Answer: There will be 313600 population on beth's 16 birthday.
Step-by-step explanation:
Since we have given that
When Beth was born , the population of her has increased = 850 per year
Let the initial population be x
and let the number of year be n
So, our linear equation becomes,
On her 9th birthday,
The population becomes 307,650.
So, it becomes,
So, initial population becomes 300000.
Now, on 16th birthday,
So, there will be 313600 population on beth's 16 birthday.
Answer: The (magnitude of the) rate of change increases over time. The object drops 16 feet in the first second, but 80 feet in the last second.
Explanation:
1) I will start by showing the table in an easy way to read and understand:
Time (seconds) Height (feet)
0 144
1 128
2 80
3 0
2) Rate of change
- An initial clarification: the rate of change decreases since it is becoming more negative every second, but, in the analysis, the reasonable is to deal with the magnitude of this rate. The results shown below that the rate as a negative value, but the comparison is set about the magnitude of the change.
- The rate of change is calculated for every pair of consecutive points using this equation:
rate of change = [change in height] / [time elapsed]
a) rate₁: [128 - 144] feet / [ 1 - 0] sec = - 16 feet / sec ⇒ the object drops 16 feet in the first second.
b) rate₂ = [80 - 128] feet / [2 - 1] sec = - 48 feet/sec ⇒ the object drops 48 feet in the next second
c) rate₃ = [0 - 80] feet / [3 - 2] sec = - 80 feet/sec ⇒ the object drops 80 feet in the last second.
The rate of change is more negative every second: it increases in magnitude over time. The object drops 16 feet in the first second, but 80 feet in the last second.
Answer:
Step-by-step explanation:
Let x represent the number of pounds of soap that she makes and eventually sells.
She intially spent $72 to purchase soap-making equipment, and the materials for each pound of soap cost $7. This means that the total cost of making x pounds of soap would be
7x + 72
Lisa sells the soap for $10 per pound. This means that her revenue for x pounds of soap would be
10 × x = 10x
If she eventually sells enough soap to cover the cost of the equipment, then
7x + 72 = 10x
10x - 7x = 72
3x = 72
x = 72/3 = 24
She would need to sell make and sell 24 soaps.
The cost would be
72 + 7 × 24 = $240
The total sales would be
10 × 24 = $240
Answer:
x <-14.5
Step-by-step explanation:
2x + 2(x+5) <+4(8 – 20)
Distribute
2x+2x+10 < 4 (-12)
4x +10 < -48
Subtract 10 from each side
4x+10-10 <-48-10
4x< -58
Divide each side by 4
4x/4 < -58/4
x <-14.5
Answer:
proper because the numerator is lower than the denominator
