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Answer: 
Step-by-step explanation:
Equilateral triangle has equal sides, let the side be
, then the perimeter is 
Therefore:



To find the altitude , we will apply Pythagoras theorem , that is

Therefore:



take the square root of both sides

Answer:
The sum of money received by Ali, Carrie and Bryan is $ 740.
Step-by-step explanation:
At first we translate mathematically each sentence:
(i) <em>Ali, Carrie and Bryan received a sum of money. </em>
- Ali's money.
- Bryan's money.
- Carrie's money.
(ii) <em>Bryan's money was </em>
<em> of Ali's money</em>.
(1)
(iii) <em>The ratio of Ali's money to Carrie's money was 4 : 1</em>.
(2)
(iv) <em>Ali had $ 160 more than Bryan</em>.
(3)
After some algebraic handling, we have the following system of linear equations:
(1b)
(2b)
(3b)
The solution of the system is:
,
, 
The sum of money is:


The sum of money received by Ali, Carrie and Bryan is $ 740.
Answer: the sand in the new terrarium is 2 inches deep.
Step-by-step explanation:
Zach has a terrarium with the dimensions of 20 by 8 and the terrarium was filled with 3 inches of sand. It means that the volume of sand that this terrarium contains is
20 × 8 × 3 = 480 inches³
Zach gets a new terrarium that is larger with the dimensions of 10 by 24. If Zach moved the existing sand in the new terrarium and the height of the sand is represented by h, then the volume of sand into he new terrarium is
10 × 24 × h = 240h
Since the volume of sand in both terrariums is equal, then
240h = 480
h = 480/240
h = 2 inches