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kati45 [8]
3 years ago
8

The ratio of green marbles to total marbles in a bag is 2:9. The ratio of red marbles to total marbles in the same bag is 1:3. W

hich of the following statements is true?
There are more green marbles in the bag.
There is the same number of red and green marbles in the bag.
There are more red marbles in the bag.
Mathematics
1 answer:
Ne4ueva [31]3 years ago
5 0

There are more red marbles in the bag..

Because,

Ratio of green marbles to total marbles=2/9=0.222

And

Ratio of red marbles to total marbles=1/3=0.333

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Answer:

  4) 16√3 in²

  5) 63 cm²

Step-by-step explanation:

The formula to use in these cases is ...

  A = (1/2)ab·sin(θ)

where a, b are the side lengths and θ is the angle between them.

It helps to know the trig functions of the "special" angles used here.

  sin(120°) = sin(60°) = (√3)/2

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4) The external angle at the base is the supplement of 120°, so is 60°. Then the length of the missing segment between the end of the base and the right angle at h is ...

  x = (8 in)cos(60°) = (8 in)(1/2) = 4 in

So, the bottom edge of the triangle is 12 in - 4 in = 8 in.

The area is ...

  A = (1/2)(8 in)(8 in)sin(120°) = (1/2)64(√3)/2 in² = 16√3 in²

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5) As in the previous problem, the difference between the given horizontal dimension and the base of the triangle is ...

  x = (18 cm)cos(180°-135°) = 18(√2)/2 cm = 9√2 cm

Then the base of the triangle is ...

  16√2 cm -9√2 cm = 7√2 cm

The area is then ...

  A = (1/2)(18 cm)(7√2 cm)(√2)/2 = 63 cm²

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