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THANK YOU

See the following : 

Let A = (0, 0)

B= (9, 0)

C = (9, 12)

D = (5, 12)

We already know  AB , BC and DC

So  we just  need to find the distance between A  and D

Using the distance formula we have

AD = sqrt  [ ( 5 - 0)^2  + (12 - 0)^2 ] =  sqrt [ 25 + 144]   =sqrt (169)   = 13

So  the perimeter =   9  + 12  + 4 + 13   =   38 units 

the ratio of the lengths of strings that play the notes f and g is 9 to 9. If a string 40 centimeters long plays a g, what is the lenght of the string that plays an F?

Ratio  9 to 9 is the same as 1 to 1. According to your question, both strings have the same lengths. But the thicknesses are not the same. 

2. A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if:the length of the hypotenuse is 24 cm, and r=4 cm;

See the following image :

Let

AE = 4

EC = a

CG = a

BG = b

BF = b

FA = 4

So  the sides are

a + b  = 24

b + 4 

4 + a      

And

a + b =  24    →   b = 24  - a

b + 4   →    28 - a

4 + a

Using the Pythagorean Theorem :

(4 + a)^2  + ( 28 - a)^2  =  24^2

Solving this for a produces

a =  4 ( 3 + sqrt (2) )   =  12  + 4sqrt (2)

4 + a =  16 + 4sqt (2)

b = 24 - a  =  24 - (12 + 4 sqrt (2) )  =  12 - 4sqrt (2)

And b + 4 =  16 - 4sqrt (2)

So....the perimeter  = 

24 + (16 - 4sqrt (2)) + (16 + 4sqrt (2) )  =

24  + 32 

56 units

2 hr  *  x m/hr    = 2 x miles

2 .5 hr * (x-10) =  2 x miles

2.5x   - 25    = 2x

.5 x = 25

x = 50                     50 miles hr going    40 coming back        100 miles           (really slow plane)

4. Given triangle ABC, AD is perpendicular to BC such that DC = 2 and BD = 3.  If angle BAC = 45 degrees, then find the area of triangle ABC.

We have something  like this   :

                            A

B          3             D              2                 C

Using the Pythagorean Theorem :

AB^2 =   BD^2 + AD^2

AC^2  =  DC^2 + AD^2

AB^2 =  9  + AD^2

AC^2 =  4  +  AD^2       subtract these

AB^2  - AC^2  =  5

AB^2  = 5 + AC^2

AB =  sqrt  (5 + AC^2)

Using the Law of Cosines

BC^2  = AB^2  + AC^2  - 2 (AB * AC)cos (45°)

Let x =   AC

5^2 = (5 + x^2)  + x^2  -  2* [ sqrt (5 + x^2) * x] (sqrt (2) /2 )

25 = 5 + x^2 + x^2  - sqrt (2)  [ sqrt (5 + x^2) * x ]

Solving this for the positive value of x  gives  x =  2sqrt (10)  =  sqrt (40) =  AC

And AB = sqrt (5 + AC^2) = sqrt (5 + 40) = sqrt (45)

So....the area of triangle  ABC = 

 (1/2) AC * AB  sin (45°) = 

 (1/2) (sqrt (40) * sqrt (45) * [ sqrt (2) / 2 ]  =

(1/4) * sqrt (3600)  =

(1/4) * 60  =

15 units^2

35 a   +   34 b = 163.50    (given)

15 a   +   17 b = 76.50      (given)      multiply this equation by -2

-30 a     - 34 b = -153.00        now add this equation to the first equation t get

5 a                  =   10.50          solve this for a   (apple's price)  then sub this value into one of the equations to find  banana price, b.

Two conditions:

probability of first break that will create two sticks greater than 1

Break must be greater than 1 OR less than 4

Probability that second break will create three sticks greater than 1

second break must be greater than 2 OR less than 3

not sure how am I supposed to calculate for probabilty... its always been my weakness...

17 min   x   2.52 %   = 42.84  %   increase due to charging

61.561 - 42.84  =  18.72 % starting capacity

Two cars start from towns 700 mi apart and travel toward each other. They meet after 7 hr. Find the speed of each car if one travels 10 mph faster than the other.

700 ml / 7hr = 100 mph = 45mph + 55mph

700 / 7 = 100      100 / 2 = 50

1)   50 - 5 = 45 mph

2)   50 + 5 = 55 mph 

See the diagram :

Let  the side of the square =  S

Then the area of the square = S^2

Note that MC, NC = (1/2)S  

And triangle MCN  is a right triangle  with MN, NC  the legs

The  area of this triangle =  (1/2) (Product of the leg lengths)  =  (1/2) [ (1/2S * (1/2) S [ =  (1/8) S^2

So....the  probability  that  the point lies within triangle MCN =

Area of triangle MCN

_________________  = 

Area of square

(1/8) S^2                  

________      =       

    S^2   

      1

_______

      8           

Lol Thanks!

Break that thing into paragraphs. 

White space is your friend.  Text is easier to read, and it's less likely to cause eye strain. 

That long, run-on narrative was, figuratively, a pain for me to read, and it will be for your teacher too. 

edited to add ~

By the way, the correct term for one piece of ammunition is cartridge, not bullet. 

The bullet is the projectile, the part that comes out the business end of the barrel. 

_.

For n values, we multiply them together and then take the  nth root of that result

Ex:    geometric mean of  18  and 8

Multiply together  =  144

Since we have 2 values, we take the square root

sqrt (144)  =12    =   geometric mean of 18 and  8

One more :

Geometric mean of   2, 32, 64

Multiply them together  = 4096

Since we have three values, take the  cube root

cube root (4096)  =   16   = geometric mean of  2, 32 and 64 

Thanks, hugo    !!!!

I knew what you meant by your first answer

[ I like to use one variable whenever possible  ..... ]

$20,000 - (10% * 20,000) =$18,000 amount of loan.

N=60; R=0.02;PV=18000; PMT=PV*R*((1 + R)^N) / ((1 + R)^(N) - 1).

PMT =$517.82 - This is the blended monthly payment.

Effective annual rate =[1 + 0.02]^12 =1.2682 - 1 * 100 =26.82%

First

We need to find which function outputs   -3

2 - x  = -3                                                      2x - x^2  =  -3

x = 5    no good....x  must be ≤ 1                  x^2 - 2x - 3  = 0

                                                                       (x - 3) ( x + 1)  = 0

                                                                        x  = 3  is the  good solution here  because  x > 1

So  f^-1(-3)  = 3

Next

We need to  find out  which function outputs  0

2- x  = 0                                                            2x  -x^2  =  0

2  = x     no good....x must be ≤ 1                     x (2 - x)  = 0

                                                                           x = 2  is the good solution here

So  f^-1 (0)  =  2

Finally  

We need to find out which function  outputs 3

2 - x = 3

x = -1

good..... x is ≤ 1

So  f^-1 (3)  = -1

So

f^-1(-3)  + f^-1(0)   + f^-1(3)  =

3      +    2       -     1   =

     4

Let his daughter's age now  = A

And the father's age now = 3A

In 15 years   ....his daughter's age = A + 15

And the father's age at that time will be   3A + 15

So

(A + 15)  + (3A + 15)  =  86    simplify

4A + 30  = 86     subtract  30 from both sides

4A  = 56   divide both sides by 4

A = 14 =  his daughter's age now

3A  = 3*14 = 42  = her father's age now

Let the daughter's age now =D
Her dad's age now                 =3D

D +15 + 3D + 15 =86, solve for D
D = 14 years - daughter's age now
14 x 3 = 42 years - her dad's age now.

its ok i got a 56 as a 7th grader... ^{_{we dont talk abou that...}}

i probably only improved like 20 this time around....

eh who cares its not like it matters anyways im only in middle school

im a real junior high student and most kids in my school will simply end the argument with 

"your g*y"

"No you"

"Ok boomer"

Or at least my time period