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Great job!

I actually solved it by myself, nevermind! :)

Here is my solution:

Let a = The average speed for the trip
Let d = The one-way distance

Next we Write a time equation: time = distance/speed
 

Against time + with time = total time

d/15 + d/10 + 2d/a

Then we multiply by 30a
2a(d) + 3a(d) = 30(2d)
2ad + 3ad = 60d
5ad = 60d
divide both sides by d
5a = 60
a = 60/5
a = 12 mph is the average speed for the trip
 

I wondered the same thing but I tried and it didn't show up...

IDK?

If you give yourself a point does it count?

rhombus is made of 4 right triangles with the same area
so using pythagorean theorem on one of the 4:
the sides of the triangle would be d/2 and (d+4)/2 and hypotenuse 10
(d/2)^2 + ((d+4)/2)^2 = 10^2 (solve for d)
1/4 * d^2 + 1/4 * (d+4)^2 = 100
d^2 + (d+4)^2 = 400 (multiplied both sides by 4)
d^2 + d^2 + 8d + 16 = 400
2 * d^2 + 8d + 16 = 400

d^2 + 4d + 8 = 200 (divided both sides by 2)
d^2 + 4d - 192 = 0 (16*12=192)
(d + 16)(d - 12) = 0 (2 answers use the positive one)
d = 12 inches
so d+4 = 16 inches
now we got measure of both diagonals
Area = 1/2 times the product of the diagonals
Area = 1/2 * 12 * 16
Area = 1/2 * 192
Area = 96 inches^2

Also, you can post anonymously if you are embarrassed (you shouldn't be though)

A rectangular solid, or cuboid, with sides of lengths 2, 10, and 22 is inscribed in a sphere. What is the side length of the cube that can be inscribed in that sphere?

Face diagonal (D_f) of the cuboid's side  10 x  22 is:>     D_f = sqrt(22² + 100²) = 24.16609195

Interior diagonal (D_s) of the cuboid is:>                           D_s = sqrt(D_f² + 2²) = 24.24871131

D_s is the diameter of a sphere and also an interior diagonal of a cube.

The side length of the cube (a) is:>               a = D_s / sqrt(3) = 14    

The volume of the cup is 14.14 innches cube.

ABC =A! + B! + C!

145  = 1!  + 4!  + 5! =1 + 24 + 120 =145

No, the answer is 105+1=106

I rarely check posts when I give points.

Generally I give points for 'effort' not for a correct answer.  

Even if I know the answer is wrong I might give it a point.

I would never intentionally give an incorrect answer but there are a lot of people who cheat here and if they're wary of the answers that are given to them here that is a good thing.

Also, people should have enough knowledge to work through an answer and then reject or accept it.

If they are a wary they can ask for clarification or they can request someone else to take a look.

SO if you think you have given a helpful or worthwhile answer then you can give yourself a point.   

105 mod 7 = 0

So:105 + 1 =106 - the smallest 3-digit integer, because:

106 mod 7 = 1

EDITED. Thank you.

Let tthe top of the clock  =  0°

At 3 PM  the minute hand will be at  this position

And  the hour hand will be at 90°

The minute hand  moves at 6° per minute

The hour hand moves at   .5°  per minute

So  when they overlap  the  distance they are from the top of the clock will be the same..so....using  rate * tme  = distance we have that

6T   = 90 + (.5)T    subtract .5T  from both sides

5.5 T  = 90          divide  both sides by 55

T  ≈  16.36  min after 3 PM

0=abs((30*3) - (5.5*M)), solve for M

M =180 / 11 =16.36363636.....etc. =16 minutes and about 22 seconds after 3 PM

We can use this equation

y  = -16t^2  + V₀sin (A) *t   + H₀

Where  V₀  =  initial velocity

H₀  =  initial height  = 0

A  = the launch angle

t  = time

42 yds  = 126 ft

The time it takes for  the kick to reach the  crossbar can be found as     

126  =  70cos(70°) * t

t  =  126 / [70 cos (50°)]  = 2,8 s

So

To find  the  height  at the end we have

y = -16 (2.8)^2 + (70)sin (50°)*(2.8)

y =  24.87 ft

It clears the bar by 14.87 ft  ≈  15 ft

The area of triangle ABJ =>   A = (3*3)/2 - (3*1)/2 = 3 u²  

OOPS!!!!!....sorry.....9/2  should be 9/4

The guys below  had the correct answer  !!! 

By Vieta, the product  of  the roots  =

6/1  = ab  =  6       (1)

And the sum of  the roots  =

2/1   =  2   = a + b

a + b =  2      square both sides

a^2 + 2ab + b^2  = 4      sub (1) into this

a^2  + 2(6) + b^2  = 4

a^2 + b^2   =  -8

Square both sides again

a^4  + 2(a^2b^2)  + b^4  =  64

a^4  + 2(ab)^2   + b^4    = 64     sub (1)  in

a^4 + 2(6)^2  + b^4  = 64

a^4  + b^4  + 72  = 64

a^4  + b^4   =  -8

noice, thank you sd99Sd99!!

Hi, but the question says...

2 1/4

= 2*4+1 / 4

= 9/4

But you wrote 9/2???

 

We can factor out one of the terms, 2 1/4.

When we factor it out we get...

2 1/4(4+3+2+1)

Adding these together we get

2 1/4(10)

This is equal to

22 1/2

alright, thank you hugomimihu!

thank you cphill! i checked, but that's not right.. hm