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mote1985 [20]
3 years ago
8

Simplify 4/96 in fractions?

Mathematics
1 answer:
Ksju [112]3 years ago
8 0
The correct answer is 1/24
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A highway between points A and B has been closed for repairs. An alternative route between there two locations is to travel betw
Kitty [74]

Answer:

The value of Y is 24 km and distance from A to C to B is AC+Y=18+24=42 km

Step-by-step explanation:

Given that A highway between points A and B has been closed for repairs. An alternative route between there two locations is to travel between A and C and then from C to B. we have to find the value of Y and the total distance from A to C to B. Let AB=Z

In ΔBCD and ΔABD

∠BCD=∠ABD       (∵each 90°)

∠D=∠D                 (∵common)

By AA similarity, ΔBCD~ΔABD

∴ their corresponding sides are proportional

\frac{Y}{Z}=\frac{X}{40}=\frac{40}{18+X}

Comparing last two terms, we get

\frac{X}{40}=\frac{40}{18+x}

⇒ X(18+X)=1600

⇒ 18X+X^2=1600

⇒ X^2+18X-1600=0

⇒ X^2-32X+50X-1600=0

⇒ (X-32)(X+50)=0

Hence, the roots are X=32, -50

X=-50 not possible as distance can never negative.

Hence, X=32 km

By applying Pythagoras theorem in ΔBCD we get

BD^2=BC^2+CD^2

40^2=Y^2+32^2

⇒ Y^2=1600-1024=576

⇒ Y=\sqrt576=24km

Hence, the value of Y is 24 km and the distance from A to C to B is AC+Y=18+24=42 km




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