Drawing this square and then drawing in the four radii from the center of the cirble to each of the vertices of the square results in the construction of four triangular areas whose hypotenuse is 3 sqrt(2). Draw this to verify this statement. Note that the height of each such triangular area is (3 sqrt(2))/2.
So now we have the base and height of one of the triangular sections.
The area of a triangle is A = (1/2) (base) (height). Subst. the values discussed above, A = (1/2) (3 sqrt(2) ) (3/2) sqrt(2). Show that this boils down to A = 9/2.
You could also use the fact that the area of a square is (length of one side)^2, and then take (1/4) of this area to obtain the area of ONE triangular section. Doing the problem this way, we get (1/4) (3 sqrt(2) )^2. Thus,
A = (1/4) (9 * 2) = (9/2). Same answer as before.
Set of equations that can be used to calculate rate for each plumber:
2A+8B+8C = 1,400 --- (1)
4A+7B+10C = 1,660 --- (2)
3A+9B+9C = 1,660 --- (3)
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2*(1) - (2)
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4A+16B+16C = 2,800
4A+7B+10C = 1,660 -
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9B+6C = 1,140 --- (4)
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3(2) -4(3)
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12A+21B+30C = 4,980
12A+36B+36C = 6,600 -
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-15B-6C = -1,620 --- (5)
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(4) + (5)
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9B+6C = 1140
-15B-6C = -1620 +
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-6B = -480 => 6B = 480 => B = 480/6 = 80
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Using (4), 9(80)+6C = 1140
720+6C = 1140 => 6C = 1140-720 = 420 => C = 420/6 = 70
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Using (1), 2A+8(80)+8(70) = 1400
2A+640+560 =1400 => 2A = 1400-640-560 = 200 => A = 200/2 = 100
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The rates are:
A = $100
B = $80
C = $70
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On Thursday, number of calls: A = 4 hrs, B = 6 hrs, C = 3 hrs
Money earned = 4*100+6*80+3*70 = $1,090
The equation factors into (x+2)(x+6) = 0. The answers to this question are -2 and -6.
I think 121
406 + 94 = 500 and 180 + 199 = 379.
Subtract that and 121 is what’s left.
