Can someone please help me with this math . I've just entered High School and I hate it already.

In the first half of a basketball game, a player scored 9 points on free throws and then scored a number of 2-point shots. In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half. Which expression represents the total number of points the player scored in the game?

a) 2x + 3x + 9

b) 2x + 3 + 9

c) 2x + 3x + 9x

d) 2 + 3x + 9

Answer:

a) 2x + 3x + 9

Step-by-step explanation:

Let the number of points shots a player scores = x

In a free throw, the player scored 9 points = 9

The player also scored a number of 2-point shots = 2x

In the second half, the player scored the same number of 3-point shots as the number of 2-point shots scored in the first half = 3x

The expression represents the total number of points the player scored in the game =

2x + 3x + 9

4 0

2 years ago

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

goldfiish [28.3K]

Answer:

P(t) = 100·2.3^t
529 after 2 hours
441 per hour, rate of growth at 2 hours
5.5 hours to reach 10,000

Step-by-step explanation:

It often works well to write an exponential expression as ...

value = (initial value)×(growth factor)^(t/(growth period))

(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...

P(t) = 100·2.3^t

__

(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours

__

(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t

P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour

__

(d) We want to find t such that ...

P(t) = 10000

100·2.3^t = 10000 . . . substitute for P(t)

2.3^t = 100 . . . . . . . . divide by 100

t·log(2.3) = log(100)

t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000

6 0

3 years ago