PLEASEEE EXPLAIN

Mathematics

1 answer:

Marina CMI [18]3 years ago

8 0

Using (-4,-8) as the starting point, the difference in the x’s is 6 and the difference in the y’s is 9.

Two thirds of those are 4 and 6 respectively.

Add those to -4 and -8, giving (0,-2) and that’s your answer.

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To fight a fire breathing dragon, a knight needs a sword made of Dragon Alloy #13, which contains 7% gold, 3% silver, and 90% ma

julia-pushkina [17]

Let $x$ and $y$ be the amounts of available alloy (AA) and pure magic steel that are used, so we also have

$x + y = 2.7$

DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of

$0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}$

$0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}$

$0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}$

For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; $x$ kg of it will contain $0.21x$ kg of gold, $0.09x$ kg of silver, and $0.70x$ kg of steel. Each kg of magic steel of course contributes 1 kg of steel; $y$ kg of it will contribute $y$ kg of steel.

Then the dwarves need

• total gold: $0.21x = 0.189$

• total silver: $0.09x = 0.081$

• total steel: $0.70x + y = 2.43$

Solve for $x$ and $y$ . The first two equations are consistent and give $x = 0.90$ , and substituting this into the third we find $y = 1.80$ . So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.