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3 years ago

What is the length of leg s of the triangle below

Mathematics

2 answers:

Alex787 [66]3 years ago

5 0

Pythagorean Theorem:
s^2 + 3^2 = 18
s^2 = 9
s = 3

answer is B

andrew-mc [135]3 years ago

5 0

Answer: The correct option is (B) 3.

Step-by-step explanation: We are given to find the length of the leg s in the triangle shown in the figure.

From the figure, we note that

the given triangle is a right-angled one, where

length of the hypotenuse, H = √18 units,

length of one leg, P = 3 units

and

length of the other leg, s = B =?.

From Pythagoras theorem, we have

$H^2=P^2+B^2\\\\\Rightarrow (\sqrt{18})^2=3^2+B^2\\\\\Rightarrow 18=9+B^2\\\\\Rightarrow B^2=18-9\\\\\Rightarrow B^2=9\\\\\Rightarrow B=3.$

Thus, the length of the leg s is 3 units.

Option (B) is CORRECT.

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3 years ago

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Answer:

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2 years ago

A metallurgist has one alloy containing 34% copper another containing 48% copper. How many pounds of each alloy must he use to m

Zielflug [23.3K]

Answer:

<h2>36.14 pounds of 34% copper alloy and 9.86 pounds of 48% copper alloy</h2>

Step-by-step explanation:

First alloy contains 34% copper and the second alloy contains 48% alloy.

We wish to make 46 pounds of a third alloy containing 37% copper.

Let the weight of first alloy used be $x$ in pounds and the weight of second alloy used be $y$ in pounds.

Total weight = $46\text{ }pounds=x+y$ $-(i)$

Total weight of copper = $37\%\text{ of 46 pounds = }34\%\text{ of }x\text{ pounds + }48\%\text{ of }y\text{ pounds }$

$\dfrac{37\times 46}{100}=\dfrac{34x}{100}+\dfrac{48y}{100}\\\\ 34x+48y=1702$ $-(ii)$

Subtracting 34 times first equation from second equation,

$34x+48y-34x-34y=1702-34\times46\\14y=138\\y=9.857\text{ }pounds \\x=36.143\text{ }pounds$

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3 years ago

Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best

Delicious77 [7]

Answer:

First bank = $6792

City bank = $6803

Star bank = $6817

Step-by-step explanation:

The lists of banks and their annual interests rates are attached.

For first bank, since the interest is 7.5%, The total interest = 7.5% of $20000 = 0.075 × $20000 = $1500

For city bank, since the interest is 8.2%, The total interest = 8.2% of $20000 = 0.082 × $20000 = $1640

For Star bank, since the interest is 9%, The total interest = 9% of $20000 = 0.09 × $20000 = $1800

The loan plus interest for the banks annually are:

First bank = $20000 + $1500 = $21500

City bank = $20000 + $1640 = $21640

Star bank = $20000 + $1900 = $21900

The monthly payments for the banks are:

First bank = $21500 / 12 months = $1792

City bank = $21640 / 12 months = $1803

Star bank = $21800 / 12 months = $1817

Since The cost to run the gym each month is $5,000. Ed's total monthly expenses for each loan option = monthly payments + cost for each month. It is calculated as:

First bank = $5000 + $1792 = $6792

City bank = $5000 + $1803 = $6803

Star bank = $5000 + $1817 = $6817

3 0

3 years ago