the idea behind the completion of the square is simply using a perfect square trinomial, hmmm usually we do that by using our very good friend Mr Zero, 0.
if we look at the 2nd step, we have a group as x² - x, hmmm so we need a third element, which will be squared.
keeping in mind that the middle term of the perfect square trinomial is simply the product of the roots of "a" and "b", so in this case the middle term is "-x", and the 1st term is x², so we can say that
so that means that our missing third term for a perfect square trinomial is simply 1/2, now we'll go to our good friend Mr Zero, if we add (1/2)², we have to also subtract (1/2)², because all we're really doing is borrowing from Zero, so we'll be including then +(1/2)² and -(1/2)², keeping in mind that 1/4 - 1/4 = 0, so let's do that.
![-3~~ = ~~-2\left[ x^2-x+\left( \cfrac{1}{2} \right)^2 ~~ - ~~\left( \cfrac{1}{2} \right)^2\right]\implies -3=-2\left(x^2-x+\cfrac{1}{4}-\cfrac{1}{4} \right) \\\\\\ -3=-2\left(x^2-x+\cfrac{1}{4} \right)+(-2)-\cfrac{1}{4}\implies -3=-2\left(x^2-x+\cfrac{1}{4} \right)+\cfrac{1}{2} \\\\\\ -3-\cfrac{1}{2}=-2\left(x^2-x+\cfrac{1}{4} \right)\implies -\cfrac{7}{2}=-2\left(x-\cfrac{1}{2} \right)^2\implies \cfrac{7}{4}=\left(x-\cfrac{1}{2} \right)^2](https://tex.z-dn.net/?f=-3~~%20%3D%20~~-2%5Cleft%5B%20x%5E2-x%2B%5Cleft%28%20%5Ccfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%20~~%20-%20~~%5Cleft%28%20%5Ccfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%5Cright%5D%5Cimplies%20-3%3D-2%5Cleft%28x%5E2-x%2B%5Ccfrac%7B1%7D%7B4%7D-%5Ccfrac%7B1%7D%7B4%7D%20%5Cright%29%20%5C%5C%5C%5C%5C%5C%20-3%3D-2%5Cleft%28x%5E2-x%2B%5Ccfrac%7B1%7D%7B4%7D%20%5Cright%29%2B%28-2%29-%5Ccfrac%7B1%7D%7B4%7D%5Cimplies%20-3%3D-2%5Cleft%28x%5E2-x%2B%5Ccfrac%7B1%7D%7B4%7D%20%5Cright%29%2B%5Ccfrac%7B1%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20-3-%5Ccfrac%7B1%7D%7B2%7D%3D-2%5Cleft%28x%5E2-x%2B%5Ccfrac%7B1%7D%7B4%7D%20%5Cright%29%5Cimplies%20-%5Ccfrac%7B7%7D%7B2%7D%3D-2%5Cleft%28x-%5Ccfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%5Cimplies%20%5Ccfrac%7B7%7D%7B4%7D%3D%5Cleft%28x-%5Ccfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2)
Answer:
6. 141
7. 28
Step-by-step explanation:
Time to rewrite the expressions!
6. (8 + 45/9)² - 14(2)
First, we need to solve what's in the parentheses.
45/9 is 5. So 8 + 5 is 13. 13² - 14(2)
Now, the exponent. 13² = 169 (nice)
169 - 14(2) Multiply 14 and 2...
169 - 28 = 141
Now to rewrite 7.
12 + 36/2 - 3(1)²
Exponents first...
3² = 9 (the 1 isn't included 'cause 3 multiplied by 1 is still 3.)
12 + 36/2 - 12
Divide... 36/2 = 18
12 + 18 - 2
30 - 2
28
Combining those like terms would end as 3n.
Explanation: The end of a subtraction equation is basically just the negative number, except you add it to the other part.
For example, 2n is really -2n, and you just add -2n to 5n (which is positive,) and you get 3n.
Answer:
13.59
Step-by-step explanation:
The calculation of amount of cash in the room is shown below:-
= 20 × $14.50
= $290
Now, the new sum is
= ∑xi + $4.00 + $5.00
= $290 + $4.00 + $5.00
= $299
Total person in the room is
= 20 + 2
= 22
So,
Mean amount of cash in the room = New sum ÷ Total person in the room
= $299 ÷ 22
= 13.59
