A coordinate plane with a straight line passing through the points (negative 6, negative 8) and (2, 8).

Mathematics

2 answers:

gizmo_the_mogwai [7]2 years ago

8 0

Answer:

Step-by-step explanation:

inna [77]2 years ago

8 0

Answer: 2 is correct

Step-by-step explanation:

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If G is the midpoint of FH find FG<br>fg=11x-7 gh= 3x+9

gavmur [86]

Solution:

we are given that

If G is the midpoint of FH, it mean that

$FG=GH$

we are also given that

$FG=11x-7 ,GH= 3x+9$

So we can write

$11x-7=3x+9\\
\\
11x-3x=7+9\\
\\
8x=16\\
\\
x=2$

So $FG=11x-7=11*\frac{1}{2}-7=11*2-7=15$

3 0

3 years ago

The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth

Art [367]

Answer:

a) $N_0=250\; k=0.15$

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies $t=0$ . And $N(0)=N_0$ . The process is:

$N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250$

b) After 2 days means $t=48$ . So, we just replace and operate:

$N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}$

c) $N(t_1)=4000; \;t_1=?$

$N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\ \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h$