All categories

3 years ago

What is the slope of the line through (1,-1) and (5,-7)

Mathematics

1 answer:

Ber [7]3 years ago

7 0

Answer:

-1.5

Step-by-step explanation:

You might be interested in

A sample of bacteria is being eradicated by an experimental procedure. The population is following a pattern of exponential deca

77julia77 [94]

Answer:

There will be 50 bacteria remaining after 28 minutes.

Step-by-step explanation:

The exponential decay equation is

$N=N_0e^{-rt}$

N= Number of bacteria after t minutes.

$N_0$ = Initial number of bacteria when t=0.

r= Rate of decay per minute

t= time is in minute.

The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.

N=200

$N_0$ = 500

t=11 minutes

r=?

$N=N_0e^{-rt}$

$\therefore 200=500e^{-11r}$

$\Rightarrow e^{-11r}=\frac{200}{500}$

Taking ln both sides

$\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|$

$\Rightarrow {-11r}=ln|\frac{2}{5}|$

$\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}$

To find the time when there will be 50 bacteria remaining, we plug N=50, $N_0$ = 500 and $r}=\frac{ln|\frac{2}{5}|}{-11}$ in exponential decay equation.

$50=500e^{-\frac{ln|\frac25|}{-11}.t}$

$\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|$

$\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}$

$\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}$

$\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}$

$\Rightarrow t\approx 28$ minutes

There will be 50 bacteria remaining after 28 minutes.

3 0

3 years ago

What is the solution to the inequality > 20?<br><br> x 4<br> x 100

professor190 [17]

Answer:

100

Step-by-step explanation:

7 0

3 years ago

PLEASE HELP ME I need it fast don’t explain

Katena32 [7]

Answer:

The answer should be A, I think.

5 0

3 years ago

I really need help!! can u pwease help ;-;

Nata [24]

Answer:

Step-by-step explanation:

6 0

3 years ago

£25 in the ratio 2:3

never [62]

2+3=5
25/5=5
5x2=10 3x5=15
so the answer is:
£10:£15

4 0

3 years ago

What is the slope of the line through (1,-1) and (5,-7)​

What is the slope of the line through (1,-1) and (5,-7)