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2 years ago

Find the value of x. Please help! Thanks.

Mathematics

1 answer:

emmasim [6.3K]2 years ago

8 0

Answer:

$\huge\boxed{x=\sqrt{30}}$

Step-by-step explanation:

ΔABC and ΔBDC are similar (AAA).

Therefore the corresponding sides are in proportion:

$\dfrac{AC}{BC}=\dfrac{BC}{CD}$

substitute

$AC=7+3=10\\{BC}=x\\CD=3$

$\dfrac{10}{x}=\dfrac{x}{3}$ cross multiply

$(10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=\sqrt{30}$

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3 years ago

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hram777 [196]

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3 years ago

A cold tablet contains the following amounts of active ingredients: acetaminophen 325 mg, chlorpheniramine maleate 2 mg, and dex

kakasveta [241]

Answer:

The number of tablets that can be prepared is 3076.

Step-by-step explanation:

The total amount of active ingredients in the tablet is the sum of the amounts provided in the formula:

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Chlorpheniramine maleate: $\frac{2mg*100}{342mg} =0.58$ %

Dextromethorphan hydrobromide: $\frac{15mg*100}{342mg}=4.39$ %

If 1 Kg= $10^{6}$ mg of acetaminophen is used, the needed amount of chlorpheniramine maleate would be:

$\frac{10^{6} mg *0.58}{95.03}=6153.85 mg$

Since there are 125 g = 125000 mg of chlorpheniramine maleate, there is enough of these ingredient to run the available acetaminophen out. Thus, the total amount of active ingredients that can be prepared with 1 kg of acetaminophen is:

$\frac{10^{6}mg*100}{95.03}=1052307.7mg$

Since each tablet weighs 342 mg, the number of tablets that can be prepared is:

$\frac{1052307.7mg}{342mg}=3076.923$

Which means that 3076 tablets can be prepared and a there will be a remanent of 0.923*342 mg = 315.69 mg of active ingredients.

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3 years ago

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2 years ago