Answer:
d. c = 100; (x – 10)²
Step-by-step explanation:
Note that (x+a)²=x²+2ax+a².
In our case, 2a=-20, so 'a' must be -10.
Since c=a², and a=-10, c=(-10²)=100.
Since a=-10, the perfect square is (x – 10)²
Answer:
Step-by-step explanation:
Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.
120 = L + 2W
Where
LW = area.
Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60
On substituting, we have
A = LW = (120 - 2W) W
From the first equation, making L the subject of the formula, we have this
L = 120 - 2W, which then we substituted above.
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
Add 4 to both sides
x - 4 < -3
x-4+4 < -3+4
x < 1
To graph this on a number line, plot an open circle at 1 on the number line. Do not fill in the open circle. Shade to the left of the open circle. The shaded region represents all x values smaller than 1.
The graph is shown below.
Answer:
1.) There are 16 juniors and 8 seniors in the Chess Club. If the club members decide to send 9 juniors to a tournament, how many different possibilities are there?
(16 over 9) = 16!/(9!*7!) = 11440
2.) How many different ways can 3 cards be drawn from a deck of 52 cards without replacement?
52*51*50 = 132600
3.) How many different ways can 3 cards be drawn from a deck of 52 cards with replacement?
52^3 = 140608
4.) A corporation has 5 officers to choose from which 3 are selected to comprise the board of directors. How many combinations are there?
(5 over 3) = 5!/(3! * 2!) = 10
5.) A combination lock has the numbers 1 to 40 on each of three consecutive tumblers. What is the probability of opening the lock in ten tries?
10/40^3 = 1/6400
Answer:
swimming: 0,75h
biking: 1,6h
running: 1h
Step-by-step explanation:
