1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inessss [21]
3 years ago
13

Solve The Complex Number System

0" alt="x^{3}-125=0" align="absmiddle" class="latex-formula">

Show Work Please
Mathematics
1 answer:
Ganezh [65]3 years ago
6 0

\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2)~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-125=0\implies x^3-5^3=0\implies (x-5)(x^2+5x+5^2)=0 \\\\[-0.35em] ~\dotfill\\\\ x-5=0\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula}

\bf \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{+25} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{-5\pm\sqrt{5^2-4(1)(25)}}{2(1)}\implies x=\cfrac{-5\pm\sqrt{25-100}}{2} \\\\\\ x=\cfrac{-5\pm\sqrt{-75}}{2}~~ \begin{cases} 75=&3\cdot 5\cdot 5\\ &3\cdot 5^2 \end{cases}\implies x=\cfrac{-5\pm\sqrt{-3\cdot 5^2}}{2}

\bf x=\cfrac{-5\pm 5\sqrt{-3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1\cdot 3}}{2}\implies x=\cfrac{-5\pm 5\sqrt{-1}\cdot \sqrt{3}}{2} \\\\\\ x=\cfrac{-5\pm 5i\sqrt{3}}{2}\implies \boxed{x= \begin{cases} \frac{-5+ 5i\sqrt{3}}{2}\\\\ \frac{-5-5i\sqrt{3}}{2} \end{cases}}

You might be interested in
What does 100 × 30% equal I'm a bit confused
oksian1 [2.3K]

Answer:

30

Step-by-step explanation:

30% in a calculator is .3

if you multiply 100 by .3 you get 30

also multiplying a number by a percentage is just taking a percentage of that number. so 30% of 100 is 30.

3 0
3 years ago
......:.. ....... ....
Fynjy0 [20]
84 degrees

The triangle is isosceles you know this from the 2 congruent sides marked 5

Thus angle F is 48 degrees

To find angle E-
180 - (48 + 48) = 84
4 0
3 years ago
Read 2 more answers
Joan makes a base salary of $275 per week and a commission of 4% of sales over $1000. If she sells $1250 of merchandise this wee
Lerok [7]

Joan makes $275/week.

In addition to $275, she also makes 4 percent on sales over $1000.

So, 1250 - 1000 = 250.

Then 250(0.04) = 10.

Let t = amount of her paycheck for the week.

t = $275 + $10

t = $285

8 0
3 years ago
1. How do you prove congruence through transformations?
konstantin123 [22]

One can prove congruence through transformation if they have the same shape and size.

The congruency postulates include:

  • SSS - Side-Side-Side
  • SAS - Side-Angle-Side
  • ASA- Angle-Side-Angle
  • AAS - Angle-Angle-Side
  • RHS - Right angle-Hypotenuse-Side

<h3>What is congruence?</h3>

In geometry, it should be noted that two figures are congruent if they have the same shape and size.

In this case, if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

One can prove triangle congruence using congruency postulates by using the SSS theorem( side side side theorem).

It should be noted that the congruence postulate is used to illustrate that the triangles are equal.

Learn more about congruence on:

brainly.com/question/2938476

#SPJ1

4 0
2 years ago
A number cube is rolled 450 times. the number 3 comes up 67 times.a. what is the theoretical probability of rolling a 3? write y
OLga [1]
1- If the other 5 numbers on the cube aren't 3 the probability is 1/6

2-(Sorry I don't speak English well and I didn't understand the question) I think it's refereed to the first sentence, so it's 67/450=1/75
7 0
3 years ago
Other questions:
  • You have $15 to spend on school supplies. after buying 3 erasers, you have $10.50 left. how much did each eraser co
    7·1 answer
  • If a car travels 350 miles in 2.5 hours, how far does it travel in one hour?
    5·1 answer
  • Point I is on line segment H J ‾ HJ . Given H I = 2 x , HI=2x, H J = 4 x , HJ=4x, and I J = 4 x − 10 , IJ=4x−10, determine the n
    5·2 answers
  • Someone please help me <br><br> serious answers only!!!!!!
    12·1 answer
  • Do you write a number divided by zero or zero divided by number
    11·1 answer
  • Margo borrows $100, agreeing to pay it back with 6% annual interest after 6 months. How much interest will she pay.
    14·1 answer
  • List the next four multiples of the fraction 3/10
    5·1 answer
  • Can someone help me!
    6·1 answer
  • Important quiz, help!!!!!
    15·1 answer
  • 4x8 i know the anwser im just tryna see something
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!