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stellarik [79]
3 years ago
7

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

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
3 0

Answer:

2\sqrt{5}

Step-by-step explanation:

this is a 30-60-90 Δ and the ratio of the sides are 1 : \sqrt{3} : 2

1 / 2 = \sqrt{5} / x

cross-multiply: x = 2\sqrt{5}

You might be interested in
Find the dimensions of the rectangle with area 256 square inches that has minimum perimeter, and then find the minimum perimeter
mezya [45]

Answer:

Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

Minimum perimeter: [16,16]

Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

b=\frac{256}{a}

The function we want to optimize is the diameter.

We can express the diameter as:

P=2a+2b=2a+2*\frac{256}{a}

To optimize we can derive the function and equal to zero.

dP/da=2+2\cdot (-1)\cdot\frac{256}{a^2}=0\\\\\frac{512}{a^2}=2\\\\a=\sqrt{512/2}= \sqrt {256} =16\\\\b=256/a=256/16=16

The minimum perimiter happens when both sides are of size 16 (a square).

4 0
3 years ago
10x4ones= ones=<br> 10x2tens= tens=
Vsevolod [243]
Well, 10x4=40 because 10+10+10+10=40 and that means your answer must be 40 ones or you asked something else.
5 0
3 years ago
A bag contains 14 red marbles and 6 blue marbles. two marbles are randomly drawn without replacement. find the probability that
Ksenya-84 [330]
We take 2 marbles from 20 marbles and the total ways is 20x19:2=190
But we need only 2 red marbles and the ways is 14x13:2=91
And finally we do the division 91:190=91/190 is the probability we need
7 0
3 years ago
What is the solution to the equation?
Charra [1.4K]

through my calculations x=8

7 0
3 years ago
Read 2 more answers
Please help I am confused i'll answer one of your questions!! I got it wrong the first time​
vaieri [72.5K]

Answer:

Step-by-step explanation:

22.2

7 0
3 years ago
Read 2 more answers
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