geno3141

Replace x with 5 in the function:

If  f(x)  =  4x - 2,  then  f(2)  =  4(2) - 2  =  8 - 2  =  6

The perimeters of similar figures have the same ratio as their corresponding sides (or radii).

Thus, if one figure has a side of 8 cm and a perimeter of 50 cm, then a similar figure that has a side of 10 cm has a perimeter that can be figured this way:  10/8  =  x/50   --->  x  =  62.5 cm.

What's the question?

Starting with  -10x² + 11x  =  -8,  we can get  -10x² + 11x + 8  =  0  that can be represented by the function:

y  =  -10x² + 11x + 8.  This give a graph of a parabola which has an infinite number of pairs of x-values that

have the same y-value (on the same horizontal line) from ground level to its maximum.

I'm not understanding what you mean by the "same horizontal plane". 

The general integral of  1/x  is  ln|x|  because ln() must contain a positive value.

If we know that x is positive, we don't need the absolute value bars.

∫[ x/(2 + x) ] dx

Let  u  =  2 + x   --->  x  =  u - 2         and        du  =  dx

∫[ x/(2 + x) ] dx   --->   ∫[ (u - 2)/u ] du   --->   ∫[ u/u - 2/u ]du   --->   ∫1 du  -  2∫1/u du

   --->   u  - 2 ln|u| + C   --->   2 + x - 2 ln| 2 + x | + C

Since  log(G)  =  365.8532 / 200     --->   log(G)  =  1.829266

To find G: use the antilog (which means raise to the power of 10):  G  =  10^1.829266

--->  G  =  67.5  (approx)

2log(x - 3)  =  1 + log(x) + log(2) - log(5)

log(x - 3)² - log(x) - log(2) + log(5)  =  1    (multiplier goes inside as an exponent)

log[ 5(x - 3)² / (2x) ]  =  1                         (subtraction --->   division; addition   --->  multiplication)

5(x - 3)² / (2x) = 10                                  (raise both sides as exponents upon 10)

(x - 3)² / (2x)  =  2                                   (divide by 5)

(x - 3)²  = 4x                                           (multiply by 2x)

x² - 6x + 9  =  4x                                     (multiply out)

x² - 10x + 9  =  0

(x - 9)(x - 1)  =  0

x  =  9   <---- answer                 x = 1   <--- won't check

x² + 2x - 24  =  -24

Add 24 to both sides:   x² + 2x  =  0

Factor:                       x(x + 2)  =  0

Set each factor equal to zero:     x  =  0         or        x + 2  =  0   --->   x  =  -2

The shortest distance from where to where?

The shortest distance from home plate to second base:

--- From home plate to first base to second base and back to home plate forms a right triangle with the right          angle at first base. The distance from home to second is the hypotenuse, so use the Pythagorean Theorem:

     c²  =  a² + b²   --->  c²  =  90² + 90²   --->   c²  =  8100 + 8100   --->   c  =  √16200

          --->   c  ≈  127.3.