She spent 5.4 on tip so her overall total is $41.40
You should have received 33 pairs of protective eyewear
To Check This:
1 dozen = 12
1/2 dozen = 6
5 dozen = 60
12x5=60+6=66
66 / 2 = 33 because a pair equals 2
Step-by-step explanation:
well, the starting equation and the target format have been given.
let's do the multiplications and compare the target with the starting information.
from there we see what is different or missing.
x² + 14x + 13 = 0
and
(x - p)² = q
x² - 2px + p² = q
x² - 2px + (p² - q) = 0
now let's compare the different parts :
x² = x²
-2px = 14x
-2p = 14
p = -7
p² - q = 13
-7² - q = 13
49 - q = 13
36 - q = 0
q = 36
so, the square (x - p)² = (x + 7)² is completed when
x² + 14x + 49 = 0
but we have only "+ 13". so we need to add 36 to get 49. but we need to do it on both sides, to keep the equation true :
x² + 14x + 13 + 36 = 36
x² + 14x + 49 = 36
(x + 7)² = 36
just as we calculated already above.
and now this can be solved by pulling the square root on both sides (a quadratic equation has always 2 solutions)
x + 7 = ±6
x1 = 6 - 7 = -1
x2 = -6 - 7 = -13
Your will be 128 because you have to add 64+64
Number8)4n+6-2n=2(n+3)
4n+6-2n=2n+6 then collect the like terms
(4n-2n-2n=0)
0n=0
2(3b-4)=4b-11
6b-8=4b-11 collect the like terms
(6b-4b=2b)(-11+8=-3)
answer
2b=-3 then divide both sides by 2
b=-1.5
