The matrix will not have an inverse if the determinant is 0; in this case, it is referred to as singular.
What is the inverse function?An inverse function is a function that gives back the initial value for which an output was provided by another function. The inverse function of y, or [tex]f^{-1}(y)[/tex], will return the value x if f(x) is a function that produces the value y.
Put negatives in front of b and c, swap the locations of a and d, then divide the result by the determinant to determine the inverse of a 2×2 matrix (ad-bc).
Not every matrix of size 2 by 2 has an inverse matrix. The matrix will not have an inverse if the determinant is 0; in this case, it is referred to as singular. Inverses exist only for non-singular matrices.
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Put negatives in front of b and c, swap the locations of a and d, then divide the result by the determinant to determine the inverse of a 2x2 matrix (ad-bc).
What is inverse function?A function known as an inverse function returns the beginning value for which an output was produced by another function. If f(x) is a function that yields the value y, then will return the value x when used as the inverse function of y, or.To find the inverse of a 22 matrix, place negatives in front of b and c, swap a and d's positions, then divide the outcome by the determinant (ad-bc).There isn't always an inverse matrix for a matrix of size 2 by 2. If the determinant is 0, the matrix will not be singular and will not have an inverse. Only matrices that are not singular have inverses.Hence, Put negatives in front of b and c, swap the locations of a and d, then divide the result by the determinant to determine the inverse of a 2x2 matrix (ad-bc).
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Please help! My test is timed and im having trouble
Solve the following problem. It may be helpful to use draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.
A grocer wants to make a 10-pound mixture of cashews and peanuts that he can sell for $3.64 per pound. If cashews cost $5.80 per pound and peanuts cost $2.20 per pound, how many pounds of each must he mix?
He will have to mix 3 pounds of cashews and 7 pounds of peanuts .
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Let c be denoted as cashew and p be denoted as peanuts
c + p = 10 ⇒ (1)
5.6c + 2.3p = 3.29*10 ⇒ (2)
Multiply eq(1) by 560
Multiply eq(2) by 100
560c + 560p = 5600
560c + 230p = 3290
Subtract and solve for "p":
330p = 2310
p = 7 (amt. of peanuts needed)
substitute the value of p in eq(1)
c + 7 = 10
c = 3 (amt. of cashews needed)
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The acceleration due to gravity on the surface of planet x is 19. 6 meters per second.
Answer:Taking into account the definition of weigth, the correct answer is option A: the mass of the object is 50 kg.First, you have to know that mass is an indicator of the amount of matter that makes up a body. Its unit in the International System is the kilogram (kg).The mass of an object will always be the same, no matter where it is located.On the other side, bodies are subjected to the action of forces, such as the force of gravity or electromagnetic forces. So, weight is the action exerted by the force of gravity on the body. That is, weight is a measure of how much force gravity exerts on the mass of an object.The weight of an object is measured in Newton (N) and will vary according to the force of gravity that acts on it.The expression for the calculation of the weight is:P= m×gwhere:P is the weight of a body.m is its mass.g is the gravity or acceleration with which bodies fall.In this case, you know that:P= 980 Nm= ?g= 19.6 Replacing in the expression for the calculation of the weight:980 N= m× 19.6 Solving:m= m=50 kgFinally, the correct answer is option A: the mass of the object is 50 kg
Step-by-step explanation:
A line passes through the point (1,-6) and (-5, -3)
The equation of the line that passes the points (1, - 6) and (- 5, - 3) is - (1 / 2) · x - 11 / 2.
How to determine the equation of the line that passes through two given pointsAccording to Euclidean geometry, a line can be constructed by setting two points on a plane. By analytical geometry, lines are described by polynomials of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableThe slope can be found by means of secant line formula:
m = (y₂ - y₁) / (x₂ - x₁)
If we know that (x₁, y₁) = (1, - 6) and (x₂, y₂) = (- 5, - 3), then the equation of the line is:
m = [- 3 - (- 6)] / (- 5 - 1)
m = 3 / (- 6)
m = - 1 / 2
b = y - m · x
b = - 6 - (- 1 / 2) · 1
b = - 6 + 1 / 2
b = - 11 / 2
The equation of the line is - (1 / 2) · x - 11 / 2.
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y = -4x
y = x
Determine weather the graphs of the question are parallel, perpendicular ir neither?
The lines y = -4x and y = x are neither parallel nor perpendicular.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given equations of line are,
y = -4x and y = x,
The graph of the equations y = -4x and y = x are shown below.
Since, the slope of the line y = -4x is = -4.
And the slope of the line y = x is 1
For the parallel lines, the slope should be equal.
And for the perpendicular lines, the multiplication of slopes should be equal to -1.
In the given equations of line, the slope is neither same nor multiplication is -1.
Therefore, the lines are neither parallel nor perpendicular.
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the question is in the picture
Answer:
4
Step-by-step explanation:
For each kilogram of mass, [tex]0.2+4(0.1)=0.6[/tex] milligrams are needed.
Thus, [tex]0.6(10)=6[/tex] milligrams are needed.
This is equal to 4 mL
Answer:
4 ml
Step-by-step explanation:
You want to know how many mL of medicine is needed for 5 days when the dose is 0.1 mg/kg per day and the concentration is 1.5 mg/mL. The dose on the first day is double that for the rest of the days.
DaysThe dose on the first day is equivalent to the dose for 2 days, so we can simply add 1 day to the time period: 5 +1 = 6 days of 0.1 mg/kg/day.
DoseThe total amount required will be ...
(0.1 mg/kg/day) × (10 kg) × (6 days) = 6.0 mg
At a concentration of 1.5 mg/mL, the quantity required is ...
(6.0 mg)/(1.5 mg/mL) = 4.0 mL
For 5 days, the dog will need 4.0 mL of medicine.
__
Additional comment
Each day except the first, the dog should receive 2/3 mL of medicine. On the first day, the dog should get 4/3 mL.
What is a inverse of 5?
The Multiplicative Inverse of number 5 is "1/5" .
The Inverse (Multiplicative) is defined as the number which when multiplied by the original number give the product as 1 .
In simple words , the product of the number and its multiplicative inverse is 1 .
the number is given to be 5 .
let the multiplicative inverse of 5 be = "x" ;
So , 5×(x) = 1 ;
dividing both sides by 5
5x/5 = 1/5 ;
Simplifying further ,
we get ;
x = 1/5 , and the product of 5 and 1/5 is 1 .
Therefore , the multiplicative inverse is 1/5 .
The given question is incomplete , the complete question is
What is the Multiplicative Inverse of 5 ?
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A bakery sells muffins for $3. 50 each. A beverage is $1. 75. A class purchases 32 items and spends a total of $87. 50.
Answer:
Number of muffins= 18
Number of beverages= 14
Amount spent on muffins= $63
Amount spent on beverages= $24.50
Step-by-step explanation:
To find the number of muffins sold, we can first assume that all the 32 items purchased were beverages.
If the class bought 32 beverages,
Total spending
= 32($1.75)
= $56
Difference in total spending
= $87.50 -$56
= $31.50
The difference in the total spending is due to the number of muffins purchased that we had assumed they were beverages.
Difference in cost for each muffin vs beverage
= $3.50 -$1.75
= $1.75
Thus, for every incorrect assumption we made, the total spending will be $1.75 lesser than the actual amount.
Sets of wrong assumption
= $31.50 ÷$1.75
= 18
This means that out of the 32 items we previously assumed to be beverages, 18 were actually muffins. The remaining number of items were indeed beverages.
Number of muffins= 18
Number of beverages
= 32 -18
= 14
Amount spent on muffins
= 18($3.50)
= $63
Amount spent on beverages
= 14($1.75)
= $24.50
Total spending
= $63 +$24.50
= $87.50
How do you do the 3x 1 problem?
The expression given in question can be written in an equation form and hence, we determine the unknown variable x.
What is expression and equation?An expression is a combination of terms and operator. The terms contain two or more numbers or both numbers and variables. An expression describes a mathematical concept or system of mathematical operation in a symbolic form. The expression which has an equal sign to express the equality among the terms is called equation. So, the only difference between equation and expression is the equal sign =.
How do we do the problem 3x-1?The above is a mathematical expression that contains two numbers 1,3 and one variable x along with a subtraction sign, -.
The number 1 is called constant number and number 3 is called the coefficient of x.
In order to do the problem, we can put any real value of x such as x= 0, 1, 2, 3, 4, 5, 6, 7 or -1, -2, -3, -4, 5 and so on.
For each value of x, we get a result either positive or negative.
3×0 -1, when x=0
-1
3×1 -1, when x=1
the result is 2
We can also write the expression in the form of equation by putting an equal sign such as 3x-1 = 0
from the equation, we can easily get the value of x.
3x -1 =0
3x = 1
x =1/3
this is the result.
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What is the GCF of 4 and 28?
What is the relationship between volume and surface area?
The surface area of any particular thing is the area or region that the object's surface occupies. Volume, on the other hand, is the quantity of space accessible in an object. There are several forms and sizes in geometry, such as the sphere, cube, cuboid, cone, cylinder, and so on. Each form has both a surface area and a volume.
What is area?The area amount denotes the size of a region on a flat or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as surface area, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. The area is the region determined by the shape of an item. The area of a form is the space in a plane covered by a figure or other two-dimensional geometric object.
Here,
The surface area of any given thing is the area or region occupied by the object's surface. Volume, on the other hand, refers to the quantity of space accessible in an object. Shapes and sizes in geometry include the sphere, cube, cuboid, cone, cylinder, and so on. Each form has a surface area as well as a volume.
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How do you find the missing number in a given integer array of 1 to 100 Python?
The idea is to find the sum of integers between 1 and 100 using the n×(n+1)/2 where n is the array’s size and subtract the actual sum of array
What is Python used for?Python is a popular computer programming language used to create software and websites, automate processes, and analyze data. Since Python is a general-purpose language, it may be used to develop a wide range of applications and isn't tailored for any particular issues.
Python code for computing sum
Find the missing number in a given array
def getMissingNumber(arr):
# get the array's length
n = len(arr)
# actual size is `n+1` since a number is missing from the list
m = n + 1
# get a sum of integers between 1 and n+1
total = m * (m + 1) // 2
# the missing number is the difference between the expected sum and
# the actual sum of integers in the list
return total - sum(arr)
if __name__ == '__main__':
array_input = input("Enter a list of integers separated by spaces: ")
array = [int(x) for x in array_input.split()]
print('The missing number is', getMissingNumber(arr))
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Write an explicit formula that represents the sequence defined by the following recursive formula
please help
The formula that represents the defined sequence is [tex]4 (-6)^{n-1}[/tex]
What is the formula for the sequence?The given recursive formula are:
[tex]a _{1} = 4[/tex]
[tex]a _{n} = -6 a _{n-1}[/tex]
Considering n = 2 ,
[tex]a _{2} = -6(a _{2-1})\\ a _{2} = -6(a _{1})\\a _{2} = 4(-6)[/tex]
Considering n = 3 ,
[tex]a _{3} = -6(a _{3-1})\\ a _{2} = -6(a _{2})\\a _{3} = -6 (4(-6))\\a _{3} = 4(-6)^2[/tex]
Considering n = 4 ,
[tex]a _{4} = -6(a _{4-1})\\ a_4}= -6(a _{3})\\a _{4} = -6 (4(-6)^{2} )\\a _{4} = 4(-6)^3[/tex]
So, the formula that represents the defined sequence is [tex]4 (-6)^{n-1}[/tex]
What is a sequence?A sequence is an ordered collection of enumerated objects in mathematics where repeats are permitted. It has members, just like a set which is also called elements, or terms. The length of the sequence refers to the total potentially unlimited number of entries. Contrary to a set, the same elements may appear more than once at various points in a sequence, and in contrast to a set, the order is important. The formal definition of a sequence is a function from natural numbers the positions of the sequence's elements to the elements at each place. A function from any index set is what is meant by an indexed family, which is a generalization of the idea of a sequence.To learn more about sequence, refer:
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What is the factor of 6x² 11x 3?
The factor of 6x² 11x 3 is 6x(x + 3).
What is factor?The factor is a number that can be multiplied by itself to produce a specific result. It is used in mathematics and science to determine the relationship between two or more variables. For example, the factor of 4 is 2 because 2 multiplied by 2 is 4. Factors can also be used to determine the probability of an event occurring or the likelihood of a given outcome. In these cases, the factor is a measure of the degree of influence that one variable has on the other.
The factor of 6x² 11x 3 is 6x(x + 3).
This can be determined by factoring out the greatest common factor (GCF) of the expression.
The GCF of 6x² 11x 3 is 6x, and the remaining factors are x + 3.
Therefore, the factor of 6x² 11x 3 is 6x(x + 3).
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Complete questions as follows-
Factorise: 6x 2+11x+3
How does finding the square root of a number compare?
Therefore , the cube of the number is three times of its multiplication where as square is two times its multiplication.
The definition of square rootA number's square root is the result of multiplying it by itself, which yields the original number. Examples of exponents include squares and square roots. Imagine the number nine. Additionally, this can be expressed as 3x3.
Here,
The original number can be obtained by multiplying the square root of a number by itself,
and the cube root of a number by multiplying it by itself three times.
Therefore , the cube of the number is three times of its multiplication where as square is two times its multiplication.
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The figure shows a loading dock and a side view of an attached ramp, whose run is 12 feet and whose rise is 39 inches. Alex is wondering whether a long rectangular box can be stored underneath the ramp, as suggested by the dotted lines. The box is 2 feet tall and 5 feet long. Answer Alex’s question.
Answer:
q alguien me explique y pueden ser español
A tractor pulls a 20 kn at a speed of 4 m/s. Determine the work done by the tractor in 1 s.
As per the distance formula, the work done by the tractor in 1s is 5000m or 5 km
The term distance in math refers the length along a line or line segment between two points on the line or line segment
Here we have given that a tractor pulls a 20 km at a speed of 4 m/s.
And we need to determine the work done by the tractor in 1 s.
While we looking into the given question, we have given that the following values are given,
Distance = 20km
Speed = 4m/s
Here we have to convert the km into m then we get,
=> 1 km = 1000 m
Then 20km = 20000m
Therefore, in 4m/s it pulls 20000m.
Then in 1s the work done is calculated as,
=> 20000/4
=> 5000
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What is sets in real life?
Sets are the term used in mathematics which means the collection of any objects or collection.
Now, According to the question:
Let's know:
What is sets?
Any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.
What is sets in real life?
We all have a group of some objects, collection of our favorite things, sets of books, a list of cities and countries in our life. These all are sets, and we come to their usage in our daily life.
Examples of sets in daily life:-
1. Kitchen is the most relevant example of sets. Our mother always keeps the kitchen well arranged. The plates are kept separate from bowls and cups. Sets of similar utensils are kept separately.
2.School bags of children is also an example. There are usually divisions in the school bags, where the sets of notebooks and textbooks are kept separately.
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Your class has 18 students. Exactly 23 of them say that science is the subject they like the most. Which model shows 23 of 18 circled?
12 students like science the most and can draw a model having 18 things out of which 12 are circled.
What is model in mathematics?
In order to create a forecast or offer insight, mathematical modelling is the act of developing a mathematical representation of a real-world phenomenon. Applying a formula and really creating a mathematical relationship are two different things.Consider the provided information.
Your class has 18 students. Exactly 2/3 of them say that, out of all their subjects, they like science the most.
First calculate 2/3 of 18.
= (2/3) * 18
= 2 * 6
= 12
Hence, 12 students like science the most.
We can draw a model having 18 things out of which 12 are circled.
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Use multiplication. 4 times what number is about 35? 35÷4
Answer:
Answer explained in picture (8.75)
So after doing the division and getting the answer we multiply 8.75 by 4 we will get 35
Using multiplication we get, 4 times 8.75 is about 35.
Here, we have,
given that,
4 times what number is about 35
now, let, the number be x.
so, we get,
4 times x is = 35
or, 4 × x = 35
or, x= 35/4
or, x = 35÷4
or, x = 8.75
Hence, Using multiplication we get, 4 times 8.75 is about 35.
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In year 9, there are 150 students.
16% of the students are left handed.
(a) Work out how many students are left handed..
Answer:
24
Step-by-step explanation:
You need to work out 16% of 150
10% of 150 = 15
1% 0f 150 = 1.5
so, 6% of 150 = 1.5 x 6 = 9
16% = 10% + 6%
so, 16% = 15+9
24 = 16%
Therefore there are 24 left handed students in Year 9.
The equation F=1.8C+32 converts temperatures in degrees Celsius, C, to degrees Fahrenheit, F. If the temperature in a town is 12°C, what is the temperature in degrees Fahrenheit?
A.45.8°F
B.53.6°F
C.96°F
D.248°F
The temperature in a town is 12°C, then the temperature in degrees Fahrenheit is 53.6°F.
How to converts temperatures in degrees Celsius, C, to degrees Fahrenheit, F?The Fahrenheit temperature scale, named after German physicist Daniel Gabriel Fahrenheit, is the most commonly used temperature measurement in the United States (and its associated territories) and several Caribbean nations. Water freezes at 32°F and boils at 212°F on a Fahrenheit scale (at sea level).
The Celsius temperature scale—originally known as centigrade before being renamed after Swedish astronomer Anders Celsius—is used almost everywhere else in the world. Water freezes at 0 degrees Celsius and boils at 100 degrees Celsius on the Celsius scale (at sea level).
To convert degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
In the question, the temperature in a town in 12°C .
by applying the equation F=1.8C+32
=1.8×12+32
=53.6°F
Hence, The temperature in a town is 12°C, then the temperature in degrees Fahrenheit is 53.6°F.
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What are the coordinates of the midpoint of the line segment with endpoints (-4, 2) and (6,- 8)?
Please explain step by step
Answer:
The coordinate of the midpoint is (\frac{11}{2},\frac{-13}{2} )\\ with endpoints B(9,−8) and C(2,−5)
Step-by-step explanation:
(2x – 10) (x+6) = 0 solve the equation
Answer:
Therefore x is either 6 or 5.
jason sampled 60 smokers who were questioned about the number of hours they sleep each day. jason wants to test the hypothesis that the smokers need less sleep than the general public which needs an average of 7.5 hours of sleep with a population standard deviation of 0.7 hours. z equals fraction numerator x with bar on top minus mu over denominator begin display style fraction numerator sigma over denominator square root of n end fraction end style end fraction if the sample mean is 7.2 hours, what is the z-score? answers are rounded to the hundredths place.
The z-score of the sample research is calculated as; -3.32
What is the z-score of the distribution?We are given the formula for z-score as;
z = (x-bar - μ)/(σ/√n)
where;
x-bar is sample mean
μ is population mean
σ is population standard deviation
We are given;
Population mean; μ = 7.5 hours
Sample mean; x-bar = 7.2 hours
population standard deviation; σ = 0.7 hours
sample size; n = 60
Thus;
z-score = (7.2 - 7.5)/(0.7/√60)
z-score = -0.3/0.0903696
z-score = -3.32
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The cafeteria at Midtown Middle School surveyed 575 students about their favorite food. Find the number of students that responded for each of the following.
Chicken = 8%
**HINT: Take 8% of 575**
Which answer is correct?
46
8
57
460
Answer:
8% of 575 is 46
8% of 575 is 46
8% of 575 is 46
8% of 575 is 46
8% of 575 is 46
8% of 575 is 46
8% of 575 is 46
8% of 575 is 46
8% of 575 is 46
What is the horizontal asymptote of 4x 7?
The function 4x+7 does not have a horizontal asymptote.
The horizontal asymptote of a function is a horizontal line that the graph of the function approaches as the x-values get larger or smaller.
In this case, the function 4x+7 does not have a horizontal asymptote. This is because the function is a linear function (a function of the form y = mx + b) and all linear functions have a slope (in this case, the slope is 4) but no horizontal asymptotes.
If you are given the graph of a function and you want to find its horizontal asymptotes, you can look at the degree of the function (the highest exponent of the variable). If the degree of the function is less than the degree of the denominator of the function, then the function will have a horizontal asymptote at y = 0.
If the degree of the function is equal to the degree of the denominator, then the function will have a slant asymptote (a line that the graph approaches as the x-values get larger or smaller). If the degree of the function is greater than the degree of the denominator, then the function will not have any horizontal or slant asymptotes.
--The question is incomplete, answering to the question below--
"What is the horizontal asymptote of y = 4x+7?
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Determine which integer in the solution set will make the equation true.
t − 72 = −12
S: {−84, −60, 6, 60}
60
6
−60
−84
Answer:
60
Step-by-step explanation:
Adding [tex]72[/tex] to both sides yields [tex]t=72-12=60[/tex].
Answer:
[tex] \sf \: a) \: 60[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of t.
The equation is,
→ t - 72 = -12
Then the value of t will be,
→ t - 72 = -12
→ t = -12 + 72
→ [ t = 60 ]
Hence, the value of t is 60.
What is the inverse formula?
The inverse formula is [tex][(f o f^{-1}) (x) ] =[( f^{-1} o f ) (x)] = x[/tex]
What is the inverse formula?The domain of f is the range of [tex]f^{-1}[/tex] and the range of f is the domain of [tex]f^{-1}[/tex], i.e., if f: A -> B (which is one-one and onto), then [tex]f^{-1}[/tex]: B -> A.If (x, y) is a point on the graph of a function f, then (y, x) will unquestionably be a point on f-1. According to the inverse function formula, f and [tex]f^{-1}[/tex] are only the inverses of one another if their makeup is x.The inverse formula is [tex][(f o f^{-1}) (x) ] =[( f^{-1} o f ) (x)] = x[/tex]A function receives input, applies specific operations on it, and outputs the result. The inverse function performs, operates, and goes back to the original function in agreement with the outcome.The original value that a function output was returned by the inverse function.To learn more about function, refer:
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What is the formula s2?
A = [tex]s^{2}[/tex] or A = side x side is the formula of [tex]s^{2}[/tex] .
When calculating a square's area, you are determining the size of its surface. You can think of it as counting the number of square units that make up the surface as a whole. The formula for calculating the area of a square is A = [tex]S^{2}[/tex], or A = side x side. They are pretty basic animals, squares.
They have four equal sides and four right angles at their intersections, making them two-dimensional shapes. Four equal sides and four equal angle make up the closed, two-dimensional object known as the square. At the vertices, the square's four sides correspond to its four angles. A square's perimeter is equal to the sum of the lengths of all of its sides, and the amount of space it takes up in total is equal to its area.
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Question :
What is the formula [tex]S^{2}[/tex] of square represents ?
Need help with the last two questions. I can't solve it with using Scientific Notation or Standard Notation. Also I need to be sure it's three significant digits that are included.
Exponents that are positive go to the right. Exponents with negative signs shift to the decimal to the left. A result is stated in scientific notation when it is a power of ten multiplied by a number that is greater than or equal to one but less than ten.
What is the Scientific Notation or Standard Notation?One approach is to fully write out each number after it has been converted from scientific notation, then calculate the total of the two values and translate the result back into scientific notation.
Therefore, The 2, 4, 5, and final 0 in the number 0.2540 are all significant because they come after the decimal point and follow numbers. Scientific notation does not consider exponential digits to be significant; 1.12106 has three significant digits, 1, 1, and 2.
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