civonamzuk

w + x + y = - 2

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w + y + z = 19

x + y + z =  12

--------- w = x + 7  (1)

w + x + z = 4

w + y + z = 19

--------- y = x + 15   (2)

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w + x + y = - 2

x = - 2 - w - y

x = - 2 - (x + 7) - (x + 15) 

x = - 8

w = - 1

y = 7

z = 13

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wx + yz = (- 1)(- 8) + 7(13) = 99

Points X and Y lie on sides AB and AC respectively of triangle ABC. If AB=7, AC=10, AX=4, and AY=8, what is the ratio of the area of triangle AXY to the area of triangle ABC?

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[ABC] = 1/2(AB * AC)

[AXY] = 1/2(AX * AY)

[AXY] / [ABC] = 16 / 35

Three tangent circles of radius 10 cm are drawn. All centers lie on line AB. The tangent AC to the right-hand circle is drawn, intersecting the middle circle at D and E. Find the length of the segment DE.

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AC = sqrt(AB² - BC²)

Mid point of AC => F

Center of middle circle => G

AG = 2r

FG / AG = BC / AB         FG = (AG * BC) / AB

DE = 2 * sqrt(DG² - FG²)

Angle bisector theorem

AB / BC = AE / CE

BC = (AB * CE) / AE

Tub capacity = 100 L           Hot water = H          Cold water = C

H => 6 min = 40 L

H + C => 3 min = 20 L + 25 L

At this point, the tub is 85% filled with water.

In one minute:     H = 6²/₃ L,       C = 8¹/₃ L,          D = 10 L        (D - drain)

Hence, it will take 3 minutes for the tub to be filled.

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 28 minutes later. How many miles did I drive?

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Time => t    (in minutes)

40t = 30(t + 28)           

t = 84 minutes     (min)

40 miles / 60 min = x miles / 24 min

x = 16

You drove 56 miles

Is he/she selling something discounted?

Ron paid $14 for a book and 4 pens. The price of each pen was 5/8 the price of the book. How much did Ron pay for the book?

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Price of 4 pens => x

Price of a book => 14-x

14 - x = 14 - 4[5/8 (14 - x)]

x = 10

Ron paid $4 for a book