Since they are similar, you need to find the ratio of similarity (I made up the term, there is probably a correct one that I can’t remember).

If you divide 16/40, you’ll find that that ratio is 2.5. So then you just multiply 16 x 2.5. You’ll get 18.

18 is the length of the top of the trapezoid.

You set 18=2x+4 and solve it algebraically. Subtract 4 from both sides.

14=2x
Divide by 2 and x=7

(You can also check that the ratio is right by 16/18 is the same decimal value as 40/45. You’ll get .88888...)

4 0

3 years ago

What can you say about the sum of consecutive odd numbers starting with 1? that is, evaluate 1, 1c3, 1c3c5, 1c3c5c7, and so on,

Mice21 [21]

Let us add consecutive odd numbers and try to find any relationship.

1. 1

2. 1+3 = 4 ( square of 2 i.e $2^{2}$ )

3. 1+3+5 = 9 ( $3^{2}$ )

4. 1+3+5+7 = 16 ( $4^{2}$ )

5. 1+3+5+7+9 = 25 ( $5^{2}$ )

6. 1+3+5+7+9+11 = 36 ( $6^{2}$ )

7. 1+3+5+7+9+11+13 = 49 ( $7^{2}$ )

If we notice, the sum of the consecutive odd integers in each case is equal to the square of the place where it lies. For example, the sum of numbers in seventh place is equal to $7^{2}$ . The sum of the numbers in the fifth line is equal to $5^{2}$ .

4 0

3 years ago