Ask question

Ask question

All categories

Nadusha1986 [10]

2 years ago

5

Which of the follwing regular polygons can make a tessellation?

1 answer:

Elodia [21]2 years ago

6 0

I think it's square and hexagon.

You might be interested in

45 mi/h = how many ft/s

Inga [223]

237,600 ft is 45 miles

4 0

3 years ago

What system of equations represents the graph

Elodia [21]

Answer:

The answer is C because the two figures are not congruent.

4 0

3 years ago

A rectangular room is 1.5 times as long as it is wide, and its perimeter is30 meters. find the dimension of the room.

Tpy6a [65]

Answer:

6 meters by 9 meters

Step-by-step explanation:

<u><em>Step 1: Formula for perimeter of rectangle</em></u>

Rectangle's perimeter = 2 (length) + 2 (width)

Rectangle's perimeter = 2 (length + width)

<u><em>Step 2: Find the length and width in terms of x</em></u>

Width = x

Length = 1.5 times width

Length = 1.5x

<u><em>Step 3: Find x</em></u>

Perimeter = 2(length + width)

30 = 2 (1.5x + x)

30/2 = 2.5x

15/2.5 = x

x = 6

<u><em>Step 4: Find the length and width</em></u>

Width = x = 6 meters

Length = 1.5x = 1.5(6) = 9 meters

Therefore, the dimensions of the room are 6 meters and 9 meters.

6 0

2 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

What is the measure of DE?<br><br><br> 16<br><br><br> 12<br><br><br> 20<br><br><br> 10

AnnyKZ [126]

set up a ratio to find the length:

15/12 = DE/16

cross multiply the 15 & 16:
15 * 16 = 240

divide that by 12 to get DE

240 / 12 = 20

DE = 20

8 0

2 years ago