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aleksandr82 [10.1K]
2 years ago
5

Help me with this, it's Pythagorean theorem.

Mathematics
2 answers:
Blizzard [7]2 years ago
6 0

Step-by-step explanation:

Let x represent the missing side length.

By Pythagoras' Theorem,

We have x² + 12² = 13².

Therefore x² = 13² - 12² = 25 and x = 5.

(x = -5 is rejected as side lengths are positive)

ziro4ka [17]2 years ago
4 0

Answer:

Let the required side of the triangle be x

By Pythagoras theorem we get,

x  = \sqrt{ {13}^{2} -  {12}^{2}  } \\   =  \sqrt{169  -  144}   \\ =  \sqrt{25}  \\  =  \sqrt{ {5}^{2} }  \\  = 5

<h3>5 is the right answer.</h3>
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Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000
AleksandrR [38]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.

<u>First, we determine the value of the 5 installments using a 5% annual compounded rate.</u>

We calculate the future value, and then the present value:

FV= {A*[(1+i)^n-1]}/i

A= annual payments

FV= {60,000*[(1.05^5) - 1]} / 0.05

FV= $331.537.88

PV= FV/(1+i)^n

PV= $259,768.60

At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.

<u>Now, if the annual rate is 6% continuously compounded.</u>

<u>First, we need to calculate the effective interest rate:</u>

r= e^i - 1

r= effective inerest rate

r= e^0.06 - 1

r= 0.0618

FV= {60,000*[(1.0618^5) - 1]} / 0.0618

FV= 339,443.23

PV= 339,443.23/1.0618^5

PV= $251,509.01

At an annual rate of 6% compounded continuously, she should choose the $255,000.

5 0
3 years ago
−<br> 3<br> (<br> 7<br> −<br> 2<br> x<br> )<br> =<br> −<br> 1<br> −<br> 4<br> x
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Answer:

5208

Step-by-step explanation:

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2 years ago
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To get 20 cups of purple paint, the table shows that we need 8 cups of blue paint and 12 cups of red paint. We can solve the problem using double (or triple) number lines.

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They each get half a slice of pizza

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4.6.3 Test (CST): Linear Equations
inn [45]

The slope of the green line if the lines are perpendicular is -1/4

<h3>Perpendicular lines</h3>

For two lines two be perpendicular, the product of their slope must be -1. Let the slope of the red and green line be m1 and m2.

Given the following

Slope of red line = 4

According the definition

4m2 = -1

m2 = -1/4

Hence the slope of the green line if the lines are perpendicular is -1/4

Learn more on perpendicular lines here: brainly.com/question/1202004

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