<u>Question 1</u>
Two triangles are said to be similar, if their sides are proportional and the corresponding angles are equal.
In the given figures, it is given that one of the angles is 80 degrees. So, the corresponding angle in the another triangle is also 80 degrees.
Also, please note that the triangles are isosceles.
We know that, in an isosceles triangle, the angles opposite to the equal sides are equal.
The equal angles are b and b.
By the angle-sum property, we have:
b + b + 80 = 180
2b + 80 = 180
2b = 180 - 80 = 100
b = 50 degrees.
Similar shapes have the same <u>angles.</u>
<u>Question 2:</u>
Even though the length of the second cuboid is twice the length of the first one, no information is given about the breadth and height.
Let b, c be the breadth and height of the first cuboid and B, H be the breadth and height of the second cuboid.
Now, we have two cases.
Case 1: b = B and h = H
In this case, the volume of the first cuboid is length × breadth × height
= lbh
Volume of second cuboid = (2l) × b × h = 2lbh
So, Simon is correct about the volumes.
Case 2: b ≠ B or h ≠ H
In this case, clearly the volumes will be different and Simon is wrong.
<u>Question 3:</u>
By Basic Proportionality Theorem and from corresponding part of similar triangles,
x = y
or x : y = 1 : 1
<u>Question 4:</u>
Since the jugs are irregular shapes, it is impossible to find their volumes only with known height.
Answer:
HERGABURGA
Step-by-step explanation:
I LIKE UR CUT G
<span>Answer: 100,000,000 + 3,000,000 + 700,000 + 20,0000 + 7,0000 + 400 + 90 + 5 = 103,727,495
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<span>Explanation:
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<span>1) The expanded form of a number is the split of the number using every digit muliplied by its place value.
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<span>2) The first (left most) digit of the given number is 1. It is in the hundred millions place. So, it represents 100,000,000 which is the first number in the expanded form.
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<span>3) The second digit (from lef to right) is 0, so its value is 0, and you do not include it in the expanded form.
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<span>4) The third digit (from the left to the right) is 3. It is in the place of the millions, so its value is 3,000,000.
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<span>5) Next number from the left is 7 and it is in the hundred thousands place, so its value is 700,000.
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<span>6) Next is 2, in the ten thounsands place => 20,000
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<span>7) Next is 7 in the thousands => 7,000
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<span>8) 4 in the hundreds => 400
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<span>9) 9 in the tens => 90
</span><span>10) Finally 5 in the ones => 5.</span>
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</span><span>Then number the number is: 100,000,000 + 3,000,000 + 700,000 + 20,000 + 7,000 + 400 + 90 + 5</span>
Let n be the larger integer and n-2 be the smaller integer.
n² - (n - 2)²
= n² - (n - 2)(n - 2)
= n² - (n² - 4n - 4)
= n² - n² + 4n + 4
= 4n + 4
= 4(n + 1)
No matter what value n is, it will always be a multiple of 4.
