7. which of the following equations illustrates the associative property of addition?
(1) (3+7)+(2+8)=(7+3)+(8+2)
(2) (5)(3-4)=(5-3)(4)
(3) (4+5)+5 = 4 +10
(4) 2(5+4)=10+8
3

3.  (4+5)+5 = 4 +10  expresses the ASSOCIATIVE PROPERTY OF ADDITION.

Step-by-step explanation:

The associative property of addition is given as:

For any three numbers A, B and C

(A +B) + C = A + ( B+ C)

Here, the ORDER OF ADDITION is not important, answer is always the SAME.

Now, in the following given expressions:

1.  (3+7)+(2+8)=(7+3)+(8+2)

Here, ( 3+ 7)in L H S is replaced with ( 7 + 3) in R H S

Similarly,  ( 2+ 8)in L H S is replaced with (8 + 2) in R H S

Hence, the given expression is expresses the Commutative PROPERTY OF ADDITION.

2. (5)(3-4)=(5-3)(4)

Here, the operation between 5 and (3-4) is MULTIPLICATION

Hence, the given expression DO NOT expresses the ASSOCIATIVE PROPERTY OF ADDITION.

3.  (4+5)+5 = 4 +10

Here, the form of ASSOCIATIVE PROPERTY OF ADDITION is

(4 +5 )+5  = 4 + (5 + 5)  = 4 + (10)

So, the given expression expresses the ASSOCIATIVE PROPERTY OF ADDITION.

4.  2(5+4)=10+8

Here, the operation between 2 and (5 + 4) is MULTIPLICATION

Hence, the given expression DO NOT expresses the ASSOCIATIVE PROPERTY OF ADDITION.

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.