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The height is the opposite leg of the right traingle  angle 44  

    the 90 ft is the adjacent leg

tan 44 = opp / adj

tan 44 = height/90

90 tan 44 = height of the kite

The angles are equal

7x+24  =x^2 + 5x

x^2 -2x -24 = 0

(x-6)(x+4) = 0

x = 6

The parallel lines cut by the transversal form consecutive (equal)  angles....so...

x^2 + 4x  =  9x + 24     rearrange  as

x^2  -  5x   -  24    = 0         factor

(x - 8) ( x + 3)   =  0

The first  factor gives us what we need

x  - 8   =  0

x  = 8

Wrong way around answer is $\boxed{8}$ =

These lines are parallel, so once we draw a line through both of them those to angles are the same

9x+24=x^2+4x

x^2-5x-24=0

we see that -8 and 3 are the roots as they add up to -5 and multiply to -24

there fore (x+8)(x-3)=0

however we notice when we plug in negative eight. The second angle gives a negative value, so therefore 3 is the answer

$\boxed{3}$

BAC  +  ABC   = DCB

BAC  +  82   = 138

BAC =  138  - 82     =  56°

BCA   = 180  -  DCB

BCA  = 180 -  138   =   42°

42 degrees

56 degrees

No, this answer was wrong. I've posted the correct one.

Turns out, the previous answer I posted was wrong.

Here's the correct solution :- 

z² = 24 - 32i

Let z = x + iy

⇒ z² = x² + i²y² + 2xiy

         = x² - y² + 2xiy

Now, the real part,

x² - y² = 24                            ...(1)

Imaginary part, 

2xy = -32

xy   = -16

x     = -16/y

From (1)

x² - 256/x² = 24

x⁴ - 256 = 24x²

x⁴ - 24x² - 256 = 0 

Solving this equation, 

x² = -8, 36

⇒x = 6 

   y = -8/3

Thus z = 6 - 8i/3 

         |z| = \({ \sqrt{6^2 + (8/3)^2}}\)

              = 6.57

Hope this helps :)

Question:

Wouldn't it be \(\sqrt40\) or \(2\sqrt10\) ?

Hi Guest!

A

Midpoint is just the average. 

The x coordinates are -2 and 5, so the average is 1.5. 

The y coordinates are 1 and 4, so the average is 2.5. 

So the midpoint is (1.5, 2.5).

B

The perpendicular segment has a negative recipical slope. 

To graph AB, the slope is (4-1)(5--2) = 3/7. 

So the new slope is -7/3. 

y = -7/3x + b

To find b, we can just plug in the points 1.5, 2.5. 

2.5 = -7/3(1.5) + b

2.5 = -3.5 + b

b = 7

y = -7/3x + 7

I hope this helped. :))

=^._.^=

f = 1/(2pi)      usually the f  is  1/(2pi)    so no change there

maximum -3   minumum -7     amplitude = 2  and shifted down 5

flipped   so  - sin or - cos

y intercept -7

soooo   - 2 cos (x)  -5

PQRS is a cyclic quadrilateral.

Since opp. angles are supplementary,

⇒∠P + ∠R = 180

⇒5y + 15 + 15y + 45 = 180

⇒20y + 60 = 180 

⇒20y         = 120

⇒y             = 6

Thus, 

∠P = 45°

∠Q = 111°

∠R = 135°

∠S = 360 - (45 +111+135)                             [Sum of all angles = 360°]

      = 69º

I have no idea. 

But I hope you get it. :)))

=^._.^=

Angle c = 180 - 144 = 36 degrees

x^2 + 3x^2 + 36 = 180 degrees

4x^2 = 144

x^2 = 36

x = 6                   take it from here !  

z = 24 -32i

Thus, 

|z| = \({\sqrt{24^2 + 32^2}}\)

     = \({\sqrt{1600}}\)

     = 40

The small  triangle at  the bottom right  has  a base of  12

It is similar to the large  triangle such  that

(5 x - 1)  / 32   =    12/24   

(5x - 1)  / 32 =  1/2       cross-multiply

2 ( 5x - 1)  =  32

5x  -  1  =  32/2

5x  - 1   =  16

5x  = 17

x  =17/5

And the small triangle at  the  top  is  similar to the large triangle  such  that

(4y -3)   /( 32 - (5x - 1) ) =  24 /32

(4y -3)  / (32  -16)   = 24  / 32

(4y -3) / 16 =  12  / 16

4y  - 3  =  12

4y  =  15

y = 15/4

180 - 48 -105 = 27 degrees  =   YXZ

The answer is 41, and the proof is ridiculously easy when you see it. No cosine rule or trig ratios needed.

You need to step away from the computer and go outside ! 

A  is a dome shaped parabola  with   vertex 5,1      so it has zeroes where it crosses the x-axis

B  this one is a bowl shaped parabola with two zeroes

C  no y = 0 values listed but if we went further to -x values we would find them

D  only dips down as low as y= 6      there are no y = 0 values.....this funtion likely has no zeroes.

Total no. of ways = 8!

                            = 40320

No. of dwarves = 4

No. of elves = 4

Hence, let all dwarves be considered as one object

No. of ways accordingly = 5!

                                       = 120

No. of ways to arrange among themselves = 4!

Thus, required no. of ways = 2880

thank you!

Not good at this counting stuff.....maybe someone else has the correct answer   !!!!

Bottle is a cylinder   and a cone combined

cylinder volume = pi r²  h    = pi 3² 8.5   in³

cone volume = 1/3 pi r² h =    1/3  pi  3²  4   in³        Add these two volumes together for the final answer