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4 years ago

I need help with transformations. A,B,C or D

Mathematics

1 answer:

netineya [11]4 years ago

6 0

Answer:

The answer is B.

Step-by-step explanation:

If you see in the question you can see the formula...

P (x,y) -----> P' (x+2,y-3)

If M (3,4) is given...

3=x and 4=y

so, To transform it

M'= (x+2) = 3+2 = 5

= (y-3) = 4-3 =1

so, M (3,4)------> M' (5,1)

others are done in same process...

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Z^4-5(1+2i)z^2+24-10i=0

mixer [17]

Using the quadratic formula, we solve for $z^2$ .

$z^4 - 5(1+2i) z^2 + 24 - 10i = 0 \implies z^2 = \dfrac{5+10i \pm \sqrt{-171+140i}}2$

Taking square roots on both sides, we end up with

$z = \pm \sqrt{\dfrac{5+10i \pm \sqrt{-171+140i}}2}$

Compute the square roots of -171 + 140i.

$|-171+140i| = \sqrt{(-171)^2 + 140^2} = 221$

$\arg(-171+140i) = \pi - \tan^{-1}\left(\dfrac{140}{171}\right)$

By de Moivre's theorem,

$\sqrt{-171 + 140i} = \sqrt{221} \exp\left(i \left(\dfrac\pi2 - \dfrac12 \tan^{-1}\left(\dfrac{140}{171}\right)\right)\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= \sqrt{221} i \left(\dfrac{14}{\sqrt{221}} + \dfrac5{\sqrt{221}}i\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= 5+14i$

and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find

$t = \tan^{-1}\left(\dfrac{140}{171}\right) \implies \cos(t) = \dfrac{171}{221}$

as well as the fact that

$0$

$\sin\left(\dfrac t2\right) = \sqrt{\dfrac{1-\cos(t)}2} = \dfrac5{\sqrt{221}}$

(whose signs are positive because of the domain of $\frac t2$ ).

This leaves us with

$z = \pm \sqrt{\dfrac{5+10i \pm (5 + 14i)}2} \implies z = \pm \sqrt{5 + 12i} \text{ or } z = \pm \sqrt{-2i}$

Compute the square roots of 5 + 12i.

$|5 + 12i| = \sqrt{5^2 + 12^2} = 13$

$\arg(5+12i) = \tan^{-1}\left(\dfrac{12}5\right)$

By de Moivre,

$\sqrt{5 + 12i} = \sqrt{13} \exp\left(i \dfrac12 \tan^{-1}\left(\dfrac{12}5\right)\right) \\\\ ~~~~~~~~~~~~~= \sqrt{13} \left(\dfrac3{\sqrt{13}} + \dfrac2{\sqrt{13}}i\right) \\\\ ~~~~~~~~~~~~~= 3+2i$

and its negative, -3 - 2i. We use similar reasoning as before:

$t = \tan^{-1}\left(\dfrac{12}5\right) \implies \cos(t) = \dfrac5{13}$

$1 < \tan(t) < \infty \implies \dfrac\pi4 < t < \dfrac\pi2 \implies \dfrac\pi8 < \dfrac t2 < \dfrac\pi4$

$\cos\left(\dfrac t2\right) = \dfrac3{\sqrt{13}}$

$\sin\left(\dfrac t2\right) = \dfrac2{\sqrt{13}}$

Lastly, compute the roots of -2i.

$|-2i| = 2$

$\arg(-2i) = -\dfrac\pi2$

$\implies \sqrt{-2i} = \sqrt2 \, \exp\left(-i\dfrac\pi4\right) = \sqrt2 \left(\dfrac1{\sqrt2} - \dfrac1{\sqrt2}i\right) = 1 - i$

as well as -1 + i.

So our simplified solutions to the quartic are

$\boxed{z = 3+2i} \text{ or } \boxed{z = -3-2i} \text{ or } \boxed{z = 1-i} \text{ or } \boxed{z = -1+i}$

3 0

1 year ago

5. Mr. Martinez is getting a rug for his den and wants to make sure it will fit.He knows the area of the den is 547.35 square fe

evablogger [386]

No.

If the Den is 547.35 Square feet, and one side length is 26.7, you divide the Area by one side length to get the other. 547.35/26.7= 20.5

20.5 is less than <span>23.5. Therefore the rug will not fit.</span>

8 0

4 years ago

CORRECT ANSWERS ONLY PLES ASAP!!!!! It costs $2 to spin the spinner shown below. If you land on an even number, you win $8. If y

Delvig [45]

Step-by-step explanation:

2 is an even number so if everytime u land on an even number u win $8 so we do this (8-2=6)

3 0

3 years ago

Read 2 more answers

PLEASE HELP

Svetradugi [14.3K]

Answer:

= 2x²( 2x+ 1) + 2x

= 2x (2x² + x + 1)

Step-by-step explanation:

Given in the question two functions,

f ( x ) = 9x³ + 2x² − 5x + 4

g ( x ) = 5x³ − 7 x + 4

To find,

f ( x ) − g ( x )

Substitute each functions

= 9x³ + 2x² − 5x + 4 - ( 5x³ − 7 x + 4 )

Remove parentheses

= 9x³ + 2x² − 5x + 4 - 5x³ + 7 x - 4

Combine like terms and add them up

= 4x³ + 2x² + 2x

Factorise

= 2x²( 2x+ 1) + 2x

= 2x (2x² + x + 1)

So the final answer in factored form is 2x²( 2x+ 1) + 2x or 2x (2x² + x + 1)

This can't be further factorise because answer will be in complex numbers

8 0

3 years ago

Which of the following pairs of triangles can be proven similar through SAS similarity?

vovikov84 [41]

Answer:

Step-by-step explanation; there i onlee one angl n 2 num nums

3 0

3 years ago