Answer:
There are two ways to do this problem algebraically or trigonometrically.
Algebraically/geometrically
The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.
The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3
Using Trig.
We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).
Therefore, sin(pi/3) = 6/r =
r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3
Answer:

Step-by-step explanation:
For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52
First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:

So then 12 C5 would be equal to:

So we have 792 was in order to select 5 diamonds from the total of 12
Now in order to select 3 clubs from the total of 12 we have the following number of ways:

So then the numbers of ways in order to select 5 diamonds and 3 clubs are:

Answer:
m = 3/5
Step-by-step explanation:
use the formula so m = -5 - -2 / 5 - 10 , so m = -5+2 / -5
m = -3/-5 so m = 3/5
Answer:
see in the picture mark brainliest if correct
<u>Question 7:
Define x :
</u>
Let the digit in the ones place be x.
The digit in the tens place is x+2.
The sum of the digit and its reverse is 66
<u>Find x:</u>
10(x + 2) + x + 10x + (x + 2) = 66
10x + 20 + x + 10x + x + 2 = 66
22x + 22 = 66
22x = 44
x = 2
<u>Find the number:</u>
The number in the ones place = x= 2
The number in the tens place = x = 2 + 2 = 4
Answer : The number is 42.
<u>Question 8:</u>
<u>Define x:</u>
Let the digit in the tens place be x.
The digit in the ones place is x+7.
The number = 10x + x + 7 = 11x + 7
If the digit interchange,
the number = 10(x + 7) + x = 10x + 70 + x = 11x + 70
<u>Find x:
</u>
9(11x + 7) = 2(11x + 70)
99x + 63 = 22x + 140
99x - 22x = 140 - 63
77x = 77
x = 1
<u>Find the number:
</u>
x = 1
x + 7 = 1 + 7 = 8
So the number is 18
Answer: The number is 18.