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Reptile [31]
3 years ago
11

Leave your answer in simplest radical form

Mathematics
2 answers:
Nata [24]3 years ago
7 0
<h2>Hello!</h2>

The answer is:

The third option,

KL=7\sqrt{2}

<h2>Why?</h2>

Since we are working with a right triangle, we can use the following identity:

Sin(\alpha)=\frac{y}{hypothenuse}

We are given:

\alpha =45\°\\LM=y=7

hypothenuse=KL

Then, substituting and solving we have:

Sin(45\°)=\frac{7}{hypothenuse}

Hypothenuse=KL=\frac{y}{Sin(45\°)}=\frac{7}{\frac{\sqrt{2} }{2} } \\\\Hypothenuse=KL=7\sqrt{2}

Hence, the answer is the third option,

KL=7\sqrt{2}

Have a nice day!

Troyanec [42]3 years ago
6 0

Answer:

|KL|=7\sqrt{2}

Step-by-step explanation:

The given triangle is a right triangle.

The m<K=45 degrees.

This means the measure of <L is  also 45 degrees.

This implies that;

|LM|=|KM|=7 units.

From the Pythagoras Theorem;

|KL|^2=|LM|^2+|KM|^2

|KL|^2=7^2+7^2

|KL|^2=2(7^2)

|KL|=\sqrt{2(7^2)}

|KL|=7\sqrt{2}

Option C is correct.

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You borrow $5,000 from your parents to purchase a used car. The arrangements of the loan are such that you make payments of $250
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Part A:
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Amount paid in first month = $250 + $50.00 = $300
Unpaid balance = $5,000 - $250 = $4,750

2nd month: Interest payable = 1% of $4,750 = $47.50
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Part B:
Number of payments = 5000 / 250 = 20
Total amount of interest = 50 + 47.5 + 45 + . . . + upto the 20th payment.
This is an arithmetic sequence with the first term as 50, common difference as -2.5 and number of terms = 20.

Sum of the first 20th term of the GP is given by
S_n= \frac{20}{2}[2(50)+(20-1)(-2.5)] \\  \\ =10(100-2.5(19))=10(100-47.5) \\  \\ =10(52.5)=\$525.00

Therefore, the <span>total amount of interest paid over the term of the loan is $525.00</span>
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