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Answered on 24 Feb Learn Practical Geometry
Sadika
To construct the quadrilateral PQRS with the given specifications, follow these steps:
Start by drawing a line segment PQPQ of length 4 cm. This will be one side of the quadrilateral.
At point PP, construct an angle of 50 degrees. To do this, use a protractor to measure and mark an angle of 50 degrees from line segment PQPQ.
At point QQ, construct an angle of 110 degrees. To do this, use a protractor to measure and mark an angle of 110 degrees from line segment PQPQ.
From point QQ, draw a ray extending from the angle bisector of angle QQ. This will be side QRQR.
Measure and mark a length of 5 cm along side QRQR. This will be point RR.
At point RR, construct an angle of 70 degrees. To do this, use a protractor to measure and mark an angle of 70 degrees from line segment QRQR.
Finally, draw a line segment connecting point RR to point PP.
By following these steps, you will have constructed the quadrilateral PQRS with the given specifications.
Answered on 24 Feb Learn Practical Geometry
Sadika
To construct the quadrilateral PQRS with the given specifications, follow these steps:
Start by drawing a line segment PQPQ of length 6 cm. This will be one side of the quadrilateral.
At point QQ, construct an angle of 120 degrees. To do this, use a protractor to measure and mark an angle of 120 degrees from line segment PQPQ.
From point QQ, draw a ray extending from the angle bisector of angle QQ. This will be side QRQR.
Measure and mark a length of 6 cm along side QRQR. This will be point RR.
From point RR, draw a ray extending from the angle bisector of angle RR. This will be side RSRS.
Measure and mark a length of 4.5 cm along side RSRS. This will be point SS.
Finally, draw a line segment connecting point SS to point PP.
By following these steps, you will have constructed the quadrilateral PQRS with the given specifications.
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 10 cm. This will be one side of the quadrilateral.
At point PP, measure and mark a distance of 7.5 cm along the line segment PRPR. This will be point QQ.
At point RR, measure and mark a distance of 6 cm along the line segment PRPR. This will be point SS.
At point QQ, draw a line segment QSQS of length 6 cm, parallel to line segment PRPR.
At point SS, draw a line segment SPSP of length 5 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.
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Affordable fees Flexible Timings Choose between 1-1 and Group class Verified Tutors Answered on 24 Feb Learn Visualizing Solid Shapes
Sadika
To draw the net of a triangular prism with an equilateral triangle base, follow these steps:
Start by drawing an equilateral triangle. Label the vertices as A, B, and C.
Draw three lines perpendicular to the sides of the equilateral triangle, dividing each side into two equal segments. Label the points of intersection with the sides as D, E, and F.
Draw three parallel lines connecting points D, E, and F to the opposite vertices of the equilateral triangle. These lines will form three rectangles.
Join the corresponding vertices of the rectangles to form the sides of the prism.
Label the vertices of the resulting net.
C_______
/ \ / \
/ \ / \
/_____\ /_____\
A D B
E_______
/ \
/ \
/___________\
F C
Answered on 24 Feb Learn Visualizing Solid Shapes
Sadika
Euler's Formula is a fundamental theorem in geometry that relates the number of vertices (V), edges (E), and faces (F) of a polyhedron. It states that for any convex polyhedron (where the faces are flat and the edges are straight), the number of vertices (V), edges (E), and faces (F) are related by the equation:
V−E+F=2V−E+F=2
This formula holds true for any convex polyhedron, including prisms, pyramids, cubes, and more.
Now, let's use Euler's Formula to find the number of faces of a tetrahedron given that it has 4 vertices and 6 edges.
Given: V=4V=4 (number of vertices) E=6E=6 (number of edges)
We need to find FF (number of faces).
Using Euler's Formula: V−E+F=2V−E+F=2
Substitute the given values: 4−6+F=24−6+F=2
Now, solve for FF: F=2+6−4F=2+6−4 F=4F=4
So, the tetrahedron has 4 faces.
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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Affordable fees Flexible Timings Choose between 1-1 and Group class Verified Tutors 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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Affordable fees Flexible Timings Choose between 1-1 and Group class Verified Tutors 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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