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Y_Kistochka [10]

3 years ago

11

What is the midpoint between (−9 − i) and (4 + 5i) on the complex plane

1 answer:

gogolik [260]3 years ago

6 0

Answer:

-2.5 + 2i.

Step-by-step explanation:

That would be (-9 + 4)/2 + (-i + 5i)/2

= -5/2 + 4i/2

= -2.5 + 2i (answer).

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Solve the system of equations below by graphing.

Katen [24]

(0.5, 1.3) is the correct answer

Step-by-step explanation:

Given equations are:

$y = 4x-0.8\ \ \ Eqn1\\2x+y-2.3=0\ \ \ Eqn2$

As we can see that the given equations are linear equations which are graphed as straight lines on graph. The solution of two equations is the point of their intersection on the graph.

We can plot the graph of both equations using any online or desktop graphing tool.

We have used "Desmos" online graphing calculator to plot the graph of two lines (Picture Attached)

We can see from the graph that the lines intersect at: (0.517, 1.267)

Rounding off both coordinates of point of intersection to nearest tenth we get

(0.5, 1.3)

Hence,

(0.5, 1.3) is the correct answer

Keywords: Linear equations, variables

Learn more about linear equations at:

#LearnwithBrainly

8 0

3 years ago

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Hii! i’ll give brainliest pls help

podryga [215]

Answer:

the first answer

Step-by-step explanation:

8 0

3 years ago

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Mr. Kuo’s checking account had a balance of $512.45

Ugo [173]

Answer:

63753.8888

Step-by-step explanation:

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3 years ago

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Someone help! I’m not good at these problems!

Evgen [1.6K]

Answer:

I beliive it is 16, but haven't done this in a bit haha

Step-by-step explanation:

So bisect means to "split in half" aka segment BD is directly in the middle of triangle ABC. This means we can look at the half of the triangle we know (ABD). We see a 16, so therefore x should be 16.

(again, hopefully I am correct)

5 0

3 years ago

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2x^3-x^2-3x=210<br> the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

------------------------------------------------------------------------------------------

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

-------------------------------------------------------------------------

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

-----------------------------------------------------------------------

$9x^{2}$ $-3x$ $-210$

--------------------------------------------------------------------------

$42x$ $-210$

$42x$ $-210$

-------------------------------------------------------------------------

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

$x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}$

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

4 0

2 years ago

Read 2 more answers