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2 years ago

If f(–5) = 0, what are all the factors of the function f(x)=x^3-19x+30? Use the Remainder Theorem.

Mathematics

2 answers:

nirvana33 [79]2 years ago

8 0

A. (x-2)(x+5)(x-3) is the correct answer to this question : )

Angelina_Jolie [31]2 years ago

4 0

Answer:

a) (x-2)*(x+5)*(x-3)

Step-by-step explanation:

We are given that f(x) = $x^{3}-19x+30$ .

Now, f(-5)=0 i.e. (x+5) is a factor of f(x),

We need to find the other two factors.

So, using Remainder Theorem, we get that f(x) is simplified into f(x) = $(x+5)$ * ( $x^{2}+5x+6$ ).

Now, after solving the quadratic equations, we get that,

f(x) = (x+5)*(x-2)*(x-3).

Hence, a) (x-2)(x+5)(x-3) are the factors of f(x).

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(100) points!!!! Help please

inysia [295]

Answer:

$\displaystyle a_8=142,11\ mg$

Step-by-step explanation:

Geometric sequence

Each term in a geometric sequence can be computed as the previous term by a constant number called the common ratio. The formula to get the term n is

$\displaystyle a_n=a_1r^{n-1}$

where $a_1$ is the first term of the sequence

The problem describes Georgie took 275 mg of the medicine for her cold in the first hour and that in each subsequent hour, the amount of medicine in her body is 91% (0.91) of the amount from the previous hour. It can be written as

amount in hour n = amount in hour n-1 * 0.91

This information provides the necessary data to write the general term as

$\displaystyle a_n=275\ .\ 0.91^{n-1}$

In the 8th hour (n=8), the remaining medicine present is Georgie's body is

$\displaystyle a_n=275\ .\ 0.91^{8-1}$

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$\boxed{\displaystyle a_8=142,11\ mg}$

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3 years ago

On a piece of paper graph......

Artyom0805 [142]

Answer:

I think it’s the first one, A

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2 years ago

Your bank account is sitting on $14,000. You started with a principal balance of $12,500. If the interest rate was 4.5% compound

Simora [160]

Answer:

$t=2.5\ years$

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=?\ years\\ P=\$12,500\\P=\$14,000\\ r=4.5\%=4.5/100=0.045$

substitute in the formula above and solve for t

$14,000=12,500(e)^{0.045t}$

Simplify

$14,000/12,500=(e)^{0.045t}$

$1.12=(e)^{0.045t}$

Apply ln both sides

$ln(1.12)=ln[(e)^{0.045t}]$

$ln(1.12)=(0.045t)ln(e)$

Remember that

$ln(e)=1$

$ln(1.12)=(0.045t)$

$t=ln(1.12)/(0.045)$

$t=2.5\ years$

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