JonathanB

acos(0.106) = 83.915216113012

cos25 = x / 1,027.483

1,027.483*cos25 = x

1027.483*cos(25) = 931.215843948137871

x= 931.215843948137871

To factor this polynomial you must first be comfortable with the idea of the difference or squares. 

Eg.   a^2 - b^2 =  (a+b) (a-b)

*This will help you solve the problem*

Now for the problem:

\(16x^4 - 81\)

\((4x^2)^2 - 9^2\)

\(a^2 - b^2 = (a+b)(a-b)\)

Set: a to \(4x^2 \)

       b to \(9\)

\((4x^2 + 9) (4x^2-9) \)

Notice that the term on the right side is another difference of squares hence you can factor it even more. The term on the left side can not be factored because it is a sum of squares.

For the term on the right set  a to 2x and b to 3

\((4x^2 + 9) (4x^2-9)\)

\((4x^2 + 9) (2x+3)(2x-3)\)

This is your final answer: \((4x^2 + 9) (2x+3)(2x-3)\)

sin A = 0.42 

A = arcsin 0.42

arcsin(0.42) = 24.834587489702

A = 24.8 degrees

Assuming you want me to solve for z

3/4 + z = 4/5    we want to isolate z

3/4 +z - 3/4 = 4/5 - 3/4  subtract 3/4 from both sides to get z by itself

z = 4/5 - 3/4  simplify

z = 16/20 - 15/20  find the lowest common denominator between the two fractions so that you can subtract the two fractions

z = 1/20 

Source: http://www.coolmath.com/algebra/12-2x2-systems-of-equations/03-solving-by-elimination-addition-01

t = 77 + 3h 

t = 92  + 2h 

the point of elimination is to eliminate one of the variables in the system of equations.

Lets eliminate t 

    t = 77 + 3h 

- 1(t = 92 + 2h)     multiply by -1

    t= 77 + 3h        now add the two equations

+ -t= -92 - 2h

    0 = -15 +h

h = 15

Now plug in 15 for h in order to solve for t. 

t = 77 + 3 (15) = 77 + 45 = 122    

So then now we know    t =122 and h =15

No Problem

*Parallel lines have the same slope*

Begin by making y a function of x

7y + 2x -10 = 0

7y + 2x= 10

7y=10 -2x

y= (10/7) - 2/7 x

knowing that the equation of a line is y = mx + b where m is the slope and b is the y intercept  you can rewrite the equation in this format.

y = - (2/7) x + (10/7)

The slope is -2/7

Using point-slope form  we can make a line parallel to the equation:

y-y1 = m (x - x1)

y - 2 = -2/7 ( x- 2)

As you can see these two lines are now parallel.

Could you help go through the problem?