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3 years ago

If f(x) = -3x - 5 and g(x)= 4x - 2, find (f-g) (x).

Mathematics

1 answer:

Eddi Din [679]3 years ago

4 0

Answer:

$-7x-3$

Step-by-step explanation:

$(f-g)(x)$ just means $f(x)-g(x)$ .

$-3x-5-(4x-2)\\-3x-5-4x+2\\-7x-3$

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HELP HELP HELP HELP HELP HELP (STEP BY STEP)

Marizza181 [45]

With some simple rearrangement, we can rewrite the numerator as

$2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1$

Then factorizing the difference of squares, $x^2-1=(x-1)(x+1)$ , we end up with

$\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}$

3 0

2 years ago

Find the range. 3 -9 7 -1 5 -4 2

ikadub [295]

Answer: The range is 94.

Hope this helps

8 0

3 years ago

A solution initially contains 200 bacteria. 1. Assuming the number y increases at a rate proportional to the number present, wri

GuDViN [60]

Answer:

1. $\frac{dy}{dt}=ky$

2.543.6

Step-by-step explanation:

We are given that

y(0)=200

Let y be the number of bacteria at any time

$\frac{dy}{dt}$ =Number of bacteria per unit time

$\frac{dy}{dt}\proportional y$

$\frac{dy}{dt}=ky$

Where k=Proportionality constant

2. $\frac{dy}{y}=kdt$ ,y'(0)=100

Integrating on both sides then, we get

$lny=kt+C$

We have y(0)=200

Substitute the values then , we get

$ln 200=k(0)+C$

$C=ln 200$

Substitute the value of C then we get

$ln y=kt+ln 200$

$ln y-ln200=kt$

$ln\frac{y}{200}=kt$

$\frac{y}{200}=e^{kt}$

$y=200e^{kt}$

Differentiate w.r.t

$y'=200ke^{kt}$

Substitute the given condition then, we get

$100=200ke^{0}=200 \;because \;e^0=1$

$k=\frac{100}{200}=\frac{1}{2}$

$y=200e^{\frac{t}{2}}$

Substitute t=2

Then, we get $y=200e^{\frac{2}{2}}=200e$

$y=200(2.718)=543.6=543.6$

e=2.718

Hence, the number of bacteria after 2 hours=543.6

4 0

3 years ago

Help Me 20 points Need Correct ASAP

trasher [3.6K]

Answer:

I also need help on this PLZ help

7 0

3 years ago

A club consists of 21 Republicans and 25 Democrats. If four people are chosen at random to be on a committee, what is the proba

Allushta [10]

Answer:

88.58% probability that at least one person from each political party will be chosen

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Also, the order which the people are chosen is not important. So the combinations formula is used to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

If four people are chosen at random to be on a committee, what is the probability that at least one person from each political party will be chosen?

Either only Republicans or Democrats are chosen, or at least one member from each party is chosen. The sum of these probabilities is 100%.

The easier way to solve this is first finding the probability that members are only from one party.

Probability of having members from only one party:

Desired outcomes:

Only Democrats:

4 from a set of 25.

Only Republican:

4 from a set of 21.

$D = C_{25,4} + C_{21,4} = \frac{25!}{4!21!} + \frac{21!}{4!17!} = 18635$

Total outcomes:

4 from 21+25 = 46 total members

$T = C_{46,4} = \frac{46!}{4!42!} = 163185$

Probability:

$p = \frac{D}{T} = \frac{18635}{163185} = 0.1142$

11.42% probability of having people from only one party in the committee

Probability of at least one person from each party:

p + 11.42 = 100

p = 88.58

88.58% probability that at least one person from each political party will be chosen

5 0

3 years ago