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Answer:
500 liters
Step-by-step explanation:
We want to find the total amount of water that was drained.
He drained 62.5 liters of water per minute and this went on for 8 minutes. The total amount of water drained is:
62.5 * 8 = 500 liters of water
ANSWER :
A 180 degrees rotation about the origin.
EXPLANATION.
Let us name the vertices of the triangle as follows.
If we reflect the triangle across the y-axis, then we have to negate the x-coordinates
to get,
If we now reflect triangle ∆A'B'C' in the x-axis, we will have to negate the y-values to obtain,
The single transformation that will map ∆ABC to ∆A''B''C'' is
This is a rotation of 180 degrees about the origin.
First, think of it as 3 different expressions.Go through them one at a time. There is:
-2a(a+b-5) ] +3(-5a+2b) ] +b(6a+b-8)
Multiply everything out.] Multiply everything out. ]Multiply everything out
-2a x a = -2a² ] +3 x -5a = -15a ] +b x 6a = 6ab
-2a x b = -2ab ] +3 x 2b = 6b ] +b x b = b²
-2a x -5 = 10a ] -15a + 2b = -15a+2b ] +b x -8 = -8b -2a² + -2ab + 10a = ] ] 6ab + b² + -8b =
-2a²+-2ab+10a ] ] <span>6ab+b²+-8b
</span>Now add everything up, but before that, remember these algebraic rules:
∞A.S.S. Add Same Signs, meaning positive add positive or negative add negative equals a positive number or 0. E.g 1+1=1 and -1+-2= 1
∞S.I.D. Subtract If Different, meaning a positive number add a negative number always equals a negative number or 0. E.g 1 + -2 = -1
∞You can only add up "similar terms", meaning you can add 'terms' ending in 'a' for example with another 'term' ending in 'a'. However. you cannot add a term ending in 'a' to an 'ab' or an 'a²'.
Following these rules, -2a²+-2ab+10a+-15a+2b+<span>6ab+b²+-8b =
</span>4ab-5a-6b+b²-2a²
Hope that helps you and that it wasn't too tricky to understand. :)
Since we do not know anything about angles, all we can do is to give the maximum and minimum lengths of the third side using the triangle inequality, which is:
the sum of lengths of the two shorter sides of a triangle must be GREATER than the third side (say X)
If 9 and 14 are the shorter sides, then the sum of 9 and 14 must be greather than the third side, X. => 9+14=23>X, or X<23. .................(1)
If 14 is the longest side, then 9+third side (X) must be greater than 14, or 9+X>14, or X>14-9=5, or X>5, or 5< X ..............................(2)
Combining conditions (1) and (2)
5 < X < 23
OR
X must be greater than 5 AND X must be less than 23
OR
X must be between 5 and 23.