CPhill

-3(x-5)=2x    simplify

-3x + 15 = 2x   add 3x to both sides

15  = 5x      divide both sides by 5

3 = x

We can use the sine here

sin(22) = h / 205     multiply both sides by 205

205^sin(22) = h = about 76.8 ft

By random guessing, she should get 1 out of 4 answers correct.

So  1/4 of 20   = 5 correct answers.

x^6 + y^6    ..... this is the sum of two cubes

First......take the cube root of both things  = x^2  and y^2   write them in parentheses with a plus between them

Then...in the next set of parentheses, write the square of the first thing above, then write the opposite sign of the one in the first set of parentheses. Then multiply  the two terms in the first set of parentheses together. Finally, write a plus and then the square of the second term in the first set of parentheses.   So we should have this.....

(x ^2  +  y^2) (x^4  - x^2*y^2 + y^4)

Consider this......20 total marbles

7 red  .....7/20 = 35%

7 white

1 blue

5 green

Welcome, aboard.....!!!!

I the cotangent = 0/2,   ......x = 0  and y = 2, therefore, we're at 90 degrees

You can verify this by taking the cotangent inverse of (0/2)

I'm assuming that 20 inches represents the diameter, so 10 inches is the radius

15.5 miles in one hour = 15.5 x 5280 ft  = 81840 ft / 60min = 1364 ft/min

And the bike travels [2 * pi * 10] inches =  (20 * pi) inches  = 62.83 inches in every revolution  = about 5.236 ft in every revolution

So.........1364/5.236 = about 260.5 revolutions per minite = 261 revs (rounded)

 x^2 - 10x+8=0     subtract 8 from both sides

x^2 - 10x  = -8      take 1/2 the coefficient on x ,  (-10),  square it and add it to both sides

So (1/2)* (-10 ) =- 5     and  (-5)^2  = 25

x^2 - -10x + 25  = -8 + 25       simplify the right and factor the left side

(x  -  5)^2  = 17       take the square root of both sides

x - 5  =  ±√17         add 5 to both sides

x = 5 ±√17

And those are the two solutions....