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Tysm, I honestly thought I would've only gotten 1 right lol

11 - correct

12 - correct

13...if these are similar....we must have that

54 / 60   =  62 / 70

9 / 10  =   31 / 35         not true....so....these are not similar

14  - correct

thank you so much!

thank you so much!

thank you so much!

36 is correct  !!!!

Current population =P(c)

Future population  =F(p)

F(p) = P(c) x [1 - 0.045]^t

F(p) = P(c) x [0.955]^t

7,000 = 8,500 x [0.955]^t     divide both sides by 8,500

0.823529... = 0.955^t           take the log of both sides

t = log(0.823529) / log(0.955)

t = ~ 4.217 years - when the population of the town will be about 7,000.

So, it will be: 2010 + 4.217 =~2014

y = x^2 -3x + 4      (1)

x + y  = 4  ⇒   y  = 4 - x    (2)

Sub (2)  into (1)

4 - x  =  x^2  - 3x + 4       subtract 4 from both sides

-x = x^2 - 3x       add x to both sides

x^2 - 2x  = 0   factor

x( x - 2)  =  0

Set each factor to 0 and solve for x and we get that

x =  0   or x  = 2

When x = 0.....y  =  4 - 0  =    4      ⇒   (0, 4)

When x  =  2.....y  =  4 -  2   =  2  ⇒    (2 , 2)

could it be 36?

Here ya go:

This one is a little difficult, NSS

Remember that   Distance /Rate  = Time

Let's call his rate in still water, R

So.......

[Distance] / [ Rate with current] + Distance / [Rate against current ] = Total Time

22.5 / [R + 6]  + 22.5 / [ R - 6 ]  =  9

Get a common denominator  on the left

[ 22.5(R - 6)  + 22.5 (R + 6 ) ]  / [ (R + 6)(R - 6 ) ]  =  9

[ 22,5R + 22.5R ] /  [ R^2 - 36]  =  9     multiply both sides by [ R^2 - 36 ]

45R  = 9 [R^2 - 36 ]    divide both sides by 9

5R  = R^2  - 36      subtract 5R  from both sides

R^2 - 5R -  36   = 0     factor

(R - 9 ) ( R + 4)  =  0

Setting each factor to 0  and solving for r produces

R  = 9     or R  = -4

But R  is positive

So...R  = 9 mph  = his rate in still water [ on the lake ]

Tysm for your help 

Your third one is correct....!!!

Second one

MLN  = BAC   ....so....

ML/LN  = BA/AC

35 / 45  =  [ -13 + 2x ] / 9

7/9  = [ -13 + 2x] / 9     multiply both sides by 9

7  =  -13 + 2x       add 13 to both sides

20  = 2x    divide both sides by 20

10  = x

If GF is parallel to AB....we have a theorem that says that a segment in a triangle drawn parallel to a base divides the sides proportionally

Specifically :

48 / 84  =  52 / [ 7x + 7]

4/7  =  52/ [7x + 7]     cross-multiply

52 * 7  =  4 [ 7x + 7 ]    simplify

364  =  4[ 7x + 7]       divide both sides by 4

91  =  7x + 7     subtract 7 from both sides

84  =  7x      divide both sides by 7

12  = x

Thank you, sorry for the late reply. I was running an errand. 

Assuming that RST  is similar to MLK

Note that

RS / ST   =  ML / LK     ....so we have that...

[4x + 8 ] / 52  = 55 / 65

[4x + 8 ] / 52  =  11/13     cross-multiply

13 [ 4x + 8 ]  = 52 * 11     simplify

52x + 104  =  572     subtract  104  from both sides

52x  =  468      divide both sides by 52

x  = 9

Second one..if DC is parallel to SR....then triangle CDE  is similar to triangle SRE

So

CE / DE  = SE / RE

65 / 70  =  [9x + 3 ] /42

13/14  = [ 9x + 3] / 42     cross-multiply

42 * 13  = 14(9x + 3 ]  simplify

546  = 126x + 42   subtract 42 from both sides

504  = 126x     divide both sides by 126

4  = x

For the one on the right you should use similar triangles.

The triangles have TWO angles that are equal ...there is 180 degrees in EVERY triangle, so the THIRD angle in each of the triangles is equal too....

C  similar to BCD   (going around the angles of the triangle in the same direction)

you can just use parentheses like this

(x^2+9)       or use the  LaTex function...

\(\sqrt{x^2+9}\)   + 3   = x+4      simplify by subtracting 3 from both sides of the equation

sqrt(x^2+9) = x+1        Now square both sides

x^2 + 9  = (x+1)^2       Now expand the R side

x^2 + 9 = x^2 + 2x +1  Subtract x^2 from both sides

9 = 2x+1 

8=2x

x=4

no it also extends to the +9..I just dont know how to extend it can you tell me?

Is ONLY x^2 under the radical sign?

3 NOT similar

4 Similar PCB

Let's re-arrange the line equations to y=mx+b form for easier work

3x-12y+ 16 = 0   is the same as

y = 1/4 x + 1 1/4        Slope = 1/4    perpindicular slope is -4

14x-13y-52=0  is the same as

y=4/13x-4              y intercept (put x=0 into the equation) = -4

So now we have the slope of our line is -4   and a point  0,-4

y = -4x + b       Sustitute 0, -4 to find b

-4 = -4(0) + b

b = -4

Line then becomes   y = -4x - 4

Here is a graph:

So...they are similar but um idk anymore >.<