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marin [14]
2 years ago
11

How do I find the missing pairs ?

Mathematics
2 answers:
Delvig [45]2 years ago
5 0
Hello we know that the triangles are proportional so they have the same ratio
the unknown side is 21 because of this.
18/6=3/1
for each 1 unit in the bottom triangle there are 3 in the top
9×3=21
Alexus [3.1K]2 years ago
4 0
The ▲TSU ~ ▲KLJ
|KS| and |KL| are similar.
|TU| and |KJ| are similar.

1st/2nd = 1st/2nd
18/6= x/9
3/1= x/9

9 is nine times more 1
so the x must be nine times more as well.
3.9=27

Hope it helps!
#MissionExam001

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The first two steps in the derivation of the quadratic formula by completing the square are shown below.
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Answer:C

Step-by-step explanation:

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What is the product of 2x + y and 5x – y + 3?
hoa [83]

Answer:  The required product is 10x^2-y^2+3xy+6x+3y.

Step-by-step explanation:  We are to find the product f the following two algebraic expressions:

E_1=2x+y,\\\\E_2=5x-y+3.

To find the product of the above two expressions, we must multiply each term of the first expression with each term of the second expression.

The multiplication is as follows:

M\\\\=E_1 \times E_2\\\\=(2x+y)\times(5x-y+3)\\\\=10x^2-2xy+6x+5xy-y^2+3y\\\\=10x^2-y^2+3xy+6x+3y.

Thus, the required product is 10x^2-y^2+3xy+6x+3y.

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3 0
2 years ago
If m and n are off then is mn even?
11111nata11111 [884]

Answer:

No, mn is not even if m and n are odd.

If m and n are odd, then mn is odd as well.

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

Proof:

If m is odd, then it is in the form m = 2p+1, where p is some integer.

So if p = 0, then m = 1. If p = 1, then m = 3, and so on.

Similarly, if n is odd then n = 2q+1 for some integer q.

Multiply out m and n using the distribution rule

m*n = (2p+1)*(2q+1)

m*n = 2p(2q+1) + 1(2q+1)

m*n = 4pq+2p+2q+1

m*n = 2( 2pq+p+q) + 1

m*n = 2r + 1

note how I replaced the "2pq+p+q" portion with r. So I let r = 2pq+p+q, which is an integer.

The result 2r+1 is some other odd number as it fits the form 2*(integer)+1

Therefore, multiplying any two odd numbers will result in some other odd number.

------------------------

Examples:

  • 3*5 = 15
  • 7*9 = 63
  • 11*15 = 165
  • 9*3 = 27

So there is no way to have m*n be even if both m and n are odd.

The general rules are as follows

  • odd * odd = odd
  • even * odd = even
  • even * even = even

The proof of the other two cases would follow a similar line of reasoning as shown above.

4 0
2 years ago
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