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Bess [88]
3 years ago
7

The shorter side of a trapezoid is equal to its height, and the longer side is 3/2 times as long. If the area is 80, find the le

ngth of the shorter side.
Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0

Answer:

  8

Step-by-step explanation:

Let s represent the length of the shorter base and height. Then (3/2)s is the length of the longer base.

The area formula for a trapezoid is ...

  A = 1/2(b1 +b2)h

Filling in the given values, we have ...

  80 = (1/2)(s +3/2s)s = 5/4s²

  64 = s² . . . . . . . . . . . . . . . . . . . multiply by 4/5

  8 = s . . . . . . . . . . . . . . . . . . . . . take the square root

The length of the shorter side is 8.

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One canned orange juice is 25% orange juice another is 5% orange juice. How many liters of each should be mixed together in orde
Cerrena [4.2K]

Answer:

X = \frac{1.6 - 0.05Y}{0.25}= 6.4 -0.2 Y  (3)

Replcaing equation (3) into equation (2) we got:

0.75(6.4 -0.2 Y) +0.95 Y = 18.4

And solving for Y we got:

4.8 -0.15 Y +0.95 Y = 18.4

0.8 Y = 13.6

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And solving for X from equation (3) we got:

X= 6.4 -0.2*17 = 3

So we need 3L of orange juice with 25% of concentration and 17 L of orange juice with 5% of concentration

Step-by-step explanation:

For this problem we can work with the concentration of water and orange juice.

Let X the amount for the orange juice with 25% content and Y the amount for the orange juice with 5% of content

Using the concentration of orange juice we have:

0.25 X + 0.05 Y = 20*0.08  (1)

And for the water we have:

0.75 X + 0.95Y = 20*0.92  (2)

If we solve for X from equation (1) we got:

X = \frac{1.6 - 0.05Y}{0.25}= 6.4 -0.2 Y  (3)

Replcaing equation (3) into equation (2) we got:

0.75(6.4 -0.2 Y) +0.95 Y = 18.4

And solving for Y we got:

4.8 -0.15 Y +0.95 Y = 18.4

0.8 Y = 13.6

Y = 17

And solving for X from equation (3) we got:

X= 6.4 -0.2*17 = 3

So we need 3L of orange juice with 25% of concentration and 17 L of orange juice with 5% of concentration

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3 years ago
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