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Lana71 [14]
2 years ago
13

a teacher asked 3 pupils to choose any 2 digit number square it and then find the remainder after dividing the result by 7. Dori

s got 6 Marie got 4, Horace got 3. Two of the pupils made a mistake. Why?
Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
4 0
First write out all the two digit square numbers

4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81

Next divide all of them by 7

16/7 = 2 2/7 or 2 and 2 remainders
25/7 = 3 4/7 or 3 and 4 remainders
36/7 = 5 1/7 or 5 and 1 remainder 
49/7 = 7
64/7 = 9 1/7 or 9 and 1 remainder
81/7 = 11 4/7 or 11 and 4 remainders

This tells us that the only possible remainders for a two digit square number divided by 7 are 1, 2 and 4
If Doris got 6 and Horace got 3, they must have made a mistake.
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C

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the circular ripple caused by dropping a stone in a pond is increasing in area at a constant rate of 20 square meters per second
mojhsa [17]

Answer:

  2/π ≈ 0.637 m/s

Step-by-step explanation:

The rate of change of area with respect to time is ...

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Filling in given values in the above equations, we can find r and dr/dt.

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3 years ago
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Vlad [161]

Step-by-step explanation:

I don't know what constructions you were taught.

a "similar" triangle is a triangle with exactly the same angles as the other triangle, but the lengths of all sides are stretched or shortened by the same scaling factor f.

by saying 1:2 she means the second triangle should have sides with twice the lengths of the first triangle (f=2).

and the extra challenge - same basic thing. she allows you to pick one of the two triangles as reference. and then you need to draw a third triangle (again with the same angles) with the side lengths extended by the scaling factor f of 4/3.

I would draw the triangles right on top of each other with the same starting corner (let's call it A) for all 3.

we would get the triangles ABC, AMN and AXY.

the points B and C would be then halfway on AM and AN.

and M and N would then a bit before X and Y on AX and AY.

the beauty is, you only need to construct 2 sides of every new triangle down to the new endpoints. the third side is automatically scaled correctly, and you only need to connect these new endpoints.

let's assume you draw a triangle (just very simple) ABC with all side lengths being 3. so, AB=3, AC=3, BC=3.

now you draw AMN by extending AB and AC to a side length of 6 (f=2) creating M and N, and you connect M and N.

and then you can create the third triangle AXY by extending AM and AN by a factor of 4/3 to side lengths of 8 (4/3 × 6 = 8) creating new end points X and Y. and you connect X and Y.

and that is it. all 3 triangles are similar (the same angles), and all sides of a triangle have the same length ratio to the sides of the other triangle(s).

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please answer this with an explanation since my homework requires it thanks and I really appreciate it
cricket20 [7]

Answer:

<h2>D. 10</h2>

Step-by-step explanation:

There are 5 students in each scenario, so we just add 5 and 5 together. The answer is 10.

I'm always happy to help :)

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