Part A: the radicand is the same as the discriminant, therefore is b2 - 4ac
In 9x^2 - 16x + 60 = 0, a = 9, b = -16, c = 60
so b2 - 4ac =
Part B: Solve 4x^2 + 8x - 5 = 0
What would make 8? (5×2)-2 = 8, so:
(2x+5)(2x-1) = 0
2x+5 = 0
2x = -5
x = -5/2
2x-1 = 0
2x = 1
x = +1/2
So the solutions are: -5/2, +1/2
Answer:
<u>The solution of this system of equation is ( 3, - 8)</u>
Step-by-step explanation:
1. Let's solve the system of equations:
First equation:
x + 2y = - 13
x = - 13 - 2y
Second equation:
12x + 5y = -4
12 * (- 13 - 2y) + 5y = - 4 (Replacing x with - 13 - 2y)
-156 -24y + 5y = - 4
-24y + 5y = - 4 + 156 (Like terms)
-19y = 152
y = - 152/19
<u>y = -8</u> (Dividing by 19)
Solving x
x + 2y = -13
x + 2 (- 8 ) = - 13
x - 16 = - 13
x = - 13 + 16
<u>x = 3</u>
2. Proving that x = 3 and y = - 8 are correct:
12x + 5y = -4
12 * 3 + 5 * -8 = -4
36 - 40 = - 4
- 4 = - 4
<u>We proved that x = 3 and y = - 8 are correct</u>
Answer:
30 minutes
Step-by-step explanation:
Walk rate = 88 paces/ minute
Average length of pace = 0.875 m
Time taken to walk 2.31 km ;
The distance in metres :
1000 m = 1 km
2.31 km = (1000 * 2.31) = 2310 m
Recall :
Time taken = distance / speed
Distance walked in a minute = 88 * 0.875 = 77 m
Time taken = 2310 / 77
Time taken = 30 minutes
Answer:
0
Step-by-step explanation:
Approximately 0.2% of the apples will be more than three standard deviations above the mean size. In a bin of 100 apples, 0.2% of 100=0.2% apples, this rounds down to zero apples that size or larger. (In a bin of 500 apples, there could be one apple of that size.)
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