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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:

• Point K(1,3)K(1,3)
• Point L(2,3)L(2,3)
• Point M(3,3)M(3,3)
• Point N(4,3)N(4,3)

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.

To construct the quadrilateral PQRS with the given specifications, follow these steps:

1. Draw a line segment PRPR of length 8 cm. This will be one side of the quadrilateral.

2. At point PP, measure and mark a distance of 5 cm along the line segment PRPR. This will be point QQ.

3. At point RR, measure and mark a distance of 2.5 cm along the line segment PRPR. This will be point SS.

4. At point QQ, draw a line segment QSQS of length 5.5 cm, parallel to line segment PRPR.

5. At point SS, draw a line segment SPSP of length 7.1 cm, parallel to line segment QRQR.

6. 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.

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:

• If x=0x=0, then 12+0=1212+0=12 which is not divisible by 9.
• If x=1x=1, then 12+1=1312+1=13 which is not divisible by 9.
• If x=2x=2, then 12+2=1412+2=14 which is not divisible by 9.
• If x=3x=3, then 12+3=1512+3=15 which is divisible by 9.

So, x=3x=3 is the value that makes 42x542x5 a multiple of 9.

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.

Introduction: Understanding Factoring

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.

Step-by-Step Factoring Process:

1. 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)

2. Grouping Terms:

   • Group the terms that share common factors.

     Example: 2(15xy−6x)+2(5y−2)2(15xy−6x)+2(5y−2)

3. 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)

4. 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)

Conclusion: Factored Expression

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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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.

1. Combine Like Terms:

   • Combine the constant terms "-19" and the simplified expression "z(1 - y) - 19 + 19xy."

     Simplified expression: z(1 - y) + 19xy - 38

2. 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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As an experienced tutor registered on UrbanPro.com, I specialize in providing high-quality online coaching for Class 7 Tuition. One of the topics frequently covered in this grade is algebraic expressions and factorization. In this response, I will address the specific factorization question: "Factorise: 16x⁴ – y⁴."

Solution:

• Step 1: Identify the Perfect Square Form:

  • Recognize that the given expression is in the form of a difference of squares.

• Step 2: Apply the Difference of Squares Formula:

  • Utilize the formula a2−b2=(a+b)(a−b)a2−b2=(a+b)(a−b) where a=4x2a=4x2 and b=y2b=y2.

• Step 3: Substitute and Simplify:

  • Substitute the values of aa and bb into the formula.
  • Factorize 16x4−y416x4−y4 as (4x2+y2)(4x2−y2)(4x2+y2)(4x2−y2).

• Step 4: Further Factorization if Possible:

  • Notice that (4x2−y2)(4x2−y2) is another difference of squares.
  • Apply the difference of squares formula again: (4x2−y2)=(2x+y)(2x−y)(4x2−y2)=(2x+y)(2x−y).

Final Factorization: The complete factorization of 16x4−y416x4−y4 is (4x2+y2)(2x+y)(2x−y)(4x2+y2)(2x+y)(2x−y).

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