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stepladder [879]
3 years ago
15

A fruit company delivers its fruit in two types of boxes: large and small. a delivery of 6 large boxes and 5 small boxes has a t

otal weight of 127 kilograms. a delivery of 2 large boxes and 3 small boxes has a total weight of 51 kilograms. how much does each type of box weigh?
Mathematics
1 answer:
Afina-wow [57]3 years ago
5 0
6 large + 5 small = 127 kg ------------ (1)
2 large + 3 small = 51kg    ------------ (2)

<u>(2) x 3 :</u>
6 large + 9 small = 153 ---------------- (2a)

<u>(2a) - (1) :</u>
4 small = 26
1 small = 6.5kg   ------------ (sub into equation 1)

6 large + 5 small = 127 kg
6 large + 5(6.5) = 127
6 large + 32.5 = 127
6 large = 127 - 32.5
6 large = 94.5
1 large = 15.75 kg

Answer: The small box weighs 6.5kg and the big box weighs 15.75 kg


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The perimeter of a triangular field is 120m. Two of the sides are 21m and 40m.Calculate the largest angle of the field.
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the largest angle of the field is 149⁰

Step-by-step explanation:

Given;

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                         B

                     ↓            ↓  

                  ↓                          ↓

                ↓                                       ↓

            A →  →  → →  →  → →  → →    →    →  C

Consider ABC as the triangular field;

Angle A is calculated by applying cosine rule;

a^2 = b^2 + c^2 - 2bc \ Cos A\\\\Cos \ A = \frac{b^2 + c^2 - a^2}{2bc} \\\\Cos \ A = \frac{40^2 + 59^2 - 21^2}{2 \times 40 \times 59} \\\\Cos \ A = 0.983\\\\A = Cos ^{-1} (0.983)\\\\A = 10.6 \ ^0

Angle B is calculated as follows;

Cos \ B = \frac{a^2 + c^2 - b^2}{2ac} \\\\Cos \ B = \frac{21^2 + 59^2 - 40^2}{2 \times 21 \times 59} \\\\Cos \ B = 0.937\\\\B= Cos ^{-1} (0.937)\\\\B = 20.5 \ ^0

Angle C is calculated as follows;

Cos \ C = \frac{a^2 + b^2 - c^2}{2ab} \\\\Cos \ C = \frac{21^2 + 40^2 - 59^2}{2 \times 21 \times 40} \\\\Cos \ C = -0.857\\\\C = Cos ^{-1} (-0.857)\\\\C = 149\ ^0

Therefore, the largest angle of the field is 149⁰.

       

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