All Answers 358602 Answers

Here's a few

First one :

AC / BC  = DF  = EF

12 / 18   =  10 / EF

2 / 3   =  10   /  EF      and we can write

3/2  =  EF / 10           multiply both sides by 10

10 (3/2)  = EF  =  15

Second one :

SSS  Similarity Theorem

Third one  :

x / 42  =  6  /36

x / 42   =  1 / 6

6x  =  42

x  =  7 cm

Fourth one :

Proportional

c²

Segment Addition Postulate

Fifth one....1st part

Corresponding Angles Postulate

2nd part

 ΔACE   similar to  Δ BCD

Segment Addition Postulate

Sixth one  :

Definition of Angle Bisector

Angle ADB  congruent to  Angle CDF

Substitution Property

Seventh One :

DB  / BA   =  CE  / AC

6  /  15  =  CE  /  25

2 / 5   =  CE  / 25     multiply through by 25

(2 / 5) (25)  =  CE   =  10

Eighth one :

CB  / CA    =  BD   / AD

7.5 / 4   =  BD   / 3        mutiply through by 3

(3/4) (7.5)   =  BD   =  x  =    5.625

No prob.....

Thank you Cphill

4x +  3  -  9x        rearrange as

4x  -  9x   +  3 

-5x  +  3

These triangles are similar by the  AA congruency postulate

So

AC  / AB  =  PR  / PQ

 [  3x + 6  ]  /  24    =  28  / 32

[ 3x + 6 ] / 24  =    7 / 8      cross-multiply

8 [ 3x + 6 ]  =  24 * 7

24x +  48   =   168      subtract 48 from both sides

24x  =  120         divide both sides by  24

x  =  5

First one :

VY  / VT   =  KY  / KT

VY / 57  =  68 / 129.2         Multiply both sides by 57

VY  =   57 * 68  / 129.2  =   30

So.....

 x =  KY + VY  =  68  +  30  =   98 units

Second one :

Note that   MA  =  MN - AN  =  67.2  - 32   =    35.2

So

MA / MN   =  MB / MP

35.2  /  67.2   =   MB  / 81.9       mutiply both sides by 81.9

81.9 * 35.2 / 67.2  = MB  =  x   =  42.9

Third one :

62 / 99.2   = [ x + 2 ] / 112    cross-multiply

112 * 62   =   99.2  [ x + 2]      simplify

6944  =  99.2x  +  198.4          subtract 198.4 from both sides

6745.6  =    99.2x          divide both sides by 99.2

68  =  x

Last one :

[3x - 20 ]  / 56   =  9 / 72

[ 3x  - 20] / 56    =   1  / 8        cross-multiply

8 [ 3x - 20 ]     =   56

24x -  160   =  56       add 160 to both sides

24x  =  216           divide both sides by 24

x  = 9

(7, 3)     slope  =  4/7

The equation is

y  -  y coordinate of point   =  slope  (x  - x coordinate of point )

y  - 3   =  (4/7) ( x  - 7)

Look at the second one carefully, NSS

To  find the first  translation....we can solve this for x

8x  - 2  = 0

8x  = 2

x  = 2/8   =  1/4  ⇒  means 1/4 units to the right

To find the second translation....... -7   means  7 units down

So.....the vertex  is   (1/4, -7)    translated 1/4 units to the right and 7 units down

Here's the parent graph and the translated graph : 

https://www.desmos.com/calculator/jp0bpqh92i

4 +  7 (.50)  =

4  +  3.50  =

$7.50

First one  :

YP / PX  = YQ / QZ

16 / 5  =   8 / 2.5

Second  one :

For QS  to be parallel to MN....we must have that

QM * NR   =  SN * MR

2 * 5   =  3 * 4        Not parallel

2 * 15  =   6 * 5     Parallel

2 * 12  =  3 * 8      Parallel

Third one  :

The angle bisector sets up the following relationship

YZ   / MY   =  XZ  / MX

7 / 3.5   =  11  /   MX

2  =   11 / MX      rearrange as

MX  = XM  =   11/2   =    5.5

Last one :

Let  WZ    =  x

So.....WY  =  8  - x

And we have the following relationship

WY / XY  = WZ / XZ

[ 8 - x ]  /  6.5   =   x  / 6            cross-multiply

6 [ 8 - x ]   =  6.5x

48  -  6x   =  6.5 x        add 6x to both sides

48  =  12.5 x              divide both sides by 2.5

3.84    =  x   =     WZ

Distributive Property

4x + 15  ≥  -9                                            8x - 6 ≤  34

Subtract 15 from both sidees                   Add 6 to both sides

4x  ≥ -24                                                   8x ≤  40

Divide both sides by  4                             Divide both sides by 8

x ≥  -  6                     and                             x ≤  5

 l 3x  +  2  l  =  2

We have two equations here

3x +  2  =  2                      3x  +  2   =   - 2

  Subtract  2 from both sides

3x   =  0                             3x   =   - 4

Divide  both sides by 3

x  = 0                              x  =   -4/3

f(x)  =  x^2  -2x  +  2

The  domain  is all real numbers

To  find the range  we  need  to plug   -b/ [2a]  into the function where  b  =  -2   and  a  = 1

So....   -b/ [2a] =  2 / [2 * 1 ]  =  2/2  = 1    ,.....and this is the x coordinate of the vertex

So....the y coordinate of the vertex is

f(1)  =  (1)^2  - 2(1)  +  2    =  1

This parabola points upward  so the vertex  is  (1,1)

And  y = 1  is the low point on the function

So.....the range  is  [1, infinity )

The  first answer is correct

The idea is to get y by itself....so.....

-10x + 11y   =  -6           add  10x to both sides

11y   =   10x   -   6        divide both sides by 11

y  =  (10/11)x  -  (6/11)

The slope  is the thing in front of x and the yintercept is the remaining term.....so....

Slope  = (10/11)      y intercept  =  ( - 6/11)       {2nd answer}

Remember, Julius, that

log ( a  * b)   =  log a + log b

So.....

Let a  =  I/I₀       and  Let b   =   2

So

L  =  10 log  [  (2 I / I₀ ) ]   = 

10  [ log [  I / I₀   *  2 ]   ]  =   distribute  the 10  over the above log property

10log (I / I₀)  +  10log (2) =

60   +  3.01  ≈

63 dB

Nth term = First term + [Number of term - 1] x Common difference.
So, the 9th term is:
4/5 = 2/3 + [9 - 1] x D, solve for D
4/5 - 2/3 = 8D
[12 - 10] / 15 = 8D
2/15 = 8D
D = 1/60
5th term = 2/3 + [5 - 1] x 1/60
                  = 2/3 + 4/60
                  =2/3 + 1/15
                  =11 / 15, which is the 5th term of this sequence.

i like all that stuff but you need an account for me to message you

Thanks for the reply! 

But I don't really get it. Why did you just add 10log(2)? Is there some sort of formula? 

Being that he was the first president, he pretty muched helped to shape what the idea of a president is. Instead of being a king like figure, George decided it should stay electoral, as well as other decisions.

120dB is the level you might experience at a rock concert!

You need to double the I value:

L = 10log(2*I/Io) 

L = 10log(I/Io) + 10log(2) → 60 + 3.01 ≈ 63dB

Hi Azsun...

I am seriously wondering why your LaTex is displaying properly when no one elses is ???

How strange...

test

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

I love this acronym Ginger!!      

I named him “Get Smart” for “Genetically Enhanced Turkey for Science, Mathematics, and Research Training”

Ah!!....I read The Jungle many years ago.....the best summary of the book comes from Sinclair himself :   "I aimed for the heart, but apparently, just hit the stomach."

Also...usually these confuse me, so I have to do it like this...

N_t+1   =   2.5N_t

N₇₊₁   =   2.5N₇   =   2.5(16,400 )   =   N₈

N₈₊₁   =   2.5N₈   =   2.5( 2.5(16,400 ) )   =   N₉

N₉₊₁   =   2.5N₉   =   2.5( 2.5( 2.5(16,400 ) ) )   =   N₁₀   =   2.5³ * 16,400   =   256,250