First consider (x+c)^2 where c is just a random constant. if we expand this by foil (which is distributive property twice), we get x^2 + 2cx+ c^2. we want to find c^2 and to do that, we can first find c. we can find c by looking at the 2cx term. this term should match with 12x, so therefore 2c = 12 so c = 6. this also implies that c^2 = 36.
note that for this problem i was working backwards which is a very powerful problem solving tool: start with what you want to attain, and then see how you can go from where you are now to get to your destination.
let me know if you have any questions!!!
X^2 + 10x + 11 = 0
x^2 + 10x = -11
x^2 + 10x + 25 = -11 + 25
(x + 5)^2 = 14 <===
x + 5 = (+-) sqrt 14
x = -5 (+-) 3.74
x = -5 + 3.74 = -1.26 <== solution
x = -5 - 3.74 = - 8.74 <== solution
Answer:
Two sets are called disjoint if they have no elements in common. For example:
The sets S = { 2, 4, 6, 8 } and T = { 1, 3, 5, 7 } are disjoint.
Another way to define disjoint sets is to say that their intersection is the empty set,
Two sets A and B are disjoint if A ∩ B = 0.
In the example above,
S ∩ T = ∅ because no number lies in both sets.
Step-by-step explanation:
Answer: 75%
Step-by-step explanation: So 15/20 simplified is 3/4 and 3 divided by 4 equals 0.75. To convert a decimal to a percentage, you multiply 0.75 by 100 to get 75%.
