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3 years ago

Find the sum of the following numbers without actually adding them1+3+5+7+9+11+13+15

Mathematics

1 answer:

Dovator [93]3 years ago

5 0

S = 1 + 3 + 5 + ... + 11 + 13 + 15

S = 15 + 13 + 11 + ... + 5 + 3 + 1

==> 2S = (1 + 15) + (3 + 13) + (5 + 11) + ... + (15 + 1)

There are 8 terms in the sum, so

2S = 8 * 16 = 128

S = 128/2 = 64

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PLEASE HELP!!!!! I DONT UNDERSTAND!!!! :(

Misha Larkins [42]

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3 years ago

Help me jim! geometry homework

Maksim231197 [3]

Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles are similar. I used the SAS similarity theorem.

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Question 2

Let's find the missing angle of the triangle on the right. For now, make that missing angle to be x.

Rule: For any triangle, the three angles always add up to 180

x+70+32 = 180

x+102 = 180

x = 180-102

x = 78

The missing angle of the triangle on the left is 78 degrees

Repeat for the other triangle as well

y+78+32 = 180

y+110 = 180

y = 180-110

y = 70

Both triangles have the angles 32, 70, 78 in whatever order you wish.

Since the angles match up like this, the triangles are similar because of the AA Similarity theorem

Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

================================================================

Question 3

We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, the two triangles are similar.

This time we use the AA Similarity theorem

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Question 4

Let's divide the longest side of the bottom triangle by the longest side of the triangle on top

48/32 = 1.5

Now let's divide the shortest sides of each triangle in the same order

36/24 = 1.5

Repeat for the middle-most sides

45/30 = 1.5

We get the same linear scale factor 1.5 each time. Therefore, the triangles are similar due to the SSS Similarity theorem

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Question 5

Any angle is equal to itself due to the reflexive property. So that will go for reason number 2.

Reason 3 is SAS similarity because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

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2 years ago

I'm trying to find out the number of how much it cost to wrap each present, day one 41 small gifts were wrapped and 45 large wer

Licemer1 [7]

Answer:

Small gift: $2

Large gift: $7

Step-by-step explanation:

Let x represent cost of wrapping each small gift and y represent cost of wrapping each large gift.

We have been given that day one 41 small gifts were wrapped and 45 large were wrapped equaling $397.

We can represent this information in an equation as:

$41x+45y=397...(1)$

We are also told that day two 30 small gifts were wrapped and 47 large were wrapped equaling $389. We can represent this information in an equation as:

$30x+47y=389...(2)$