The answer is 18 + 6√3 or 18 + <span>√108.</span>
In a<span> 30°-60°-90° triangle, the hypotenuse (c) is twice the length of the shorter leg (a):
c = 2a </span>⇒ a = c ÷ 2 = 12 ÷ 2 = 6<span>
In a </span>30°-60°-90° triangle, the longer leg is equal to the shorter leg multiplied by √3:
b = √3a = √3 · 6
Now we have the length of all three sides:
a = 6
b = 6√3 = √6² · √3 = √36 · √3 = √(36 · 3) = √108
c = 12
So, the perimeter (P) of the triangle is:
P = a + b + c = 6 + 6√3 + 12 = 18 + <span>6√3 = 18 + </span>√108
Answer:
(3x+2) ^2
x = -2/3
Step-by-step explanation:
9x^2+12x+4 = 0
We need to recognize that this is perfect squares
(a + b)2 = a^2 + 2ab + b^2;
Where a = 3x and b =2
a^2 = 9x^2 2ab = 2*3x*2 = 12x and b^2 = 2^2 =4
So we can factor this as (3x+2) ^2
If you want to solve
We can use the zero product property
(3x+2) ^2 =0
Take the square root of each side
3x+2 =0
Subtract 2 from each side
3x=-2
Divide by 3
3x/3 = -2/3
2 dollar bills, one nickel, and three pennies ($2.08) :)
Answer:
Step-by-step explanation:
1. Do what is inside the parantheses
2. Simplify both terms
3. Solve
An atm personal identification number (pin) consists of four digits, each a 0, 1, 2, . . . 8, or 9, in succession.
a. How many different possible pins are there if there are no restrictions on the choice of digits?
Solution: The are total 10 numbers between 0 and 9.
Also there are no restrictions on the choice of digits. Therefore, the possible number of different PINs is:
Therefore, there are 10,000 different possibles PINs.
