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
jeyben [28]
3 years ago
6

Find all complex solutions of 3x^2+2x+5=0 . (If there is more than one solution, separate them with commas.)

Mathematics
1 answer:
barxatty [35]3 years ago
8 0

Answer:

\large\boxed{-\dfrac{1}{3}-\dfrac{\sqrt{14}}{3}i,\ -\dfrac{1}{3}+\dfrac{\sqrt{14}}{3}i}

Step-by-step explanation:

Use

ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

3x^2+2x+5=0\\\\a=3,\ b=2,\ c=5\\\\b^2-4ac=2^2-4(3)(5)=4-60=-56\\\\\sqrt{b^2-4ac}=\sqrt{-56}=\sqrt{(4)(-14)}=\sqrt4\cdot\sqrt{-14}=2\sqrt{-14}

Use

i=\sqrt{-1}

\sqrt{-14}=\sqrt{(-1)(14)}=\sqrt{-1}\cdot\sqrt{14}=i\sqrt{14}

Therefore:

x=\dfrac{-2\pm 2i\sqrt{14}}{2(3)}=-\dfrac{2}{6}\pm\dfrac{2i\sqrt{14}}{6}=-\dfrac{1}{3}\pm \dfrac{\sqrt{14}}{3}i

You might be interested in
What is the answer Barbara also works part-time at themepark the radio of the number of hours Barbara works at the park to the m
Angelina_Jolie [31]
1:9.....this is basically saying that for every 1 hr she works, she makes $ 9

5 hrs ..(5 * 9) = 45..... 5:45 or 5 to 45 or 5/45
6 hrs...(6 * 9) = 54......6:54 or 6 to 54 or 6/54
8 hrs...(8 * 9) = 72......8:72 or 8 to 72 or 8/72
7 0
3 years ago
⁠ <br> 23<br> 56<br> − ⁠ <br> 1<br> 8<br><br><br> Write the answer in simplest form.
lidiya [134]

Answer:

Convert to a simplified fraction.

1/169

Step-by-step explanation:

i think this is right im not sure <em>IM SO SORRY IF THIS IS THE WRONG ANSWER</em>

4 0
3 years ago
How do you do this? I can't remember
Hitman42 [59]
14.75 depending on if the model is 8 & the actual is 1 in the 1:8 scale factor because you would just multiply the actual by 8 because it is the scale factor. the answer could also be .23 is the model is 1 & the actual is 8 because you would divide the actual by 8! hope this helps!!
3 0
3 years ago
Read 2 more answers
two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the s
Korvikt [17]

Answer:

37.59 nautical miles

Explanation:

Distance = Speed x Time

The speed of the first ship = 12 knots

Thus, the distance covered after 1.5 hours

\begin{gathered} =12\times1.5 \\ =18\text{ miles} \end{gathered}

The speed of the second ship = 22 knots

Thus, the distance covered after 1.5 hours

\begin{gathered} =22\times1.5 \\ =33\text{ miles} \end{gathered}

The diagram representing the ship's path is drawn and attached below:

The angle at port = 90 degrees.

The triangle is a right triangle.

Using Pythagorean Theorem:

\begin{gathered} c^2=a^2+b^2 \\ c^2=18^2+33^2 \\ c^2=324+1089 \\ c^2=1413 \\ c=\sqrt[]{1413} \\ c=37.59\text{ miles} \end{gathered}

The two ships are 37.59 nautical miles apart after 1.5 hours.

8 0
1 year ago
Plz i need help What is the volume of the rectangular prism? show how you did it
Vesnalui [34]

The formula for volume is V=LWH

So in this example we have 10.4*5*8

So 8*5=40

40*10.4=416

So the volume is 416 cubic mm

Hope that helped

4 0
3 years ago
Other questions:
  • Eric is saving $60 every week to buy a new laptop that costs $480. He has already saved $180.
    5·2 answers
  • Find the difference.... 23/4-12/4
    8·2 answers
  • What does this equation mean? 35= 5 x 7
    11·2 answers
  • What is the value of 5k + m when k = -3 and m = -<br> -9?<br> A. -60<br> B. -30<br> C.-24<br> D. -6
    9·1 answer
  • A club sold $555 worth of
    13·2 answers
  • The formula for the volume of a cylinder is Y = gr). Solve y = grn for h, the height of the cylinder. O A. = O B. has Yr2 OC. h
    12·1 answer
  • Piz help me fast asap thx​
    13·2 answers
  • Find the 12 term of the geometric sequence 2,10,50,
    7·2 answers
  • What is the answer for B
    7·2 answers
  • Big Points for this one. This is my big cousins account, I’m in 5th grade and I need help
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!