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3.14 * 4/3 * 1728   =  7234.56     [ if this is the volume of a sphere, the answer should be in cubic units ]

3.0702

I was also looking for this answer, but 520 doesn't seem to be the right answer. i did it again and got 530.

If one side =x
the other side=x+7, then we have:
13^2=x^2 + (x+7)^2, solve for x
 
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Solve for x:
169 = x^2+(x+7)^2

169 = x^2+(x+7)^2 is equivalent to x^2+(x+7)^2 = 169:
x^2+(x+7)^2 = 169

Expand out terms of the left hand side:
2 x^2+14 x+49 = 169

Divide both sides by 2:
x^2+7 x+49/2 = 169/2

Subtract 49/2 from both sides:
x^2+7 x = 60

Add 49/4 to both sides:
x^2+7 x+49/4 = 289/4

Write the left hand side as a square:
(x+7/2)^2 = 289/4

Take the square root of both sides:
x+7/2 = 17/2 or x+7/2 = -17/2

Subtract 7/2 from both sides:
x = 5 or x+7/2 = -17/2

Subtract 7/2 from both sides:
Answer: |  x = 5                                    or                            x = -12(discard)
So, the sides are: 5, 12, 13

I was also looking for this answer, but 520 doesn't seem to be the right answer. If anyone has another answer please help. 

The odd numbers can be given by    -1 + 2n           if you want the 100th odd number n= 100    -1 + 2(100) = -1 + 200 = 199

Let the distance travelled by both=d
Let the time travelled by both=t
Then we have:
d=50t + 150, and
d=85t
solve the following system:
{d = 50 t+150 |     (equation 1)
d = 85 t |     (equation 2)
Express the system in standard form:
{d-50 t = 150 |     (equation 1)
d-85 t = 0 |     (equation 2)
Subtract equation 1 from equation 2:
{d-50 t = 150 |     (equation 1)
0 d-35 t = -150 |     (equation 2)
Divide equation 2 by -5:
{d-50 t = 150 |     (equation 1)
0 d+7 t = 30 |     (equation 2)
Divide equation 2 by 7:
{d-50 t = 150 |     (equation 1)
0 d+t = 30/7 |     (equation 2)
Add 50 × (equation 2) to equation 1:
{d+0 t = 2550/7 |     (equation 1)
0 d+t = 30/7 |     (equation 2)
Collect results:
Answer: |  d = 2550/7            and                t=30/7
 

Yes.....adding, subtracting or multiplying two integers always produces an integer.....not so for division, however........ for example,  12 / 5    is not an integer....

.067 * 318.9   = about 21.37 million

Call the time that Tom traveled, x + 3   hrs

Call the time that Bill traveled, x hrs

And  rate  * time = distance traveled.....and when Bill catches Tom, they have traveled the same distance.....so....

50(x + 3)  = 85x   simplify

50x + 150  = 85x     subtract 50x from both sides

150  = 35x         divide both sides by 35

x = 150/35 hs   = 30/7 hrs  = the time Bill traveled

So.....the distance traveled by each when they cross paths =

85(30/7)  = about 364.3 miles

-2(-2b-4)  =

-2 (-2b)  -2(-4)  =

4b + 8

Here's a picture of the given problem and the solution :

We can use the Law of Cosines to find angle QPS....and we have

QS^2  = QP^2 + SP^2  - 2(QS)(QP)cosQPS

9^2  = 5^2 + 8^2  - 2(5)(8)cosQPS

81  = 25 + 64 - 80cosQPS

[ 81  - 25 - 64 ] = -80cosQPS

cosQPS  =  [ -8] / -80

cosQPS  = 1/10      and using the cosine inverse, m< QPS =

arccos [1/10] = QPS = about 84.26°

And we can use this Law again to find RT

Note :  PR  = PQ + QR  = 5 + 11   = 16

And   PT = PS + ST  = 8 + 2 = 10

And angle QPS = angle RPT  ....so we have

RT^2  = PR^2 + PT^2  - 2(16)(10)cosRPT

RT^2  = 16^2 + 10^2 - 2(16)(10)cos(84.26)

RT^2  = 16^2 + 10^2 - (320)*(1/10)

RT^2  = 256 + 100 - 32  = 324

RT  = 18

Since x=t+1      t = x-1     sustitute    y= 3(x-1)+2  = 3x-3+2 = 3x-1     then dy/dx = 3 

I don't think it can be done if you have to move TWO bottles at a time (each move). (unless moving one bottle TWICE counts as moving TWO bottles ONCE)

Look down at the lower left of the calculator screen....there are either of two settings you can select:   Degrees or Radians

4n=3m+1

This must mean that:

n=1

and

m=1

This is due to the two graphs of 4n and 3m+1 being equal at (1,1) if (m,n) now, because n,m are different, for all intents and purposes being synonymous with x,y, then certainly they can be equal at other points on a plane, but this is the first time that they are equal. If you were to try to find a series to explain the relationship between the two you'd say:

For all cases were 4n=3m+1,

m=(4n-1)/3

and

n=(3m+1)/4

You're probably only working with whole numbers, so it would be best to only focus on cases where whole number intersections occur. Take for example if:

n=7

Then

m=9

This is the basic sine graph with an amplitude of 6, a horizontlal shift to the "left" of 30° and a vertical shift "upwards" of 3.....here's the graph :

https://www.desmos.com/calculator/wc09fvfdzz

Another way to look at it:

the basket is  28/40 full of pears.....thus it is  12/40 EMPTY      12/40 (30 oranges) = 9 oranges can still fit in it.

20 = 32 t-16 t^2, solve for t:

20 = 32 t-16 t^2 is equivalent to 32 t-16 t^2 = 20:
32 t-16 t^2 = 20

Divide both sides by -16:
t^2-2 t = -5/4

Add 1 to both sides:
t^2-2 t+1 = -1/4

Write the left hand side as a square:
(t-1)^2 = -1/4

Take the square root of both sides:
t-1 = i/2 or t-1 = -i/2

Add 1 to both sides:
t = 1+i/2 or t-1 = -i/2

Add 1 to both sides:
Answer: |  t = 1+i/2       or       t = 1-i/2

-1 1/9 can be expressed as -10/9  which is the ratio of two whole numbers.  This means it is rational.

.

25% of 70% is 17.5%   

17.5% like sprinkles and chocolate

Since 40% like sprinkles, those who like both are a proportion 17.5/40 of those who like sprinkles

17.5/40 = 0.4375  or ≈ 44% 

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My second line above should, of course, say "Divide through by 4 and rearrange"

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One way is as follows:

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It 3 something