Need to find a and b

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use

QveST [7]

$\bf 27\implies 3^3\\\\
i^3\implies i\cdot i\cdot i\implies i^2\cdot i\implies -1\cdot i\implies -i\\\\
-----------------------------\\\\
x^3-27i=0\implies x^3+3^3(-i)=0\implies x^3+(3^3i^3)=0
\\\\\\
x^3+(3i)^3=0\\\\
-----------------------------\\\\
\textit{difference of cubes}
\\ \quad \\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
(a+b)(a^2-ab+b^2)= a^3+b^3\\\\
-----------------------------\\\\$

$\bf (x+3i)[x^2-3ix+(3i)^2]=0\implies 
\begin{cases}
x+3i=0\implies \boxed{x=-3i}\\\\
x^2-3ix+(3i)^2=0
\end{cases}
\\\\\\
\textit{now, for the second one, we'd need the quadratic formula}
\\\\\\
x^2-3ix+(3i)^2=0\implies x^2-3ix+(3^2i^2)=0
$

$\bf x^2-3ix+(-9)=0\implies x^2-3ix-9=0
\\\\\\
\textit{quadratic formula}\\\\
x= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}\implies x=\cfrac{3i\pm\sqrt{(-3i)^2-4(1)(-9)}}{2(1)}
\\\\\\
x=\cfrac{3i\pm\sqrt{(-3)^2i^2+36}}{2}\implies x=\cfrac{3i\pm\sqrt{-9+36}}{2}
\\\\\\
x=\cfrac{3i\pm\sqrt{27}}{2}\implies \boxed{x=\cfrac{3i\pm 3\sqrt{3}}{2}}$

7 0

3 years ago

Calculator

KengaRu [80]

Answer:

19.8 years old

Step-by-step explanation:

If Z=(x-μ)/σ where Z=-1.32, σ=3.2, and μ=24, then:

-1.32=(x-24)/3.2

-4.224=x-24

19.776=x

19.8

Therefore, the age of a concert attendee with a z-score of -1.32 is 19.8 years old.

4 0

3 years ago

Jacob's Boat Rentals charges a one-time fee plus a $5 hourly rate to rent a boat. The cost to rent a boat for 2 hours is $25 and

maks197457 [2]

Hi there! The answer is $15

Let the one-time fee be represented by X.
The total cost of hiring a boat for 2 hours is X + $5 per hour × 2 hours = X + $10

The total cost can also be expressed as $25.
Now we can set up an equation.
X + 10 = 25

Subtract 10.
X = 15

Therefore, the one-time fee to rent a boat is $15.

We can check this by plugging in the data for the rent of 3 hours.
$15 + $5 per hour × 3 hours =
$15 + $15 = $30, which is the correct answer.

In short:
The answer is $15
~ Hope this helps you!

7 0

3 years ago

Lucy earns $15.75 per hour. Last week she worked 25 hours. What is her gross pay:

Bumek [7]

Lucy's gross pay per week is $393.75.

Lance's tax payment amount is $10983.

Lance's net pay is $41,317.

Lance's every paycheck of two will be around $2179 per month.

1) Lucy earns $15.75 per hour.

Last week she worked 25 hours.

Solution:

Lucy's gross pay per week is $15.75 * 25 hours.

Lucy's gross pay per week = 15.75 * 25 = $393.75

2) Lance has a yearly salary of $52,300

He pays 21% as taxes.

Solution:

a) Lance tax pay amount = 21/100*52,300 = $10983

b) Lance's net pay = $52,300 - $10983 = $41,317

c) Per month salary = $52,300/12 = $4358

Each paycheck will be 4358/2 = $2179

To learn more about salary sums, refer

brainly.com/question/64928

#SPJ13

4 0

1 year ago

Keith takes 12 hours to clean the store, and mike takes 10 hours to finish the job. how hong will they take together?

svlad2 [7]

Find the average value
12 hours + 10 hours = 22 hours
22 hours/2 = 11 hours
Together it will take Keith and Mike 11 hours to clean the store.

6 0

4 years ago