Learn Maths with Free Lessons & Tips

To draw a parallelogram given the lengths of its adjacent sides, you can follow these steps:

1. Draw a line segment of length 2.8 cm. This will be one of the adjacent sides of the parallelogram.
2. From one endpoint of the first line segment, draw another line segment of length 3.8 cm. This will be the second adjacent side of the parallelogram. Make sure this line segment is parallel to the first one.
3. From the other endpoint of the first line segment, draw a line parallel to the second line segment, and from the other endpoint of the second line segment, draw a line parallel to the first line segment.
4. The intersection of these two lines will form the fourth vertex of the parallelogram.
5. Connect the vertices to form the parallelogram.

By following these steps, you'll have drawn a parallelogram with adjacent sides of lengths 2.8 cm and 3.8 cm.

To draw a rectangle given the lengths of its adjacent sides, you can follow these steps:

1. Draw a line segment of length 4.5 cm. This will be one of the adjacent sides of the rectangle.
2. At one endpoint of the first line segment, draw a line segment perpendicular to it of length 2.3 cm. This will be one of the adjacent sides of the rectangle.
3. From the other endpoint of the first line segment, draw a line parallel to the second line segment, and from the other endpoint of the second line segment, draw a line parallel to the first line segment.
4. The intersection of these two lines will form the fourth vertex of the rectangle.
5. Connect the vertices to form the rectangle.

By following these steps, you'll have drawn a rectangle with adjacent sides of lengths 4.5 cm and 2.3 cm.

A polyhedron is a three-dimensional geometric figure with flat faces, straight edges, and vertices.

Out of the options provided, a cone is not a polyhedron.

• A cube is a polyhedron because it has flat faces, straight edges, and vertices.
• A prism is a polyhedron because it has flat faces, straight edges, and vertices.
• A cuboid is a polyhedron because it has flat faces, straight edges, and vertices.

However, a cone does not have flat faces; it has a curved surface. Therefore, a cone is not considered a polyhedron.

If 3x123x12 is a multiple of 3, it means the sum of its digits is also a multiple of 3.

Let's sum the digits:

3+x+1+2=6+x3+x+1+2=6+x

For 3x123x12 to be a multiple of 3, 6+x6+x must be divisible by 3.

We know that if a number is divisible by 3, then the sum of its digits is also divisible by 3.

Let's try different values of xx from 0 to 9 and see if 6+x6+x is divisible by 3:

• If x=0x=0, then 6+0=66+0=6, which is divisible by 3.
• If x=1x=1, then 6+1=76+1=7, which is not divisible by 3.
• If x=2x=2, then 6+2=86+2=8, which is not divisible by 3.
• If x=3x=3, then 6+3=96+3=9, which is divisible by 3.
• If x=4x=4, then 6+4=106+4=10, which is not divisible by 3.
• If x=5x=5, then 6+5=116+5=11, which is not divisible by 3.
• If x=6x=6, then 6+6=126+6=12, which is divisible by 3.
• If x=7x=7, then 6+7=136+7=13, which is not divisible by 3.
• If x=8x=8, then 6+8=146+8=14, which is not divisible by 3.
• If x=9x=9, then 6+9=156+9=15, which is divisible by 3.

Therefore, the value of xx that makes 3x123x12 a multiple of 3 is x=0x=0, x=3x=3, or x=6x=6.

To determine the value of xx such that 35x35x 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 35x35x can be written as 350+10x350+10x.

Now, let's consider the sum of the digits:

3+5+x=8+x3+5+x=8+x

For the entire number to be divisible by 9, the sum 8+x8+x must be a multiple of 9.

To find the value of xx, we need to find a digit such that 8+x8+x is divisible by 9.

Let's try different values of xx from 0 to 9:

• If x=0x=0, then 8+0=88+0=8 which is not divisible by 9.
• If x=1x=1, then 8+1=98+1=9 which is divisible by 9.

So, x=1x=1 is the value that makes 35x35x a multiple of 9.

Are you seeking the best online coaching for Class 7 Tuition? As a registered tutor on UrbanPro.com specializing in Class 7 Tuition, I am here to provide guidance on solving mathematical problems. Let's delve into the question of divisibility.

Problem Analysis: The problem at hand is to determine which number among the given options (15, 12, 3, 9) divides 345111 without leaving a remainder. Let's analyze each option systematically.

Options Analysis:

1. Option 15:

   • Check if 345111 is divisible by 15.
   • Divisibility rule for 15: A number is divisible by 15 if it is divisible by both 3 and 5.
   • Calculate the sum of the digits of 345111. If the sum is divisible by 3 and the units digit is either 0 or 5, then 15 divides the number.

2. Option 12:

   • Check if 345111 is divisible by 12.
   • Divisibility rule for 12: A number is divisible by 12 if it is divisible by both 3 and 4.
   • Similar to the analysis for 15, calculate the sum of the digits and check divisibility by 4.

3. Option 3:

   • Check if 345111 is divisible by 3.
   • Divisibility rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
   • Apply the rule to 345111.

4. Option 9:

   • Check if 345111 is divisible by 9.
   • Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
   • Apply the rule to 345111.

Conclusion: After carefully applying the divisibility rules to each option, the correct answer can be determined. Share the result with the student, emphasizing the importance of understanding and applying these rules to solve similar problems in the future.

By choosing the best online coaching for Class 7 Tuition on UrbanPro.com, students can receive personalized guidance and support to excel in their studies.

To divide the expression 10(x3y2z2+x2y3z2+x2y2z3)10(x3y2z2+x2y3z2+x2y2z3) by 5x2y2z25x2y2z2, you can simplify by dividing each term in the numerator by the denominator:

Now, simplify each term:

1. 10x3y2z25x2y2z2=2x3−2y2−2z2−2=25x2y2z210x3y2z2=2x3−2y2−2z2−2=2
2. 10x2y3z25x2y2z2=2x2−2y3−2z2−2=25x2y2z210x2y3z2=2x2−2y3−2z2−2=2
3. 10x2y2z35x2y2z2=2x2−2y2−2z3−2=2z5x2y2z210x2y2z3=2x2−2y2−2z3−2=2z

Combine the simplified terms:

2+2+2z2+2+2z

So, the result of the division is 4+2z4+2z.

To simplify the expression 12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10), you can start by simplifying the coefficients and factoring the quadratic expression in the numerator:

12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10)

First, factor the quadratic expression in the numerator:

12(y2+7y+10)=12(y+5)(y+2)12(y2+7y+10)=12(y+5)(y+2)

Now, substitute this factorization back into the original expression:

12(y+5)(y+2)6(y+5)6(y+5)12(y+5)(y+2)

Next, simplify the coefficients and cancel out common factors:

2(y+5)(y+2)y+5y+52(y+5)(y+2)

Finally, cancel out the common factor of (y+5)(y+5):

2(y+2)2(y+2)

So, the simplified expression is 2(y+2)2(y+2).