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2 years ago

43.

Mathematics

1 answer:

aleksklad [387]2 years ago

4 0

Answer:

4.12 kg

Step-by-step explanation:

Regular cakes:

1 dozen normal sponge cakes: 264 g plain flour

Vegetarian cakes:

1 dozen cakes: 264 g plain flour

4 eggs are replaced by 4 * 30 g of flour = 120 g flour

total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g

Proportion for regular cakes:

12 cakes to 264 g flour = 100 cakes to x grams flour

12/264 = 100/x

12x = 26400

x = 2200

2200 g flour for 100 regular cakes

Proportion for vegetarian cakes:

12 cakes to 384 g flour = 60 cakes to y grams flour

12/384 = 60/y

12y = 384 * 60

12y = 23040

y = 1920

1920 g flour for 60 vegetarian cakes

Total flour needed:

2200 g + 1920 g = 4120 g

4120 g * 1 kg/(1000 g) = 4.12 kg

Answer: 4.12 kg

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Answer:

(a) LM=12 units, LN=35 units, MN=37 units

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Step-by-step explanation:

(a)

Since points L and M have same x coordinates, it means they are in the same plane. Also, since the Y coordinates of L and N are same, they also lie in the same plane

Length $LM=\sqrt {(7-7)^{2}+(16-4)^{2}}=12 units$

Length $LN=\sqrt {(42-7)^{2}+(4-4)^{2}}=35 units$

Length $MN=\sqrt {(42-7)^{2}+(4-16)^{2}}=37 units$

Alternatively, since this is a right angle triangle, length MN is found using Pythagoras theorem where

$MN=\sqrt {(LN)^{2}+(LM)^{2}}=\sqrt {(12)^{2}+(35)^{2}}=37 units$

Therefore, the lengths LM=12 units, LN=35 units and MN=37 units

(b)

Perimeter is the distance all round the figure

P=LM+LN+MN=12 units+35 units+37 units=84 units

(c)

Area of a triangle is given by 0.5bh where b is base and h is height, in this case, b is LN=35 units and h=LM which is 12 units

Therefore, A=0.5*12*35= 210 square units

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