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Answered on 24 Feb Learn Introduction To Graphs
Sadika
To plot the given points K(1,3)K(1,3), L(2,3)L(2,3), M(3,3)M(3,3), and N(4,3)N(4,3), we can plot them on a Cartesian coordinate system:
All these points lie on the line y=3y=3, which is a horizontal line passing through the y-coordinate 3. This line is commonly known as the horizontal line y=3y=3.
So, the points KK, LL, MM, and NN all lie on the horizontal line y=3y=3.
Answered on 24 Feb Learn Practical Geometry
Sadika
To construct the quadrilateral PQRS with the given specifications, follow these steps:
Draw a line segment PRPR of length 8 cm. This will be one side of the quadrilateral.
At point PP, measure and mark a distance of 5 cm along the line segment PRPR. This will be point QQ.
At point RR, measure and mark a distance of 2.5 cm along the line segment PRPR. This will be point SS.
At point QQ, draw a line segment QSQS of length 5.5 cm, parallel to line segment PRPR.
At point SS, draw a line segment SPSP of length 7.1 cm, parallel to line segment QRQR.
Connect point QQ to point SS with a straight line segment.
By following these steps, you will have constructed the quadrilateral PQRS with the given specifications.
Answered on 24 Feb Learn Visualizing Solid Shapes
Sadika
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Answered on 24 Feb Learn Playing with Numbers
Sadika
To determine the value of xx such that 42x542x5 is a multiple of 9, we can sum the digits of the number and see if the result is a multiple of 9.
The number 42x542x5 can be written as 420+10x+5420+10x+5.
Now, let's consider the sum of the digits:
4+2+0+1+0+x+5=12+x4+2+0+1+0+x+5=12+x
For the entire number to be divisible by 9, the sum 12+x12+x must be a multiple of 9.
To find the value of xx, we need to find a digit such that 12+x12+x is divisible by 9.
Let's try different values of xx from 0 to 9:
So, x=3x=3 is the value that makes 42x542x5 a multiple of 9.
Answered on 24 Feb Learn Playing with Numbers
Sadika
To determine if a number is divisible by 3, you can sum its digits and check if the result is divisible by 3.
Let's sum the digits of the number 10011:
1+0+0+1+1=31+0+0+1+1=3
Since the sum of the digits (3) is divisible by 3, then 10011 is also divisible by 3.
Answered on 26 Feb Learn Playing with Numbers
Nazia Khanum
To find a 5-digit number divisible by 11 with the given digits (2, 3, 4, 5, 6), we can use the following approach:
Alternate Sum Method:
Example: 6−5+4−3+2=46−5+4−3+2=4.
Check Divisibility:
Let's apply the method:
Since 4 is not divisible by 11, let's try another arrangement until we find a suitable number.
After a few iterations, we find the arrangement 5, 6, 4, 3, 2, which yields 2−3+4−6+5=22−3+4−6+5=2. This number, 56432, is divisible by 11.
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Answered on 26 Feb Learn Factorization
Nazia Khanum
As a registered tutor on UrbanPro.com specializing in Class 7 Tuition, I understand the importance of providing clear and structured explanations for mathematical problems. Let's delve into the factorization of the given polynomial expression:
Factorize the polynomial expression: 54x² + 42x³ – 30x⁴
The first step in factoring a polynomial is to identify the common factor of all the terms. In this case, the common factor is 6x².
Now, we need to factorize the quadratic expression inside the parentheses. For this, we can use methods like grouping or the quadratic formula.
Combine the factored common factor with the factored quadratic expression:
Answered on 26 Feb Learn Factorization
Nazia Khanum
As a seasoned tutor registered on UrbanPro.com, I specialize in providing top-notch online coaching for Class 7 Tuition. Today, I'll guide you through the process of factorizing the expression: 2x²yz + 2xy²z + 4xyz.
To factorize the given expression, we'll look for common factors in each term and factor them out.
Identify Common Factors
Factorize the Expression
2xyz(x + y + 2)
Common Factor of 2: Factoring out 2 helps simplify the expression and identify a common factor in each term.
Common Factor of xyz: Each term contains a factor of xyz. Factoring this out leaves us with the expression (x + y + 2).
Final Factored Expression: Combining the common factors, the fully factorized expression is 2xyz(x + y + 2).
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Answered on 26 Feb Learn Factorization
Nazia Khanum
Greetings! I am an experienced tutor registered on UrbanPro.com, specializing in Class 7 Tuition and online coaching. Below is a detailed explanation of how to factorise the given expression: 30xy – 12x + 10y – 4.
Factorising is a fundamental concept in algebra, involving the decomposition of an expression into its constituent factors. In this case, we are tasked with factorising the expression 30xy – 12x + 10y – 4.
Identify Common Factors:
Observe the expression and identify common factors shared by all terms.
Example: 2(15xy−6x+5y−2)2(15xy−6x+5y−2)
Grouping Terms:
Group the terms that share common factors.
Example: 2(15xy−6x)+2(5y−2)2(15xy−6x)+2(5y−2)
Factor Out the Greatest Common Factor (GCF) from Each Group:
Factor out the common factor from each group.
Example: 2⋅3x(5y−2)+2(5y−2)2⋅3x(5y−2)+2(5y−2)
Identify and Factor Out Common Binomial Factor:
Notice the common binomial factor in both groups.
Example: 2(3x+1)(5y−2)2(3x+1)(5y−2)
By following these steps, the given expression 30xy – 12x + 10y – 4 can be factored as 2(3x+1)(5y−2)2(3x+1)(5y−2).
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Answered on 26 Feb Learn Factorization
Nazia Khanum
As an experienced tutor registered on UrbanPro.com, I understand the importance of providing clear and concise explanations to help students grasp challenging concepts. In this response, I will break down the expression "z – 19 + 19xy – xyz" step by step, ensuring a thorough understanding for Class 7 students seeking online coaching.
Step 1: Identify Common Factors
Factorizing the expression involves identifying common factors among the terms.
Observe that "z" is a common factor in the terms "z" and "-xyz."
Factorized expression: z(1 - y) - 19 + 19xy
Step 2: Simplify Further
Now, let's simplify the remaining terms.
Combine Like Terms:
Combine the constant terms "-19" and the simplified expression "z(1 - y) - 19 + 19xy."
Simplified expression: z(1 - y) + 19xy - 38
Factorize the Constant Terms:
Observe that "19" and "38" have a common factor of 19.
Simplified and factorized expression: z(1 - y) + 19(x - 2y)
Conclusion:
In conclusion, the expression "z – 19 + 19xy – xyz" can be factorized as follows:
z(1−y)+19(x−2y)z(1−y)+19(x−2y)
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