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olchik [2.2K]
3 years ago
6

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

Mathematics
1 answer:
GaryK [48]3 years ago
8 0

Answer:

x = \sqrt{21}/3

Step-by-step explanation:

In a 30-60-90 triangle, the longer leg is \sqrt{3} times the shorter leg.

So,   x\sqrt{3} = \sqrt{7}

        x = \sqrt{7}/\sqrt{3} = \sqrt{21}/3

You might be interested in
If 400 reduced by two times my present age is 296, how old am I now?
vitfil [10]

Answer:

52 years.

Step-by-step explanation:

Represent my current age by c.  Then 400 - 2c = 296, or

104 = 2c

Then c must be 104/2, or 52 years.

4 0
4 years ago
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). y= <img src="https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bx%5E2%
lisabon 2012 [21]

Answer:

One possible answer is:

f(x) = (2/x) + 3 and g(x) = x².

Step-by-step explanation:

Explanation:

We are to write this equation as y = f(g(x)).  This means we want it to be a composite of functions; in f(x), we take the value of g(x) and use in place of x.

If we let g(x) = x², this means everywhere we see an x in f(x), we will replace it with x².  To make our equation y = 2/x² + 3, working backward we would substitute x for x²; this would give us f(x) = 2/x + 3.

6 0
3 years ago
. Osteen has 32 marbles in his collection. 18 of his marbles are red, four are blue, and the rest are
nalin [4]

Answer: B

Explanation:  

32 marbles in total.

18 red marbles

4 blue marbles

10 green marbles.

You are asked what part of Osteen's marbles are red?

Probability = number of possible outcomes/total number of out outcomes.

P(Red) = 18/32 = 9/16

Both, 18 and 32 are divisible by 2 which gives 9/16. Since 9/16 cannot be reduced any further, we live it as it is. If you wanted to plug this into a calculator that would give 0.5625 which is 56.25% of Osteen's marbles are red.

P(Blue) = 4/32 = 1/8. 1/8 = 0.125 which 12.5% of his marbles are blue.

P(Green) = 10/32 = 5/16. 5/16= 0.3125 which 31.25 of his marbles are green. When you add 0.5625 + 0.125 + 0.3125 = 1 which is 100%. All probabilities add up to 1.

Hope this elaborate explanation helps.

6 0
2 years ago
Solve for y 16y^2-25=0
Pepsi [2]

Answer:

\large\boxed{x=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}

Step-by-step explanation:

16y^2-25=0\\\\METHOD\ 1:\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\16=4^2\ \text{and}\ 25=5^2\ \text{therefore we have}\\\\4^2y^2-5^2=0\\\\(4y)^2-5^2=0\\\\(4y-5)(4y+5)+0\iff4y-5=0\ \vee\ 4y+5=0\\\\4y-5=0\qquad\text{add 5 to both sides}\\4y=5\qquad\text{divide both sides by 4}\\\boxed{y=\dfrac{5}{4}}\\\\4y+5=0\qquad\text{subtract 5 from both sides}\\4y=-5\qquad\text{divide both sides by 4}\\\boxed{x=-\dfrac{5}{4}}

METHOD\ 2:\\\\16y^2-25=0\qquad\text{add 25 to both sides}\\\\16y^2=25\qquad\text{divide both sides by 16}\\\\y^2=\dfrac{25}{16}\to y=\pm\sqrt{\dfrac{25}{26}}\\\\y=-\dfrac{\sqrt{25}}{\sqrt{16}}\ \vee\ x=\dfrac{\sqrt{25}}{\sqrt{16}}\\\\\boxed{y=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}

7 0
3 years ago
Read 2 more answers
2,826 rounded to the nearest tenth
jasenka [17]

Answer:

2,826

Step-by-step explanation:

A tenth is the first place value after the decimal point

In this case, 2,826.<u>0</u>0

To round a number to the tenths place, we look at the hundredths place

If the number is 5 or more, we add 1 to the tenths place, and leave the numbers to the right 0's

If the number is 4 or less, we keep the number as it is in the tenths place, and leave the numbers to the right 0's

In this case, the hundredths place is a 0, which is less than 4, so we keep the 0 in the tenths place, and leave the to the right 0's.

Thus, our final answer is 2,826.

8 0
2 years ago
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