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ELEN [110]
4 years ago
10

Rewrite (2x+1)(x-2) using the distributive property then simplify

Mathematics
1 answer:
Contact [7]4 years ago
3 0
(2x+1)(x-2) = 2x^2 - 4x +x -2= 2x^2-3x-2
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A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical is given by the equatio
GaryK [48]

Answer:

a)  N=N_0e^{-0.069t}

b)  N=696.9 grams

c)  t=10 days

Step-by-step explanation:

a)

We are going to use separation of variables to solve.

Get all your t's to one side and your N's to opposing side.

\frac{dN}{dt}=-0.069N

Multiply both sides by dt:

dN=-0.069N dt

Divided both sides by N:

\frac{dN}{N}=-0.069 dt

Integrate both sides:

\ln|N|=-0.069t+C

The equivalent exponential form is:

e^{-0.069t+C}=N

Using law of exponents you can write this as:

e^{-0.069t}e^C=N

e^C is just a positive constant that I'm going to replace with K:

e^{-0.069t}K=N

Applying the symmetric property of equality:

N=e^{-0.069t}K

Applying the commutative property of multiplication:

N=Ke^{-0.069t}

K actually represents the initial amount of chemical substance since when plugging in 0 for t you get K for N, like so:

N=Ke^{-0.069 \cdot 0}

N=Ke^{0}

N=K(1)

N=K

We are given at time 0 the amount of chemical substance,N, is K. They want us to represent this value with N_0 instead. So the exponential equation is:

N=N_0e^{-0.069t}

b)

We are given N_0=800 at t=0.

We are asked to find how much of the chemical substance, N, remains after 2 days.  So we replace t with 2 in N=800e^{-0.069t}:

N=800e^{-0.069 \cdot 2}

Put into calculator:

N=696.9 (this was rounded to the nearest tenths)

c)  

The last part is asking for how many days will it take a initial 800 grams to go down to half of 800 grams.

We need to see the following equation:

\frac{1}{2}(800)=800e^{-0.069t}

400=800e^{-0.069t}

Divide both sides by 800:

\frac{400}{800}=e^{-0.069t}

Reduce the fraction:

\frac{1}{2}=e^{-0.069t}

Convert to logarithmic form:

\ln(\frac{1}{2})=-0.069t

Divide both sides by -0.069:

\frac{\ln(\frac{1}{2})}{-0.069}=t

Input into calculator:

10.0=t

t=10.0

t=10

6 0
3 years ago
8 + what equals -6?
vekshin1

The answe is      8 + (-14) = -6

...

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3 years ago
Your sale of salmon has increased 22% each year for the last three years. Assuming this trend holds and you purchased 2,946 salm
sineoko [7]

Answer:

5,350

Step-by-step explanation:

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3 years ago
What expression is equal to 7(3 - x) + 1?
Nesterboy [21]

7(3-x)+1 .. first you're going to distribute

21-7x+1 .. then combine like terms

22-7x .. subtract 22 from both sides to get the variable X alone.

-7x=-22

x=3.14

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3 years ago
Use the order of operation to simplify the expression. <br> (2/7)^2 x (7/12)^2
ella [17]
4/49 x 49/144
49/144
I hope this helps :-)
8 0
3 years ago
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