Express (-3 - i) - (5 + 3i) in the form of a + ib.

Answer:

Step-by-step explanation:

2+2 = 4

▶Add 2 to 2 , you may count it with your fingers.

This are for beginners ✔

Answer:

The answer, my man, is 4.

Explanation:

2+2-2*2/2=2

Or... 2 plus 2 minus 2 times 2 divided by 2 equals 2.

A more complex way of doing this is: 2+2=4

Hopefully, this helps! :D

The question is missing parts. Here is the complete question.

Let M = [tex]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]. Find [tex]c_{1}[/tex] and [tex]c_{2}[/tex] such that [tex]M^{2}+c_{1}M+c_{2}I_{2}=0[/tex], where [tex]I_{2}[/tex] is the identity 2x2 matrix and 0 is the zero matrix of appropriate dimension.

Answer: [tex]c_{1} = \frac{-16}{10}[/tex]

             [tex]c_{2}=\frac{-214}{10}[/tex]

Step-by-step explanation: Identity matrix is a sqaure matrix that has 1's along the main diagonal and 0 everywhere else. So, a 2x2 identity matrix is:

[tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]

[tex]M^{2} = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]

[tex]M^{2}=\left[\begin{array}{cc}31&10\\-2&15\end{array}\right][/tex]

Solving equation:

[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+c_{1}\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right] +c_{2}\left[\begin{array}{cc}1&0\\0&1\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

Multiplying a matrix and a scalar results in all the terms of the matrix multiplied by the scalar. You can only add matrices of the same dimensions.

So, the equation is:

[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+\left[\begin{array}{cc}6c_{1}&5c_{1}\\-1c_{1}&-4c_{1}\end{array}\right] +\left[\begin{array}{cc}c_{2}&0\\0&c_{2}\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]

And the system of equations is:

[tex]6c_{1}+c_{2} = -31\\-4c_{1}+c_{2} = -15[/tex]

There are several methods to solve this system. One of them is to multiply the second equation to -1 and add both equations:

[tex]6c_{1}+c_{2} = -31\\(-1)*-4c_{1}+c_{2} = -15*(-1)[/tex]

[tex]6c_{1}+c_{2} = -31\\4c_{1}-c_{2} = 15[/tex]

[tex]10c_{1} = -16[/tex]

[tex]c_{1} = \frac{-16}{10}[/tex]

With [tex]c_{1}[/tex], substitute in one of the equations and find [tex]c_{2}[/tex]:

[tex]6c_{1}+c_{2}=-31[/tex]

[tex]c_{2}=-31-6(\frac{-16}{10} )[/tex]

[tex]c_{2}=-31+(\frac{96}{10} )[/tex]

[tex]c_{2}=\frac{-310+96}{10}[/tex]

[tex]c_{2}=\frac{-214}{10}[/tex]

For the equation, [tex]c_{1} = \frac{-16}{10}[/tex] and [tex]c_{2}=\frac{-214}{10}[/tex]

Answer:

The correct answer is s = -11.

Step-by-step explanation:

To solve this problem, we must move all of the variable terms to one side of the equation and move all of the constant terms to the other side.  Let's keep the variable terms on the left and move the constants to the right.  Our first step will be to add 18 to both sides of the equation to cancel out the -18 on the left side:

-18 + 18 - 3s = 15 + 18

-3s = 33

Our next and final step will be to divide both sides by -3 to get the variable s completely isolated on the left side of the equation.

-3s/-3 = 33/-3

s = -11

Therefore, the correct answer is s = -11.

Hope this helps!

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Answer: 7

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Absolute value is the distance between that number and zero. To find the absolute value, you basically just take the negative sign away if there is one. So you need to find the absolute value of 4x+6. Since you can't simplify this equation, you just keep it the way it is. The absolute value of 4x+6 is 4x+6.

So now you have 4x + 6 - 1. Since 6 and 1 are both constant variables, you can  directly subtract it. 6-1 equals 5. Now you have 4x-5.

Now you have 4x-5 = -1 = 3x. You should isolate the variables as well as "removing" an equal sign. To bring away the -1, you have to add 1. -1 + 1 equals 0, AKA nothing. But you also have to do it with all the other expressions too...

4x - 5 + 1 = 4x-6

3x+1 = 3x+1

Now the equation is 4x-6 = 3x+1

So now you have to get rid of the 6. To do that, add 6 to each side of the equation.

4x-6+6 = 4x

3x+1+6 = 3x+7

Now the equation is 4x = 3x+7

Did you notice that you have to add 1x to 3x to get 4x?

3x+1x = 4x (AKA the left side of the equation)

Also, you added the 7.

So that means 7 is the 1x.

So x equals 7.

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Answer:

y = -14x - 80

Step-by-step explanation:

jst did it and i got it right

The equation of the line passing through the points (−6,4) and (−5,−10) is y = -14x - 80.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The line through the points (−6,4) and (−5,−10).

(y + 10) = (-10-4)/(-5+6)[x + 5]

y + 10 = -14(x + 5)

y + 10 = -14x - 70

y = -14x - 80

Thus, the equation of the line passing through the points (−6,4) and (−5,−10) is y = -14x - 80.

Learn more about the straight line here:

brainly.com/question/3493733

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Answer:

Step-by-step explanation:

Hello,

[tex](\forall x \in \mathbb{R}) (fog)(x)=f(g(x))=f(2x+2)=h(x)=4x^2+8x+8\\\\=(2x+2)^2-2^2+4(2x+2)\\\\=(2x+2)^2+4(2x+2)-4\\\\\text{So, we conclude by.}\\\\\large \boxed{\sf \bf f(x)=x^2+4x-4}[/tex]

If g(x) = 2x + 2 and h(x) = 4x2 + 8x + 8, then function f is 16x²+48x+40

A relation is a function if it has only One y-value for each x-value.

The given functions are  g(x) = 2x + 2 and h(x) = 4x² + 8x + 8.

fog=h

Now we have to find f(x)

fog=h

f(g(x))=h

f(2x+2)=4x² + 8x + 8.

=4(2x+2)²+8(2x+2)+8

=4(4x²+4+8x)+16x+16+8

=16x²+16+32x+16x+16+8

=16x²+32x+16x+16+16+8

=16x²+48x+40

Hence,  function f is 16x²+48x+40

To learn more on Functions click:

https://brainly.com/question/21145944

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Answer:

[tex]1 \rightarrow E, 2\rightarrow B, 3\rightarrow C, 4\rightarrow D, 5\rightarrow A[/tex]

Step-by-step explanation:

1.     [tex]\frac{d^2y}{dx^2}+25y=0[/tex]

    The characteristic equation for the given differential equation is:

        [tex]r^{2} +25=0[/tex]

    [tex]\Rightarrow r^2=-25[/tex]

    [tex]\Rightarrow r=\pm 5i[/tex]

   Since the roots are complex

Now, the general solution is:

 [tex]y=A\cos 5x+B\sin 5x[/tex]

2.    [tex]\frac{dy}{dx}=\frac {2xy}{x^2}-5y^2[/tex]

     [tex]\Rightarrow \frac{dy}{dx}-\frac 2xy=-5y^2[/tex]

  Divide both sides by [tex]y^{-1}[/tex]

  Let, [tex]v=y^{-1} \Rightarrow \frac{dv}{dx}=-y^{-2}\frac{dy}{dx}[/tex]

    [tex]\Rightarrow -\frac{dv}{dx}-\frac 2xv=-5[/tex]

    [tex]\Rightarrow \frac{dv}{dx}+\frac 2xv=5[/tex]

 Here, [tex]p(x)=\frac 2x\; \text{and}\;\; q(x)=5[/tex]

 I.F. [tex]=e^{\int \frac 2xdx}=x^2[/tex]

 Now, the general solution is:

    [tex]vx^2=\int x^2 5dx=\frac {5x^3}3+c[/tex]

      [tex]\Rightarrow \frac {x^2}y-\frac {5x^3}3=c[/tex]

      [tex]\Rightarrow 3x^2-5x^3y=Cy[/tex]

3.     [tex]\frac{d^2y}{dx^2}+16\frac{dy}{dx}+64y=0[/tex]

   The characteristic equation is:

     [tex]r^2+16r+64=0[/tex]

  [tex]\Rightarrow r^2+8r+8r+64=0[/tex]

  [tex]\Rightarrow r(r+8)+8(r+8)=0[/tex]

  [tex]\Rightarrow (r+8)(r+8)=0[/tex]

  [tex]\Rightarrow r=-8,-8[/tex]

 Since the roots are real and repeated.

 Now, the general solution is:

 [tex]y=Ae^{-8x}+Bxe^{-8x}[/tex]

4.    [tex]\frac {dy}{dx}=10xy[/tex]

   [tex]\Rightarrow \frac {dy}{y}=10xdx[/tex]

 Integrating both sides

     [tex]\int\frac {dy}y=\int 10xdx+\log c[/tex]

   [tex]\Rightarrow \log y=5x^2+\log c[/tex]

   [tex]\Rightarrow y=e^{5x^2}+c[/tex]

5.      [tex]\frac {dy}{dx}+24x^2y=24x^2[/tex]

      Here, [tex]p(x)=24x^2 \; \text{and}\;\; q(x)=24x^2[/tex]

  I.F.[tex]= e^{\int 24x^2dx}=e^{8x^3}[/tex]

  Now, the general solution is:

     [tex]y.e^{8x^3}=\int 24x^2 e^{8x^3}dx=24\int x^2e^{8x^3}dx[/tex]

               Let, [tex]8x^3=t \Rightarrow 24x^2dx=dt\Rightarrow x^2dx=\frac {dt}{24}[/tex]

   [tex]\Rightarrow ye^{8x^3}=\int e^tdt[/tex]

   [tex]\Rightarrow ye^{8x^3}=e^{8x^3}+c[/tex]

   [tex]\Rightarrow y=1+ce^{-8x^3}[/tex]

Answer:

  150 radians

Step-by-step explanation:

Arc length as a function of angle is ...

  s = rθ

Then the angle is ...

  θ = s/r = (1800 cm)/(12 cm) = 150 . . . radians

This is because the given value is closer to 9,000 than it is to 10,000.

The digit in the thousands place is 9. The digit to the right of this is 0, which is not 5 or greater. So we round down to the nearest thousand. So basically everything after the 9 is replaced with 0.

Answer:

-5x + 4y = -11.

Step-by-step explanation:

If it's a circle then it must be x^2 not x.

x^2 + y^2 + 4x - 10y = 12

Using implicit differentiation:

2x + 2y y' + 4 - 10 y' = 0

y'( 2y - 10) = -2x - 4

y' = (-2x - 4)/(2y - 10)

y' = (-x - 2) / (y - 5) = the slope of the tangent.

At  (3, 1),  y' = (-3-2) / (1 - 5)

=  5/4.

So the required equation is

y - y1 = 5/4(x - x1)  where x1 = 3 and y1 = 1.

y - 1 = 5/4(x - 3)

y = 5/4(x - 3) + 1

Multiply through by 4:

4y = 5(x - 3) + 4

4y = 5x - 15 + 4

In standard form the equation is:

-5x + 4y = -11.

Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Rewriting what is given: (0.09)(n)=30

Where n is the unknown number and 0.09 is the numerical form of 9%. Solving for n gives:

n=(30/0.09)=333.333....

27% as a number is 0.27. So 27% of n is:

(0.27)(n)=(0.27)(333.333...)=90

27% of that number is 90.

Answer:

The answer is ( 0.74 ) or ( 74/100 ).

Answer:

Step-by-step explanation:

[tex]-6n - 6(- 8 n + 2)[/tex]

Use -6 to open the bracket

[tex]-6n+48n-12\\42n - 12\\= 6(7n -2)[/tex]

Step-by-step explanation:

y = 18800 (1 − 0.05)ˣ

y = 18800 (0.95)ˣ

y = 18800 (0.95)⁹

y = 11849

Answer:

V/2 - 21 = -15

V/2 - 21 + 21 = -15 + 21

V/2 + 0 = 6

V/2 * 2 = 6 * 2

V = 12

Answer:

8770 feet

Step-by-step explanation:

Add 370 to 8400:

8400 - 370

= 8770 feet

Answer:

Below.

Step-by-step explanation:

3x + 5y = 15

Subtract 3x from both sides:

5y = -3x + 15

Divide through by 5:

y = -3/5 x + 3   <-----------slope-intercept form

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a given line segment can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-9, -5) and (-1, -9)

The midpoint M is

We have the final answer as

Hope this helps you

Answer:

0

Step-by-step explanation:

_7x+4y=5 *(3)

_21x+12y=15

21x_12y=_15

____________

If I am right

I think !that is the answer

Answer:

y = 2x + 7

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

We are only focusing on the line of best fit.

Step 1: Find 2 coordinates

(0, 7) y-intercept

(2, 11) random

Step 2: Find slope m

m = (11 - 7)/(2 - 0)

m = 4/2

m = 2

y = 2x + b

Step 3: Rewrite linear equation

y = 2x + 7

Answer:

y = 2x + 7

Step-by-step explanation:

Answer:

C. less than the whole number

Step-by-step explanation:

Think of the product as 1/2(0.5)×3 ; the answer would equal 1.5, half of 3. Any number less than 1, multiplied by a whole number, always comes out with a product less than the whole numbers. i.e. 1/3(0.3)×9 = 3

1/4(0.25)×8 = 2

1/5(0.20)×5 = 1

(Anyone correct me if I'm wrong.)

Answer: C) less than the whole number

Step-by-step explanation: I tried examples and they are less than the whole number. The first choice is also equal to the fraction but that’s not for most cases.

Answer:

[tex]P = 10 + 2\sqrt{53}[/tex] units

Step-by-step explanation:

Given

Shape: Kite WXYZ

W (-3, 3),  X (2, 3),

Y (4, -4),  Z (-3, -2)

Required

Determine perimeter of the kite

First, we need to determine lengths of sides WX, XY, YZ and ZW using distance formula;

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

For WX:

[tex](x_1, y_1)\ (x_2,y_2) = (-3, 3),\ (2, 3)[/tex]

[tex]WX = \sqrt{(-3 - 2)^2 + (3 - 3)^2}[/tex]

[tex]WX = \sqrt{(-5)^2 + (0)^2}[/tex]

[tex]WX = \sqrt{25}[/tex]

[tex]WX = 5[/tex]

For XY:

[tex](x_1, y_1)\ (x_2,y_2) = (2, 3)\ (4,-4)[/tex]

[tex]XY = \sqrt{(2 - 4)^2 + (3 - (-4))^2}[/tex]

[tex]XY = \sqrt{-2^2 + (3 +4)^2}[/tex]

[tex]XY = \sqrt{-2^2 + 7^2}[/tex]

[tex]XY = \sqrt{4 + 49}[/tex]

[tex]XY = \sqrt{53}[/tex]

For YZ:

[tex](x_1, y_1)\ (x_2,y_2) = (4,-4)\ (-3, -2)[/tex]

[tex]YZ = \sqrt{(4 - (-3))^2 + (-4 - (-2))^2}[/tex]

[tex]YZ = \sqrt{(4 +3)^2 + (-4 +2)^2}[/tex]

[tex]YZ = \sqrt{7^2 + (-2)^2}[/tex]

[tex]YZ = \sqrt{49 + 4}[/tex]

[tex]YZ = \sqrt{53}[/tex]

For ZW:

[tex](x_1, y_1)\ (x_2,y_2) = (-3, -2)\ (-3, 3)[/tex]

[tex]ZW = \sqrt{(-3 - (-3))^2 + (-2 - 3)^2}[/tex]

[tex]ZW = \sqrt{(-3 +3)^2 + (-2 - 3)^2}[/tex]

[tex]ZW = \sqrt{0^2 + (-5)^2}[/tex]

[tex]ZW = \sqrt{0 + 25}[/tex]

[tex]ZW = \sqrt{25}[/tex]

[tex]ZW = 5[/tex]

The Perimeter (P) is as follows:

[tex]P = WX + XY + YZ + ZW[/tex]

[tex]P = 5 + \sqrt{53} + \sqrt{53} + 5[/tex]

[tex]P = 5 + 5 + \sqrt{53} + \sqrt{53}[/tex]

[tex]P = 10 + 2\sqrt{53}[/tex] units

C is the answer.

That is all.

24. 1st one

Step-by-step explanation:

the X cancals out the x leaving the z so it is the 1st one

Answer:

24. [tex]-\frac{3}{2} z[/tex]

25. 6

Step-by-step explanation:

For number 24:

To simplify this down, we can break it up into this:

[tex]\frac{3}{-2} \cdot \frac{x}{x} \cdot \frac{z}{1}[/tex]

3 divided by -2 is [tex]-\frac{3}{2}[/tex], x over x is just 1, and z over 1 is z.

So [tex]-\frac{3}{2} z[/tex].

For number 25:

If we know the value of y and z we can just substitute inside the equation.

[tex]\frac{-18}{-3}[/tex]

A negative divided by a negative is the same as a positive over a positive.

[tex]18\div3=6[/tex]

Hope this helped!

Answer:

15 nickels and 8 dimes

Step-by-step explanation:

Create a system of equations where d is the number of dimes and n is the number of nickels:

0.1d + 0.05n = 1.55

n = d + 7

Solve with substitution by plugging in d + 7 as n:

0.1d + 0.05(d + 7) = 1.55

0.1d + 0.05d + 0.35= 1.55

0.15d + 0.35 = 1.55

0.15d= 1.2

d = 8

Plug in 8 as d to find n:

n = d + 7

n = 8 + 7

n = 15

So, there are 15 nickels and 8 dimes

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{28 \frac{3}{4} }}}}}[/tex]

Step-by-step explanation:

[tex] \sf{63 \frac{1}{4} \div 2 \frac{1}{5} }[/tex]

Convert mixed fraction into improper fraction

⇒[tex] \sf{ \frac{63 \times 4 + 1}{ 4} \div \frac{5 \times 2 + 1}{5} }[/tex]

⇒[tex] \sf{ \frac{252 + 1}{4} \div \frac{10 + 1}{5} }[/tex]

⇒[tex] \sf{ \frac{253}{4} \div \frac{11}{5} }[/tex]

We know that division by fraction is the inverse of multiplication. If any number or fraction is divided by a fraction, we multiply the dividend by the reciprocal of the divisor.

⇒[tex] \sf{ \frac{253}{4} \times \frac{5}{11} }[/tex]

Reduce the numbers with Greatest common factor 11

⇒[tex] \sf{ \frac{23}{4} \times \frac{5}{1} }[/tex]

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator

⇒[tex] \sf{ \frac{23 \times 5}{4 \times 1} }[/tex]

⇒[tex] \sf{ \frac{115}{4} }[/tex]

Convert improper fraction into mixed fraction

⇒[tex] \sf{28 \frac{3}{4} }[/tex]

Hope I helped!

Best regards!

Answer:

3×30=90

3×8=24

90-24=66

66÷4=16.5