All categories

2 years ago

Find the length of side x in simplest radical form with a rational denominator.

Mathematics

1 answer:

Leto [7]2 years ago

7 0

<h3>Answer: $2\sqrt{5}$ </h3>

======================================================

Explanation:

Both legs are the same length, as indicated by the tickmark.

a = $\sqrt{10}$
b = $\sqrt{10}$
c = x

Use the pythagorean theorem to solve for x

$a^2+b^2 = c^2\\\\( \sqrt{10} )^2 + ( \sqrt{10} )^2 = x^2\\\\10 + 10 = x^2\\\\x^2 = 20\\\\x = \sqrt{20}\\\\x = \sqrt{4*5}\\\\x = \sqrt{4}*\sqrt{5}\\\\x = 2\sqrt{5}\\\\$

You might be interested in

Find the Product and Combine similar terms.<br>1. -1(7+4b) =<br>2. x(x²–2xy+y²) =<br>3. -5x(-3+x) =

sergejj [24]

-1(7+4b) - distribute the -1 to the expression
(-1 * 7) + (-1 * 4b) — ( + and - = - )when it is multiplied
= -7 - 4b — there is no like term to added to subtracted so it will stay as like

x(x^2 - 2xy+y^2) distribute x to all
= x(x^2) - x(2xy) + x(y^2)
= x^3 - 2x^2y + xy^2 in multiplication exponent add to similar variable
No like term to connect

-5x(-3+x)
= -5x(-3) -5x(+x). (- and - is +)
= 15x -5x. similar variable x so connect the like connect like term by subtracting them
= 10x

3 0

2 years ago

In a gambling game, you roll 2 die and if you toss 2 sixes, you win $100, otherwise you lose $5.

Natalka [10]

Answer:

a. $\frac{1}{36}$ chance you win.

b. The expected value of the game is -$2.08.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

You roll 2 die and if you toss 2 sixes

For each roll, 6 possible values, 1 of which is 6. So the probability of rolling two sixes is:

$p = (\frac{1}{6})^2 = \frac{1}{36}$

a. What is the chance you win?

$\frac{1}{36}$ chance you win.

b. What is the expected value of the game?

1/36 probability of winning 100.

35/36 probability of losing 5. So

$E = \frac{1}{36}*100 - \frac{35}{36}*5 = \frac{100 - 175}{36} = -\frac{75}{36} = -2.08$

The expected value of the game is -$2.08.

7 0

2 years ago

Please Help

Jlenok [28]

Histograms are useful when we have data which can be divided into several classes or groups. The histogram shows the trend of each class and the trend among the different classes. For example when we have about 50 different values ranging from 1 to 20, it will be a better approach to draw a histogram in this case by dividing the data into small ranges e.g 1 to 4, 5 to 9 and so on and counting the frequency for each class.

Dot plot is useful when we have a small number of individual values. In this case we can visualize how many times each individual value occurred in the data. This is useful when the number of values in the data is less.

In the given scenario, we have 12 values in total ranging from 1 to 5. So making a dot plot would be the best choice. A histogram would not be useful in this case.

Therefore, the correct answer is option D. Dot plot, because a small number of scores are reported individually

7 0

3 years ago

Read 2 more answers

Use interval notation to express the following:<br> The set of all numbers less than 2.

AlexFokin [52]

Answer:

( - infinity, -3 ] [ -2, infinity )

square bracket means it includes the end point.

Step-by-step explanation:

(-∞, -3]U [-2,∞)

3 0