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x^2 - y^2   =  14

(x + y)  ( x - y)  =  14

Factors of 14   =  1,2,7,14

So

7 * 2    =   14

14  *  1   =  14

No pair  of   integers   x, y   will satisfy this  because no two  positive integers sum is 7 and difference is 2

Ditto for   14  and 1

x^2  +  ax  +  25

Reverse the steps  in completing the square

Take the  square root of 25  = 5,  -5

Double these   = 10 ,  -10   =     a

The  amount of the first salt concentration   =  x /10    where x is in grams

Final  salt concentration (per gram)  in Tube A  after  mixing =   x / (10 + 10)  = x /20

So....the amt  poured into   B *  concentration per gram  =  10 grams *  (x/20)  =      x/2  grams

So....the  final concentration  in   B   is    (x/2)  /  (10 +20)  =   =   x/60

And   the amout  poured into C * concentration  =  10 ( x/60)  =  x/6   grams

So....the final concentration in C  is    (  x/6) / (10  + 30)  =  x/ 240

x/240  = .005

x = 240 * .005  =  1.2 

So....the first  salt concentration   = 1.2  / 10     =   12% 

t = tom now

t-5     5 years ago

t+2    in two years

t+2 = 2(t-5)

t + 2 = 2t -10

t = 12 y/o

3/8    +  2/10   =

3/8  +  1/5     ......here's an easy way once we have reduced both fractions to lowest  terms

[  multiply  each demoninator by the other  fraction's numerator  and sum these products  ]  / [ multiply the denominators]   =

[ 8 * 1  +  5 * 3   ]   / [   8 * 5 ]  =

[8  + 15  ]  / 40  =  

23 / 40

I will give this a try:

His gas tank was 1/4 full when he filled up for a cost of $45

Had the tank been completely empty, it would have cost him: 1/0.75 * 45 =$60

When he arrived at his destination, he still  had 1 / 16 of his gasoline left, which means his car consumed: 15 / 16 of his gasoline.

15/16 * $60 =$56.25 the cost of gasoline that his car consumed.

So: 270 / $56.25 =4.8 miles/dollar, or that is how far he drove per dollar.

Fractional representation  of a repeating  decimal   =

[ number written without the decimal  - non-repeating part  ]

_______________________________________________________________________________

[ same  no. of  9s  as digits in repeating part   same number of  0s as digits in non-repeating part ]  

Fractional representation of first repeating decimal      =     [  48 - 4 ]   /  90  =  44/90 =  22/45

Fractional representation of second decimal  =   [ 37   - 0 ] / 99   = 37/99

So ....   22/45  +  37/99  =     [  22 * 99   +   37*45  ]  /  [ 45 * 99  ]   =  427/495

Call the side of the square , S

The area of triangle BDE =  (1/2)DE * height=  (1/2)(1) (S)  = S/2

Call the intersection of AC and BD =  F

Call the intersection of BE  and AC  = G

Angle BFG  =90      BF = S/sqrt (2)

Triangle BFG is right  and we have that

(1/2) BF * FG  =1

(1/2) S/sqrt (2) * FG  =1

S/sqrt(8)  *FG  =1

FG =  Sqrt (8)/ S

Area of triangle DFC =  (1/2)S  * height   =  (1/2)S (S/2)  =  S^2/4

CG =   S/sqrt (2)  - FG    =

S/sqrt (2)  - sqrt(8) / S  =

[S^2  - sqrt (2)sqrt (8)]  / [Ssqrt (2)] =

[S^2 - 4] / [ Ssqrt (2)]

And angle GCE  = 45....sin GCE = 1/sqrt (2)

CE = S - 1

So....the area of triangle  GCE  = (1/2) CG * CE sin  GCE  =

(1/2) [ S^2 - 4 ]  / [  S sqrt (2) ]  * (S - 1) (1/sqrt (2))  =

(S-1)(S^2-4)/ [ 4S]

So  

Area of  BDE   -  (  white area  of BDE  )   = 1

Area of BDE  - ( area of DFC   - area of CGE )   =   1

S/2  - ( S^2/4   -  (S-1)(S^2 - 4) / [4S]  )     = 1

Simplifying this we get

S +  4/S  = 8      multiply through by S

S^2  + 4  = 8S     rearrange

S^2  - 8S  =  -4      complete the square on S

S^2 -8S + 16  = -4 + 16

(S - 4)^2 =  12   take the positive root

S - 4 = sqrt (12)

S = 4 + sqrt (12)

S = 4 + 2sqrt (3)

S = 2 ( 2 + sqrt (3))   ≈  7.464  =   x

Brent works 9 to 5 - 1 hour for lunch =7 hours

Garth works 9 to 4 - 1 hour for lunch = 6 hours

1/7  +  1/6 == 1 /J [1 Job], solve for J

J =3.230769......hours =3 hours + 13 minutes + 51 seconds + [1 hour for lunch].

So: 9 am +  4 hours =1:00 pm + ~14 minutes =~1:14 pm - when both working together will go home !!

You must consider the probability that drawing BB, BWB, WWB, or WWBB.  This gives you a probability of 2/9 + 12/81 + 25/81 + 3/81 = 58/81.

so basically, you are asking: 5/16 x 8/15 (once it is simplified and all, sry I couldn't give you a more detailed answer.)

So we multiply 8 and 5 to get 40 and 16 and 15 to get 240 and now it is 40/240.

40/240 needs to be turned into into a decimal too, and we can multiply 240 with 5 to get 1000 as our "power of ten".

At the same time, 40 needs to be multiplied with 5 as well, so we get 200/1000, which in decimal is 0.200.

We then simplify it to 0.2 and that is the answer!!!

Oh yeah and could you please put that in a decimal? thanks!

we start by finding the lcm of 10 and 4, which is 20.

so we multiply 3 by 2 and get 6.

Then, we multiply 1 with 5 and get 5.

Lastly, we add 6 and 5 to get 11/20 so 11/20 is the answer

The triangle is an isosceles triangle. The height is 6 with the altitude bisecting the base. The base is x while the sides of the triangle are unknown. The angles of the triangle on the base are both 60 degrees. I am supposed to use the Pythagorean theorem to find x the base of the triangle.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

h = 6         ∠θ = 60º        x = ?

(x / 2)² = (h / sin∠θ)² - h²

x = 6.92820323  or   x = 4√3 

\(\frac{4}{5}+\frac{3}{4}\)

\(5*4=20\)

\(4*4=16\)

\(3*5=15\)

\(\frac{16}{20}+\frac{15}{20}=\frac{31}{20}=1.55\)

-hihihi

😎😎😎

\(m=\frac{0-(-3)}{5-4}\)

\(m=3\)

\(y-(-3)=3(x-4)\)

\(y+3)=3(x-4)\)

So D

-hihihi

😎😎😎

Drawing a perpendicular  from the  top right  vetex of the  octagon  to the side of the  square  forms a 45-45-90  right triangle

The hypotenuse  =   1/2  the side of the octagon  = 1

The  legs  are   sqrt (2)   / 2

So....1/4 of the shaded area  forms a trapezoid with   one  base of 2    one base of 2 + 2(sqrt 2) / 2  = 2 + sqrt (2)

and a height of  sqrt (2) / 2

So....the area of one of these trapezoids  is    (1/2)  height ( sum of bases)  =

(1/2)  sqrt (2)/2   *  ( 2 + 2 + 2 sqrt (2) )   =

(1/4) sqrt (2)  * ( 4 + 2 sqrt (2) )

So....the total red area  =  4 times this  = 

sqrt (2)  ( 4 + 2sqrt (2) )  =

4sqrt (2)  + 4  =

4 ( 1 + sqrt (2) )  ≈   9.657  units^2

3 #   *  16 oz/#   ÷ 10 chops =   4.8 oz/chop

.1833333333333 = 11/60   just using the web2 calculator

.183,,,, = x

100x = 18 . 3333333

1000x = 183.33333

1000x - 100x = 900x = 183.3333 ... - 18.3333... = 165

900x = 165

• x = 165/900 = 11/60

3/4 ton *  2000 pounds/ton = 1500 pounds