other assets. In the financial markets, a sale is an agreement between a buyer and seller involving the price of a security and its delivery for agreed-upon compensation.Sales play a key role in the building of loyalty and trust between customer and business. Trust and loyalty are the main reasons why a customer would choose to recommend your company to a friend or family member or write a great review of your product or service online.In general business operations, sales refer to any transactions where money or value is exchanged for the ownership of a good or entitlement to a service. In an accounting context, sales refers to a company's revenue earned from the sales of products or services (net sales).There are two main types of sales that sales representatives deal with: inside sales and outside sales. Inside sales. Inside sales are any sales done remotely or from the home office. These sales include phone, email, CRM platforms, and VOIP sales.Let x represent the number of eggs that she uses for one batch of brownies.
Let y represent the number of eggs that she uses for one batch of cookies.
Last month, she made 2 batches of brownies and 3 batches of cookies. This means that
2x + 3y = 16 - - - - - - - - - -1
The month before, she baked 1 batch of brownies and 1 batch of cookies, which required a total of 6 eggs. This means that
x + y = 6 - - - - - - - - - - - - - 2
Multiplying equation 1 by 1 and equation 2 by 2, it becomes
2x + 3y = 16
2x + 2y = 12
Subtracting, it becomes
y = 4
Substituting y = 4 into equation 2, it becomes
x + 4 = 6
x = 6 - 4 = 2
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Forty percent of the pupil in m. Alcantara' grade 6 claa are 12 year old. Another 0. 25 are 13 year old and the ret of the cla i 11 year old. Write 11 a a fraction,decimal,and percent
Answer:
7/20
0.35
35%
Step-by-step explanation:
12 year olds: 40%
12 year olds: 25%
11 year olds: 100% - 40% - 25% = 35%
35% = 35/100 = 7/20
35% = 0.35
35% = 35%
this question is not making sense to me, i need a quick answer.
Answer:
x-intercept: (-21/2,0)
y-intercept : (0,-21)
A sum of money is to be divided between Alyah, Byron and Cecil. Alyah receives $1 plus one-third of what is left. Byron then receives $6 plus one-third of what remains. Cecil receives the rest, which amounts to $40. How much did Byron receive? (A) $26 (B) $28 (C) $30 (D) $32 (E) $34
Answer:
(A) $26
Step-by-step explanation:
You want to know the amount Byron received from the distribution to Alyah, Byron, and Cecil, given Cecil received $40.
SetupLet x represent the amount being distributed, and a, b, c represent the amounts received by Alyah, Byron, and Cecil, respectively.
The given relations tell us ...
a = 1 + 1/3(x -1)
b = 6 + 1/3(x -a -6)
c = x -a -b = 40
SolutionSubstituting for b gives us ...
40 = x - a - (6 +1/3(x -a -6)) = x -a -6 -1/3x +1/3a +2 = 2/3x -2/3a -4
44 = 2/3(x -a) . . . . . . . add 4, factor out 2/3
66 = x -a . . . . . . . . . multiply by 3/2
Substituting for a gives us ...
66 = x -(1 +1/3(x -1)) = x -1 -1/3x +1/3 = 2/3x -2/3 = 2/3(x -1)
99 = x -1 . . . . . . . multiply by 3/2
100 = x . . . . . . add 1
DistributionThen ...
a = 1 + 1/3(100 -1) = 1 + 99/3 = 34
b = 6 + 1/3(100 -34 -6) = 6 + 1/3(60) = 26
Byron received $26.
__
Additional comment
Based on results, the "what is left" is the amount after the $1 or $6 distributions are made.
Alyah: $34, Byron: $26, Cecil: $40, for a total of $100.
<95141404393>
What is the relationship between the base and the height of an area formula?
A triangle's area is 1/2(b*h), where b is the base and h is the height. A triangle's base can be any of its sides, and its height is the length of the altitude from the opposite vertex to that base.
What is area?The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
The area of a triangle is 1/2(b*h), where b is the base and h is the height. A triangle's base is any one of its sides, and its height is the length of the altitude from the opposite vertex to that base.
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What is a parabola parent function?
The parent function of a parabola is y = x².
A function is said to be a parent function if it is expressed in the simplest form and satisfies the definition of a particular type of function.
The simplest function that satisfies the definition of a parabola is given by y = x². It is also called quadratic function.
Its graph passes through the origin (0,0) and lies in first and second quadrant.
One or more parabolas can be easily obtained by transforming the parent function of the parabola.
Therefore, the parent function of parabola is given by y = x².
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What are two important first steps in data analysis? -Cleaning the data and exploring it -Cleaning and scrubbing the data -the box plot and the 5 number summary -correlation and regression
The two important first steps in data analysis are data cleaning and exploring it, so, option A is correct.
What is correlation?A measure of the relationship between two variables is a correlation. Variables can be related in a number of ways, including linearly, non-linearly, and in other ways. Variables can also have varying degrees of association with one another. The most popular linear coefficient used to determine how closely two variables correlate is called Pearson's correlation coefficient, or PCC.
The steps of data analysis are shown below,
First, define the question. Identifying your purpose is the first stage in any data analysis procedure.
Gathering the data is the second step.
Third step: data cleaning.
The fourth step is data analysis.
Five: Present your findings.
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How many integers are there between 1 and 100 which have 4?
There are 19 such integers with 4 as a digit between 1 and 100, including 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, and 94.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 3.14 and 1*(1/2) are two examples of numbers that are not integers. The collection of whole numbers and their antipodes is known as the integers. The set of integers does not include fractions or decimals. Integers include, for instance, 2,5,0,12,244,15, and 8.
4-digit numbers are ones with only four digits, the first of which must be one or higher and the remaining three of which may be any number between zero and nine. Four-digit numerals include 5693, 1023, and 9825 as examples. The INTEGER data-type stores whole numbers with a precision of 9 or 10 digits, ranging from -2,147,483,647 to 2,147,483,647. Because it is a reserved value, the number 2,147,483,648 cannot be utilized. The INTEGER value is generally used to store counts, amounts, and other data since it is stored as a signed binary integer.
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How do you check XY coordinates?
What is the value of 4 3 answer?
The value of 4 to the 3rd power =64
According to the power rule of exponents,
am = m times a x a x a
Thus, 43 can be written as 4 × 4 × 4 = 64.
Thus, the value of 4 to the 3rd power i.e., 4^3 is 64
Exponent is the process of representing huge numbers as powers, according to the definition. Exponent, then, is the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.
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