geno3141

4n√(8m⁵n³)  =  4n√(4m⁴n²)√(2mn)  =  4n(2m²n)√(2mn)  =  8m²n²√(2mn)

2m√(18m³n⁵)  =  2m√(9m²n⁴)√(2mn)  =  2m(3mn²)√(2mn)  =  6m²n²√(2mn)

Combining:  8m²n²√(2mn) - 6m²n²√(2mn)  =  2m²n²√(2mn)

2r² - 28r + 38  =  0

Divide all the terms by 2:

r² - 14r + 19  =  0

Since this can't be factored easily, if you use the quadratic formula:

a = 1     b = -14     c = 19

r  =  [-b ± √(b² - 4·a·c)]/(2·a)   --->   r  =  [- -14 ± √( (-14)² - 4·1·19)]/(2·1)

--->   r  =  [14 ± √( 196 - 76)]/(2)    --->   r  =  [14 ± √(120)]/(2)   --->   r  =  [14 ± √4√(30)]/(2)

--->   r  =  [14 ± 2√(30)]/(2)   --->   r  =  7 ± √(30)

The formula for the surface area of a sphere is :  SA  =  4·π·r²

Since the radius is 14:  SA  =  4·π·(14)²

tan(45)  =  60/x

Multiply both sides by x:

tan(45)·x  =  60

Divide both sides by tan(45):

x  =  60/tan(45)

Attempting to solve this:

5r + 10 - 5r  =  10

Since the 5r terms cancel, we are left with 10 = 10, a statement that is never false.

No matter what number you put into the original equation, the left side will equal the right side.

An infinite number of answer work.

2.5x - 7  =  -2

Add 7 to both sides:

2.5x  =  5

Divide both sides by 2.5

x  =  5/2.5  =  2

5·2^-x  =  5/2^x

Let's calculate how much time it will take the car to cover the next 1500 feet.

It's speed is 25 mi/hr which is 25 x 5280 ft/hr  =  132,000 ft/hr. 

  D = r·t     --->     1500 ft  =  132,000 ft/hr x t

--->   t  =  1500/132,000 hr = 0.011363636... hr  or  0.681818... min  or 40.91 sec.

The peace officer must travel 1500 feet + 834 feet in that same time (which is 2334 feet)

  D = r·t     --->     2334 ft  =  r x 0.011363636 hrs

     --->   rate  =  2334 ft / 0.01136363 hrs   --->   rate  =  205,392 ft/hr

Dividing this by 5280 to get into miles per hour   --->   38.9 mi/hr.

The reciprocal of a/b is b/a.

Since 5 = 5/1, its reciprocal is 1/5.

Each side is a square of the area of one side is 6 cm x 6 cm  =  36 cm².

There are 6 sides, so the total surface are is 6 x 36 cm²  =  216 cm².

1 mm = 0.1 cm.

To find the volume, multiply the total area by the thickness:  216 cm² x 0.1 cm  =  21.6 cm³.

(This won't include any amount that is needed for "wrap-around".)