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6 cos^2 x + 5 cos x = -1   add 1 to both sides

6 cos^2 x + 5 cos x  + 1 = 0         factor

(3cosx +1) (2cosx + 1)  = 0

Set each factor to 0

3cosx + 1  =  0                                           2cosx + 1 = 0

3cosx  = -1                                                  2cosx = -1

cosx = -1/3                                                   cosx  = -1/2

arccos (-1/3)  = about109.5° + n360°          arcos (-1/2)  =   120°  + n360°

And at  about     250.5” + n360°                and                     240 °  +  n360°   

Where n is an integer

Here's the graph, Shades :   https://www.desmos.com/calculator/knlolptzrg

FV=$634.87 .  This is the formula you use to calculate this:

FV=PV[1 + R]^N, Where R=Interest rate per period, N=number of periods,  PV=Present value, FV=Future value.
 

500(1 + .04/4)^(6*4)  = $634.87

idk

I think you might want to find this:

sinx  = (200/900)  = (2/9)       using the sine inverse, we have

arcsin (2/9) = about 12.84°

Factor out constants:
  =  20 integral x/(x^2-25) dx
For the integrand x/(x^2-25), substitute u = x^2-25 and  du = 2 x  dx:
  =  10 integral 1/u du
The integral of 1/u is log(u):
  =  10 log(u)+constant
Substitute back for u = x^2-25:
Answer: |  =  10 log(x^2-25)+constant   

square root of 57.6= 7.58

2.63 * 10^1

Yes, I think that is how the answer is supposed to look. Thank you so much!

I'm not certain exactly what you mean: let me try this:

Since  35  =  5 x 7,  log(35)  =  log(5) + log(7);

so  35  =  10^{log(5) + log(7)}.

60 inch string

4 sides of square

Each side is exactly the same length

So that means 60/4 or 15 is the lenght of a side

find area by multiplying side by other side

15*15 = 225

225 square inches

If a 60 inch long string forms a border around a square picture, each side of the picture must be 60 / 4  = 15 inches long.

To find the area of the picture, multiply the length times the width:  15 x 15  =  225 square inches.

The ratio is:  M/R

If this ratio is the original ratio, not reduced, this would be correct:  M + R  =  K;  so  R  =  K - M.

However, if this is a reduced ratio, then we need to find a value x such that  M/R  =  Mx/Rx  and  Mx + Rx  =  K.

Solving this, we get:  Rx  =  K - Mx  and  R  =  (K - Mx) / x.

Simple enough.

Does ln(3) equal ln(1) + ln (2)

No, it does not.

We see blue, because the atmosphere of the Earth scatters the blue light from the sun more than it does for the red light. The scattering causes the blue light particles to cover the sky up more than the red particles. But this changes when sunset and sunrise happens. The angle of which the sunlight hits the atmosphere also affects the scattering. Because the light is cose to a 90 degree angle, the scattering is different at this point than other times.

w(-4 + z)  =  mz + 17

-4w + wz  =  mz + 17                                (using the distributive law)

wz - mz  =  17 + 4w                                  (subtracting mz from both sides; adding 4w to both sides)

(w - m)z  =  17 + 4w                                 (factoring)

z  =  (17 + 4w) / (w - m)                            (dividing both sides by w - m)

log₅(x) + log₅(2x + 3)  =  1

Since logs are added when the original problem was multiplied, going backwards we have:

log₅[ x · (2x + 3) ]  =  1

log₅( 2x² + 3x )  =  1

Writing the log in exponential notation:

2x² + 3x  =  5¹

--->   2x² + 3x  =  5     --->     2x² + 3x - 5  =  0     --->     (2x + 5)(x - 1)  =  0

                                                                         --->     Either  2x + 5  =  0     or     x - 1  = 0

                                                                         --->     Either     x  =  - 5/2     or     x  =  1

Since  log₅(x)  is undefined if x is a negative number, the value  -5/2  must be ignored; thus the answer is  x  =  1

\(A_{rectangle}=40\times20=800\;ft^2\)

sin(200/900 = 0.003878499725