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3 years ago

Find the length of the hypotenuse of a right triangle if a = 3 and b = 4.

Mathematics

2 answers:

natulia [17]3 years ago

7 0

It’s B, because of the Pythagorean theorem.

Mandarinka [93]3 years ago

4 0

Answer:

5..(b)

Step-by-step explanation:

Pythagoras theorem states that

Hypotenuse(squared)=opposite(squared)+ adjacent(squared)

hypotenuse=?,opposite=3,adjacent=4

hyp(squared)=3(squared)+4(squared)

hyp(squared)=9+16

hyp(squared)=25

find the square root of both sides

hypotenuse=5

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3 years ago

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kirill [66]

It's going to be kind of crazy, but you need to use Pythagorean's Theorem for this. That will look like this: $(2 \sqrt{x} +1)^2=( \sqrt{x} +1)^2+(2 \sqrt{x} )^2$ . FOIL out the left side to get $4x+4 \sqrt{x} +1$ . FOIL out the first of the 2 expressions on the right to get $x+2 \sqrt{x} +1$ , and the second of the 2 to get 4x. Our equation now looks like this: $4x+4 \sqrt{x} +1=x+2 \sqrt{x} +1+4x$ . Combine like terms to get an equation that still has square roots in it that we have to deal with: $4x-x-4x=-2 \sqrt{x}$ and $x=2 \sqrt{x}$ . We will square both sides to get rid of the square root sign. $x^{2} =2x$ . This is a polynomial now that can be factored to solve for x. Bring the 2x over by subtraction and set the polynomial equal to 0. $x^{2} -2x=0$ . Factor out an x, leaving us with x(x-2)=0. That means that x = 0 or x - 2 = 0 and x = 2. Of course if we are solving for the length of a side we know it can't have a side length of 0, so it must have a side length that is a multiple of 2. x = 2

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2 years ago

Read 2 more answers

Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, port

GrogVix [38]

Answer:

$a=49.5 -1.28*15=30.3$

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.

If the score is lower than 30.3 we consider this score as risk averse

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(49.5,15)$

Where $\mu=49.5$ and $\sigma=15$

We are interested in the bottom 10% of the data.

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.9$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

$P(X$