Sam spent two-fifth of his work day by answering email. He works for 9 hours.
Steps to translate and solve a word problem using algebraic expressions:
- Assign the unknowns to variables
- Translate the word into operators plus, less, multiply, or division
- Isolate the unknown
In the given problem, let p is the variable to express the total hours Sam worked yesterday.
He spent two-fifth of hi work day by answering email = 2/5 p
He spent 3.6 hours answering email yesterday, means:
2/5 p = 3.6
p = 5 x 3.6/2 = 9 hours
Hence, Sam worked for 9 hours.
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Which set of numbers are closed under addition?
The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.
What are integers ?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .
According to the Property of Closure, A set has the closure property under a particular operation if the result of the operation is always an element in the set. If a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”
Hence , the set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.
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How do you find the inverse of a 2x2 function?
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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What is the sum of 3 consecutive odd numbers whose sum of squares?
The sum of the squares of three consecutive odd number 11, 13, 15 is 515.
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 the second number = x.
so the first number = x-2
the third number = x + 2
according to the question, the sum of the squares of the numbers = 515
so the formula is:
x² + (x-2)² + (x + 2)² = 515
(a-b)² = a² + b² - 2ab
and,
(a+b)² = a² + b² + 2ab
So, let’s apply these to our equation:
x² + x² + 2² -2*2x + x² + 2² + 2*2x = 515
There are three x² and 2*2 = 4 and 2*2x = 4x. Let’s apply all that to the equation,
3x² + 4 - 4x + 4 + 4x = 515
there is a -4x and a +4x, -4x + 4x = 0, so let’s remove that.
3x² + 4 + 4 = 515
3x² + 8 = 515
3x² = 515 - 8
3x² = 507
x² = 507/3
x² = 169
x = √169
√169 (square root(169)) = 13
x = 13
if x = 13, then the first number = 13–2 = 11 and the third number = 13 + 2 = 15
Hence , the sum of the squares of three consecutive odd number 11, 13, 15 is 515.
11*11 + 13*13 + 15*15 = 515
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A line passes through the point(-5,-6) and has a slope of -2 .
The line passing through point (-5, -6) is y = -2x - 16.
Define Equation of line.
A line in geometry is a collection of points that can be stretched infinitely in two different ways.To put it another way, a line is created by continually extending the two end points in any direction. As a result, we can assert that a line lacks end points. However, because it just has length and no width, it is a one-dimensional geometric form. Based on the information provided, we can create multiple forms of equations for lines algebraically, such as point slope form, slope-intercept form, and two point form.Two Point Form Formula,y - y₁ = m (x - x₁)
Given point is (-5, -6) and slope is -2.
We know the formula is,
y - y₁ = m (x - x₁)
Let, (x₁, y₁) = (-5, -6)
and, m = -2 (slope)
Now, plug in the value
y - (-6) = -2(x - (-5) )
y + 6 = -2(x + 5)
y + 6 = -2x - 10
y = -2x - 10- 6
y = -2x - 16
Hence, the line passing through point (-5, -6) is y = -2x - 16.
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What is the value of (-3.8) +0+ (-1.6) + 6.4?
Answer:
Step-by-step explanation:
solved & got 8.6
1. Which of the following equations shows how substitution can be used to solve the following syster
y = 2x + 3
2x + 5y = 3
2x + 5y = 2x + 3
2x + 5(2x + 3) = 3
2(2x + 3) +5y = 3
y = 3
How do you do the inverse of a matrix step by step?
A matrix's inverse can be calculated in a number of stages.
To find the inverse of a matrix, you can use the following steps:
Find the determinant of the matrix. The determinant is a scalar value that represents the size and orientation of the matrix. It is denoted as "det" or "|A|".Find the adjoint of the matrix. The adjoint is a matrix that is related to the inverse of the matrix. It is denoted as "adj" or "adj A".Subtract the determinant from the adjoint of the matrix. The result is the inverse of the matrix. It is denoted as "A^-1".Here is an example:
Find the inverse of the matrix A:
[1 2]
[3 4]
Find the determinant of the matrix: det(A) = 14 - 23 = -2
Find the adjoint of the matrix: adj(A) = [4 -2]
[ -3 1]
Divide the adjoint of the matrix by the determinant: A^-1 = adj(A)/det(A) = [-2 1] / -2 = [1 -1/2]
[ 3/2 -1/2]
Matrix A's inverse is A-1= [1 -1/2].
[3/2 -1/2]
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Need help ASAP!!
What is the value of the function y=2x−3 when x=−1?
1) −5
2) −1
3) 2
4) 3
Answer:
-5
Step-by-step explanation:
-2-3 is -5 :>
Answer:
y=-5
Step-by-step explanation:
What do 14 and 18 have in common?
Solve pls brainliest
Answer:
The answers are in the picture I attached to this response.
Step-by-step explanation:
(1) The equation of a line, in slope-intercept form, is: [tex]y = mx + b[/tex], where m is the slope, and b is the y-intercept.
⭐ What is the slope (m) mean?
The slope is the steepness of the line.⭐ What is the y-intercept (b) mean?
The y-intercept is the y-value for when the x-value = 0To find the slope, we need to use the formula: [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](y_1, y_2)[/tex] are coordinates you are given.
In this problem, you are given the coordinates (2,6) and (4,9). Let's substitute these coordinates into the slope formula.
[tex]m = \frac{9-6}{4-2}[/tex]
[tex]m = \frac{3}{2}[/tex]
Now, substitute the value of m into the equation of a line.
[tex]y = \frac{3}{2}x + b[/tex]
All we have to do now is substitute the value of b. We are already given that the line intersects the y-axis at (0,3), which means that (0,3) is the y-intercept.
[tex]y = \frac{3}{2}x + 3[/tex]
⭐ How do we graph this equation?
Start at the y-axis with the y-intercept (3). From there, use your slope to plot new points. The numerator of the slope is known as the "rise" (how much you shift up or down), and the denominator of the slope is known as the "run" (how much you shift left or right). You will know if you have to go UP or DOWN, or LEFT or RIGHT if the number is negative or positive.(3) Start by taking the square root of 44 on a calculator.
You should get an irrational number (a number that's digits never terminate or repeat).
Whenever you have questions like these, you are expected to round the number to the nearest tenth.
[tex]\sqrt{44} = 6.6332495807107996982298654733414\\\\\sqrt{44} = 6.6[/tex]
Choose a place on the number line to start your positive integers (1,2,3 . . .) and plot the point 6.6.
6.6 should be a bit after 6.5, which is in between 6 and 7.
What is the relationship between volume of prism and pyramid when their bases and height are the same?
A triangular prism and a triangular pyramid with identical bases and heights are related by the fact that the prism's volume is three times that of the pyramid.
When a pyramid and a prism have bases and heights that are equivalent, the pyramid can fit inside the prism. In reality, when this is the case, the pyramid occupies precisely one-third of the prism's volume. This fact enables us to see a correlation between the volumes of a prism and a pyramid when their bases and heights are equal. That is, a prism with an identical height and base has a volume that is 1/3 that of a pyramid.
Volume of a prism = (area of base) * height Volume of a pyramid = 1/3 (area of the base) * heightTo know more about volume of 3d object click on link below:
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What does an XY scatter plot show?
A Scatter (XY) Plot has points that show the relationship between two sets of data.
Scatter Plots
A Scatter (XY) Plot has points that show the relationship between two sets of data.
In this example, each dot shows one person's weight versus their height.
Example:
The local ice cream shop keeps track of how much ice cream they sell versus the noon temperature on that day. Here are their figures for the last 12 days:
Ice Cream Sales vs Temperature
Temperature °C Ice Cream Sales
14.2° $215
16.4° $325
11.9° $185
15.2° $332
18.5° $406
22.1° $522
19.4° $412
25.1° $614
23.4° $544
18.1° $421
22.6° $445
17.2° $408
And here is the same data as a Scatter Plot:
It is now easy to see that warmer weather leads to more sales, but the relationship is not perfect.
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A farmer has a piece of land measuring 840m by 396m.He divides it into squares plots of equal sizes.Find the maximum area of one plot
Answer:
Step-by-step explanation:
To find the maximum area of one plot, we need to find the greatest common factor of 840 and 396. One way to do this is to use the prime factorization method.
First, we prime factorize 840 and 396:
840 = 2 * 2 * 2 * 3 * 5 * 7
396 = 2 * 2 * 3 * 3 * 11
Then, we find the common factors:
2 * 2 * 3 = 12
So, the greatest common factor of 840 and 396 is 12.
The maximum area of one plot is therefore (840 * 396) / 12 = 140 * 33 = 4620 square meters.
If a parcel of land originally worth $35,000 increases in values 18% per year, what will the land be worth about in the eighth year?
Answer:
131560.072
Step-by-step explanation:
Because it is increase so we add humdred to the percent and then divide by hundred - 18+100/100 = 1.18
eight years - 1.18 raised to the pwer of 8
worth - 35000
hence it will be - 1.18 raised to the power of 8 x 35000
thank you
Find area of the fig.
The area of the composite figures are as follows;
10. Area of the trapezoids are; 96 cm², 80 cm², 96 cm², 80 cm²
Area of the rectangle at the center = 320 cm²
11. Area of the field on the left is 18,600 m²
Area of the field on the right is 11,000 m²
What is a composite figure?A composite figure is a figure that consists of two or more regular shapes.
10. The width of each trapezoid are;
(28 - 20)/2 = 4
(24 - 16)/2 = 4
The area of each trapezoid are;
The area of each of the left and right trapezoid = 4 × (20 cm + 28 cm)/2 = 96 cm²
Area of the top and bottom trapezoid = 4 × (16 cm + 24 cm)/2 = 80 cm²
Area of the rectangle at the center = 16 cm × 20 cm = 320 cm²
11. Area of ΔDEI = 0.5 × 80 m × 60 m = 2400 m²
Area of trapezoid EIGF = 0.5 × (60 m + 50 m) × (60 m + 20 m) = 4400 m²
Area of the triangle ΔAGF = 0.5 × 50 m × 80 m = 2000 m²
Area of ΔAHC = 0.5 × 40 m × (20 m + 80 m) = 2000 m²
Area of ΔABC = 0.5 × 30 m × (20 m + 80 m) = 1500 m²
Area of quadrilateral AHCB = 2000 m² + 1500 m² = 3500 m²
Area of triangle ΔCDH = 0.5 × 40 m × (80 m + 60 m) = 2800 m²
Adding together, we get;
2400 + 4400 + 2000 + 2000 + 1500 + 3500 + 2800 = 18,600
The area of composite figure is 18,600 m²\
Area of ΔEFH = 0.5 × 20 m × 40 m = 400 m²
Area of trapezoid GFHJ = 0.5 × (20 m + 40 m) (40 m + 40 m) = 2400 m²
Area of triangle ΔAGJ = 0.5 × 40 m ×(20 m + 60 m) = 1600 m²
Area of triangle ΔABK = 0.5 × 30 m × 60 m = 900 m²
Area of trapezoid BCF_K = 0.5 × (40 m + 30 m) × (40 m + 20 m) = 2100 m²
Area of triangle ΔCIE = 0.5 × 40 m × (40 m + 40 m) = 1600 m²
Area of triangle ΔCDE = 0.5 × 50 m × (40 m × 40 m) = 2000 m²
Adding the areas together, we get;
400 + 2400 + 1600 + 900 + 2100 + 1600 + 2000 = 11000
The area of the field is 11,000 m²
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How to find the missing number in a given array from number 1 to n in Java?
Finding the missing number from the N numbers in the given array arr[] of size N-1 with integers in the range [1, N] is the task. The list must not contain any duplicates.
Java method for locating a missing integer in an array of integers from 1 to N:
Make a temp array temp[] of size n + 1 with a value of 0 for each element.
For each element in the input array arr[i], perform the following.
If (temp[arr[i]] == 0), then temp[arr[i]] is 1.
traverse temp[] and output an element of an array with the value of 0. (This is the missing element).
class GFG; import java.io.*; import java.util.*
public static void findMissing(int arr[], int N)
{
int i;
int temp[] = new int[N + 1];
for (i = 0; i <= N; i++) {
temp[i] = 0;
}for (i = 0; i < N; i++) {
temp[arr[i] - 1] = 1;
} int ans = 0;
for (i = 0; i <= N; i++) {
if (temp[i] == 0)
ans = i + 1;
} System.out.println(ans);
}
public static void main(String[] args) {
int arr[] = { 1, 3, 7, 5, 6, 2 };
int n = arr.length; // Function call
findMissing(arr, n);
}
}
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For the graphed function f(x) = -(3)x1+3, calculate the average rate of change from x = 1 to x = 3.
-4
-2
2
4
Answer:
The average rate of change is -4
Step-by-step explanation:
The given function is f(x) = -(3)x1+3
We want to find the average rate of exchange of this function from x=1 to x=3.
This is the slope of the secant line joining the points (1,f(1)) and (3,f(3)).
From the graph, f(1)=2 and f(3)= -6
The average rate of exchange
=f(3)-f(1)/3-1
=-6-2/3-1
=-8/2
=-4
What are the next two terms of the following sequences?
With process
Answer:
[tex]\frac{5}{36} , \frac{6}{49}[/tex]
Step-by-step explanation:
The numerator of these terms is increasing by 1
The denominator is being squared... Look at this
The denominator of the first term is 2² which equals 4
the next denominator is 3² = 9
the next 4² = 16
the next 5² = 25
so, what what's next?
6² = 36 and 7² = 49
Hope I helped! :)
Answer:
The next two terms of the following sequence is 5/36 and 6/49.
Step-by-step explanation:
The pattern in this sequence is that the numerators of the sequence are all positive integers that increase by 1, so I added 1 to each preceding numerator. The denominators of the sequence are consecutive perfect squares (e.g., 4, 9, 16, 25, 36, etc.), so I made each following denominator the next perfect square.
You have 2 slices of pizza, and I gave you 3 slices of pizza. Can you write the simple expression to find the total number of slices of pizza?
The expression to find the total number of slices of pizza is 2 + 3
How to determine the expression to find the total number of slices of pizza?From the question, we have the following parameters that can be used in our computation:
Initial slices of pizza = 2
Additional slices of pizza = 3
This means that
The expression to find the total number of slices of pizza is
Total number of slices of pizza = Initial slices of pizza + Additional slices of pizza
Substitute the known values in the above equation, so, we have the following representation
Total number of slices of pizza = 2 + 3
Hence, the expression is 2 + 3
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Please help thank you! 3/y -5=x(y+7) translated into words
The given equation can be expressed as xy²+7xy+5y-3=0.
What is an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. In English, a well-formed formula with two expressions joined by an equals sign is referred to as an equation; however, cognates of this word in other languages may have slightly different meanings. For instance, the French definition of an equation is one or more variables.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables. The values of the variables that must fulfill the equality to constitute the answer are known as the unknowns, together with the variables for which the equation must be solved. Equations can be classified as either conditional equations or identities.
Given,
(3/y)-5=x(y+7)
(3-5y)/y=(xy+7x)
3-5y=xy²+7xy
xy²+7xy+5y-3=0
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Consider the following 8 numbers, where one labelled ï is unknown.
14, 28, 28, x, 36, 6, 4, 50
Given that the range of the numbers is 59, work out 2 values of x.
Answer:
177x
Step-by-step explanation:
Which graph represents this equation? y=3/2x^2-6x A. The graph shows an upward parabola with vertex (minus 2, minus 6) and passes through (minus 5, 7), (minus 4, 0), (0, 0), and (1, 7) B. The graph shows an upward parabola with vertex (2, minus 6) and passes through (minus 1, 7), (0, 0), (4, 0), and (5, 7) C. The graph shows an upward parabola with vertex (3, minus 4.5) and passes through (minus 1, 3.5), (0, 0), (6, 0), and (7, 3.5) D. The graph shows an upward parabola with vertex (minus 3, minus 4.5) and passes through (minus 7, 3.5), (minus 6, 0), (0, 0), and (1, 3.5)
The graph that represents the equation y = 3/2x² - 6x is
B. The graph shows an upward parabola with vertex (2, minus 6) and passes through (minus 1, 7), (0, 0), (4, 0), and (5, 7)
What is graph of quadratic equation?The shape of a quadratic function's graph. is a U-shaped curve,
The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of the quadratic function, is where the parabola will open up.
The vertex is the highest point on the graph or the maximum value if the parabola opens downward.
In the problem the graph opens up and points are plotted and attached, the graph shows that option is the correct choice
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What are the required conditions for similarity of triangles?
Required Conditions for similarity of traingles are:-
all the corresponding angles have equal measure or all the corresponding sides are proportional to each other .What are similar traingle?
Triangles with have the same shape but can distinct sizes are said to be similar triangles. In other words, if two triangles are similar,then they need to follow either of the 2 mentioned condition if their corresponding sides are proportionately equal and their corresponding angles are congruent.
Conditions for similarity of traingles are:-
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Cali baked a box of brownies. she took some to school but left 2/3 at home for her brothers. her brother, todd, had eaten 1/4 of what she left. what portion of the entire pan did todd eat?
Answer:
1/6 pan
Step-by-step explanation:
You want to know the portion of the whole represented by 1/4 of 2/3.
Fraction of fractionTodd ate 1/4 of 2/3 of the pan of brownies. That fraction of the original whole amount is ...
(1/4)×(2/3) = (1·2)/(4·3) = 2/12 = 1/6
Todd ate 1/6 of the entire pan.
What is the first value of x?
When an initial/input value is zero, the output of a function is its initial value.
Define the initial/first value of x for the function?The starting value represents the input at zero, whereas the rate of change relates to how rapidly the output varies in respect to the input.
How quickly the output alters in relation to the input is referred to as a function's rate of change. This is similar to how quickly the y-value shifts with relation to the x-value on a graph.You can use the changing rate to ascertain additional details about the function once you are aware of it. Making predictions about the behavior of the function for different input values is one thing you can accomplish using the rate of change.Thus, if x = 0 in a function, the initial value is defined. It serves as the scenario's beginning point in real life.
A linear equation's y-intercept is frequently thought of as initial value of the function.
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An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 700 meters, and Plane B was at an altitude of 424 meters. Plane A is gaining altitude at 16 meters per second, and Plane B is gaining altitude at 22 meters per second. Let x be the number of seconds that have passed.
(A) For each plane, write an expression for the altitude of the plane after x seconds.
(B) Write an equation to show when the two planes would be at the same altitude.
(A) The expression for each plane are as follows;
Plane A; 700 + 16xPlane B; 424 + 22xB). The equation to show when the two planes would be at the same altitude is; 700 + 16x = 424 + 22x.
Which equation shows when the two planes would be at the same altitude?It follows from the task content that the initial altitudes of plane A and B are 700 and 424 respectively.
Hence, since plane A gains altitude at 16 meters per second; The expression for the altitude after x seconds is;
700 + 16xAlso, since plane B gains altitude at 22 meters per second; The expression for the altitude after x seconds is;
424 + 22xTherefore, when the two planes are at the same altitude; the equation which is true is;
700 + 16x = 424 + 22x.Read more on linear expressions and equations;
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What does an octagon shape look like?
what is the slope of (-18,18) and (-14,3)
Answer:
-15/4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
=(3-18)/(-14- -18)
=-15/4
Answer:
Slope = [tex] \sf \frac{-15}{4} [/tex]
Step-by-step explanation:
Now we have to,
→ find the required slope.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Then the slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (3 - 18)/(-14 -(-18))
→ m = -15/(-14 + 18)
→ [ m = -15/4 ]
Hence, the slope is -15/4.
Which criterion if any could prove the triangles are congruent?
The criterion if any could prove the triangles are congruent are SSS, SAS, ASA, AAS, and RHS congruence properties.
Two triangles are congruent if all the three corresponding sides of two triangles are the same. There are a few more criteria also. Thus, congruent triangles are mirror images to each other. The mathematical symbol represents congruence is ≅.
In the triangles ΔABC, ΔEFG as shown below, we can identify corresponding angles and corresponding sides are equal.
Diagram attached at the end of solution.
ΔABC≅ΔEFG
Corresponding Angles: ∠A≅∠E,∠B≅∠F,∠C≅∠G
Corresponding sides: AB≅EF,BC≅FG,AC≅EG.
Corresponding vertices: A and E,B and F,C and G
Two triangles of the same size and shape are called congruent triangles. When we rotate, reflect, or translate a triangle, its position or appearance seems identical to the other, also called congruent.
Based on the experiments, there are mainly 5 conditions or rules to compare the two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS congruence properties.
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How many rows in the Excel?
In Microsoft Excel 2007, a maximum of 1,048,576 rows may be used. 15.784 columns. A spreadsheet in Excel is composed of columns and rows.
what are columns and rows ?Row refers to a group of objects placed next to or across from one another. A column is defined as a vertical arrangement of objects based on category. The arrangement is done from left to right. The setup is created from top to bottom. The sum is shown on the far right.
here
The rows are horizontally arranged and designated by the numbers 1, 2, 3, and 4.
The letters that go horizontally down the columns are identified by the letters A, B, C, D, etc.
When a column and a row cross, cells are what result.
In Microsoft Excel 2007, 1,048,576 rows is the maximum number permitted. 15,384 rows.
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