<u>Equivalent and Fully Simplified:</u>
8+7x+4y
<u>Equivalent and not fully simplified:</u>
8+12x-5x+4y
15+7x+4y-7
<u>Note Equivalent:</u>
15-7x-4y
8+17x+4y
8+11y
Step-by-step explanation:
Given expression is:
We will simplify the expression one by one
Now we can categorize the expressions in boxes given below
<u>Equivalent and Fully Simplified:</u>
8+7x+4y
<u>Equivalent and not fully simplified:</u>
8+12x-5x+4y
15+7x+4y-7
<u>Note Equivalent:</u>
15-7x-4y
8+17x+4y
8+11y
Keywords: Expressions, simplification
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Let a, b, and c be the times each pump will fill the tank when working alone.
Therefore, in 1 hour;
1/a +1/b = 1/(6/5) = 5/6 ---- (1)
1/a+1/c = 1/(3/2) = 2/3 ---- (2)
1/b+1/c = 1/(2) = 1/2 ---- (3)
From equation (1)
1/a = 5/6-1/b
Substituting for 1/a in eqn (2)
5/6-1/b+1/c = 2/3
-1/b +1/c = -1/6 => 1/c = 1/b - 1/6 --- (4)
Using eqn (4) in eqn (3)
1/b+1/b-1/6 = 1/2
2/b-1/6 = 1/2
2/b =1/2+1/6 = 2/3
1/b = 1/3
Then,
1/c = 1/3 - 1/6 = 1/6
1/a = 5/6 - 1/3 = 1/2
This means, in 1 hour and with all the pumps working together, the tank will be filled to;
1/a+1/b+1/c = 1/2+1/3+1/6 = 1 (filled fully).
Therefore, it will take 1 hour to fill the tank when all pumps are working together.
Answer:
Step-by-step explanation:
the answer is C, the curve is a one to one function
The arrangement of mother's eye level, ground level and playground forms a right angles triangle.
The legs of this triangle are 12.6 m (eye level to ground) and 20 m (building to playground).
Using trigonometry and assuming the depression angle is Ф;
tan Ф = 20/12.6 = 1.5873
Ф = tan ^-1(1.5873) = 57.78°
