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Answered on 24 Feb Learn Playing With Numbers
Sadika
The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be expressed uniquely as a product of prime numbers, except for the order of the factors. In other words:
For example, let's take the number 12:
12=2×2×312=2×2×3
This is one possible prime factorization of 12. According to the Fundamental Theorem of Arithmetic, any other factorization of 12 into prime numbers will involve the same prime factors (in this case, 2 and 3), just in a different order.
This theorem is fundamental in number theory and is essential for many mathematical proofs and concepts, including the understanding of factors, divisors, and properties of numbers.
Answered on 24 Feb Learn Playing With Numbers
Sadika
To simplify the expression 18+{1+(5−3)×5}18+{1+(5−3)×5}, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, let's simplify the expression inside the innermost parentheses:
5−3=25−3=2
Now, let's simplify the expression inside the curly braces:
1+2×5=1+10=111+2×5=1+10=11
Now, substitute the result back into the original expression:
18+1118+11
Now, we just need to perform the addition:
18+11=2918+11=29
So, the simplified expression is 2929.
Answered on 24 Feb Learn Practical Geometry
Sadika
To draw a line segment of length 12.8 cm and divide it into four equal parts using compasses, follow these steps:
Draw the Line Segment:
Measure and Mark the Length:
Divide the Line Segment into Four Equal Parts:
Verify by Actual Measurement:
By following these steps carefully, you can divide the line segment of length 12.8 cm into four equal parts using compasses. Make sure to verify the division by actual measurement to ensure accuracy.
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Answered on 24 Feb Learn Knowing our Numbers
Sadika
The smallest three-digit number whose value does not change when its digits are reversed is a palindrome. Palindromic numbers are the same when read forwards and backwards.
The smallest three-digit palindromic number is 101.
This number reads the same forwards and backwards, so its value does not change when its digits are reversed.
Answered on 24 Feb Learn Knowing our Numbers
Sadika
To write the given numbers in ascending order:
To determine how many of these numbers are even, we look at the units place of each number. If the units place is an even digit (0, 2, 4, 6, 8), then the number is even.
Looking at the units place of each number:
Out of the given numbers, 3 of them are even.
Answered on 24 Feb Learn Ratio and Proportion
Sadika
To find the ratio of 75 cm to 1.5 m, we need to convert both quantities to the same unit of measurement.
Since 1 meter (m) is equal to 100 centimeters (cm), we can convert 1.5 m to centimeters: 1.5 m×100 cm/m=150 cm1.5m×100cm/m=150cm
Now, we have:
To find the ratio, we divide the first quantity by the second: Ratio=75 cm150 cmRatio=150cm75cm
Ratio=75150Ratio=15075
Ratio=0.5Ratio=0.5
So, the ratio of 75 cm to 1.5 m is 0.5.
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Answered on 24 Feb Learn Basic Geometrical ideas
Sadika
In the given figure where ll, mm, and nn are three parallel lines, and xx and yy intersect these lines, the points lying on the line xx would depend on the specific intersection points between xx and the lines ll, mm, and nn.
If we denote the intersection points between xx and ll, mm, and nn as AA, BB, and CC respectively, then the points lying on the line xx would include AA, BB, and CC.
So, the points lying on the line xx are AA, BB, and CC.
Answered on 24 Feb Learn Understanding elementary Shapes
Sadika
To determine which point lies between the other two, we can compare the sum of the lengths of two line segments with the length of the third segment.
Let's compare the sum of AB and BC with AC:
AB + BC = 5 cm + 3 cm = 8 cm
Since AB + BC = AC (8 cm), this means that points A and C are consecutive and point B lies between them.
So, point B lies between points A and C.
Answered on 24 Feb Learn symmetry
Sadika
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Answered on 24 Feb Learn symmetry
Sadika
Let's address each shape one by one:
(a) Rectangle: A rectangle has two lines of symmetry: one vertical line passing through the center, and one horizontal line passing through the center. These lines divide the rectangle into four congruent quadrants.
(b) Square: A square has four lines of symmetry: two diagonal lines passing through the center, and two lines of symmetry, one vertical and one horizontal, passing through the center and perpendicular to each other. These lines divide the square into four congruent quadrants.
(c) Parallelogram: A parallelogram has no lines of symmetry, except in the special case where it is a rectangle or a square. In general, a parallelogram does not have any lines of symmetry because its opposite sides are parallel but not necessarily congruent.
(d) Right-angled triangle: A right-angled triangle has one line of symmetry, which is the perpendicular bisector of the hypotenuse (the side opposite the right angle). This line divides the triangle into two congruent right-angled triangles.
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