All categories

3 years ago

ABC is a right triangle. If AC = 12 and BC = 13, find AB.

Mathematics

2 answers:

Yakvenalex [24]3 years ago

6 0

Answer:

Step-by-step explanation:

Alright, lets get started.

There is a right triangle given, please refer the diagram I have attached.

Using Pythagorean theorem,

$AC^2+AB^2=BC^2$

Plugging the value of sides in theorem

$12^2 + AB^2 = 13^2$

$144+AB^2=169$

$AB^2 = 169-144$

$AB^2 = 25$

Taking square root on both sides

$AB = 5$ .................. Answer

Hpe it will help :)

AysviL [449]3 years ago

3 0

Since BC is the hypotenuse...

α = 12
c = 13

Hence..

13² = 12² + ß²
ß = √(13² - 12²)
= √(169 - 144)
= √25
= 5

Hence, AB = 5

I hope this helps!

You might be interested in

To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying a $1 for each five-number s

defon

There are 45 numbers out of which 5 numbers are required to win an enormous sum of money

No of ways in which 5 numbers can be selected out of 45 numbers.

$C_{45}^5=\frac{45!}{40!5!} =1221759$

out of which there is only combination foe contest winning

$P=\frac{1}{1221759}$

When 100 different tickets are bought then

Probability of winning: $\frac{100}{1221759}$

Probably of winning≈0,000082

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

P.S. Hello from Russia :^)

4 0

3 years ago

How do I solve problem 10?

Grace [21]

If you extend the line from 1 through the parallel line you create a transversal and a triangle.

Consecutive angles inside the parallel lines are supplementary therefor the exterior angle of the triangle on the left side measures 118 degrees. This angle creates a linear pair with the left base angle therefore that angle measures 62 degrees.

144 forms a linear pair with the right base angle of the triangle making its measure 36 degrees.

The third angle of the triangle would then measure 82 degrees. Finally this third angle forms a linear pair with angle 1 making angle 1 measure 98 degrees.

6 0

3 years ago

Write an exponential function in the form y=ab^x that goes through points (0, 17) and (2,153).

garik1379 [7]

Answer:

y = 17*(3)ˣ

Step-by-step explanation:

y=abˣ

(0,17) : 17 = a*b⁰ = a

(2,153) : 153 = a*b² = 17*b²

b² = 153/17 = 9

b = ± 3 ... (0,17) and (2,153) in first quadrant b = 3

function: y = 17*(3)ˣ

4 0

2 years ago

Of the total population of the United States, 20% live in the northeast. If 200 residents of the United States are selected at r

Snezhnost [94]

Answer:

0.0465 = 4.65% probability that at least 50 live in the northeast.

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .