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how do you simplify this (3-7k)*-2

\((3-7k)\times (-2)=\color{blue}14k-6\)

or

\(\frac{1}{2}\times(7k-3)\)

  !

Thanks Chris but that page doesn't seem to explain it either.

It just does what you did and says.

This is it!  Like it or lump it!   LOL   

Never mind, maybe I will see the logic after I think about it :)

what is n*4/32, when n is 5?

\(\large\frac{5\times4}{32}=\frac{20}{32}=\frac{5}{8}\)

!

Melody......see a mehod of solving these "complex root"  form equations here :

http://tutorial.math.lamar.edu/Classes/DE/ComplexRoots.aspx

4+|6-2|+8^2/ 4+6*3+4^0=

\(4+|6-2| +\frac{8^2}{4}+6\times3+4^0=43\)

  ! \(Excuse \ me \ please, Melody!\)

4+|6-2|+8^2/ 4+6*3+4^0=

\(4+|6-2|+8^2/ 4+6*3+4^0\\ =4+|4|+64/ 4+6*3+1\\ =4+4+16+18+1\\ =43\)

thank you. 
I'll try putting everything in the eqation underneath the six so it looks more like a numertor/denominator relationship. hopefully that'll solve this situation. you've been a great help.

5 - 3(x + 6) ≤ -1 - 6(x + 3) + 6x    simplify.

5 - 3x - 18 ≤ -1 - 6x -18  + 6x

-13 -3x ≤ - 19     add 13   to both sides

 -3x ≤  -6     divide both sides by. 3, reverse the inequality. sign

x ≥ 2

Here's the graph :   https://www.desmos.com/calculator/ugnmbxdwv2

Hi Chris,

Where did this line come from?  

Let the characteristic equation be  :  r^2   + 1    =  0

7/15 into a decimal is simply dividing 7 by 15.

7 divided by 15 equals about 4.7

A more accurate answer is 4.66666666666...

Great explanation asinus. Trig isn't my cup of tea so l couldn't have done any better myself. :)

Alright. so this can not be te solution?

6/2(1+2)
6/2(3)
3(3)

9

Personally, I know this to be false, Im just having difficulty explaining it to my peers

If i have a triangle in which the only known side is the hypotenuse "c" and i know all of the angle values "\(\alpha,\beta,\gamma\)", how do you get the remaining sides "a and b"?

\(c:sin\gamma= a:sin\alpha=b:sin\beta\)

\(\large a=\frac{c\times sin\ \alpha}{sin\ \gamma}\)

\(\large b=\frac{c\times sin\ \beta}{sin\ \gamma}\)

  !

y'' + y = 0, y(0)=2, y'(0)=1

Let the characteristic equation be  :  r^2   + 1    =  0

The complex roots are i and − i

The general solution to the differential equation is then......:

y.(t)  = c₁cos(t)  + c₂sin(t)

And since  y(0)=2, we have

2 = c₁cos(0)  + c₂sin(0) 

2 = c₁

And   y'(t)  = −2sin((t) + c₂cos((t)

And  y'(0)=1   .....so.....

y'(0)  = −2sin(0) + c₂cos(0)  =  1  .→ c₂ = 1

So....the specific solution is :

y.(t)  = 2cos(t)  + sin(t)

Solve ( d^2 y(x))/( dx^2) + y(x) = 0, such that y(0) = 2 and y'(0) = 1:
Assume a solution will be proportional to e^(λ x) for some constant λ.
Substitute y(x) = e^(λ x) into the differential equation:
( d^2 )/( dx^2)(e^(λ x)) + e^(λ x) = 0
Substitute ( d^2 )/( dx^2)(e^(λ x)) = λ^2 e^(λ x):
λ^2 e^(λ x) + e^(λ x) = 0
Factor out e^(λ x):
(λ^2 + 1) e^(λ x) = 0
Since e^(λ x) !=0 for any finite λ, the zeros must come from the polynomial:
λ^2 + 1 = 0
Solve for λ:
λ = i or λ = -i
The roots λ = ± i give y_1(x) = c_1 e^(i x), y_2(x) = c_2 e^(-i x) as solutions, where c_1 and c_2 are arbitrary constants.
The general solution is the sum of the above solutions:
y(x) = y_1(x) + y_2(x) = c_1 e^(i x) + c_2/e^(i x)
Apply Euler's identity e^(α + i β) = e^α cos(β) + i e^α sin(β):
y(x) = c_1 (cos(x) + i sin(x)) + c_2 (cos(x) - i sin(x))
Regroup terms:
y(x) = (c_1 + c_2) cos(x) + i (c_1 - c_2) sin(x)
Redefine c_1 + c_2 as c_1 and i (c_1 - c_2) as c_2, since these are arbitrary constants:
y(x) = c_1 cos(x) + c_2 sin(x)
Solve for the unknown constants using the initial conditions:
Compute ( dy(x))/( dx):
( dy(x))/( dx) = ( d)/( dx)(c_1 cos(x) + c_2 sin(x))
 = -(c_1 sin(x)) + c_2 cos(x)
Substitute y(0) = 2 into y(x) = c_2 sin(x) + c_1 cos(x):
c_1 = 2
Substitute y'(0) = 1 into ( dy(x))/( dx) = c_2 cos(x) - c_1 sin(x):
c_2 = 1
Solve the system:
c_1 = 2
c_2 = 1
Substitute c_1 = 2 and c_2 = 1 into y(x) = c_2 sin(x) + c_1 cos(x):
Answer: |y(x) = 2 cos(x) + sin(x)

Use any of the three trig functions: sine, cosine or tangent.

$148,500 / 12 =$12,375 This is simple interest for 1 year

$12,375 / $225,000 =0.055 x 100 =5.5% Simple interest on the house.

22.99+12.75+4.50x

35.74+4.50x

Mean [−4° −6°+ 2° −5° 3°] = -10/5 =-2

help i need someone! what is 3 4/3 - 5 2/5? in fraction form

1. A circle has an area of 100pi centimeters squared. what is the diameter?

A_circle =  pi * (diameter/2)^2

100pi =  pi  * (diameter/2)^2      "cancel"  pi

100  = (diameter/2)^2       take the positive root  of both sides

10  = diameter/2    muliply. both sides by. 2

20  = diameter  [in cm ]

2. a circle has an area of 16pi centimeters squared. what is the radius?

A_circle =  pi * (radius)^2

16pi  = pi * (radius)^2    "cancel"  pi

16  = (radius)^2     take the positive root  of both sides

4  = radius  [in cm ]

3. a circle has an area of 256pi centimeters squared. what is the circumference?

256pi  =   pi * (radius)^2

256pi  = pi * (radius)^2    "cancel"  pi

256  = (radius)^2     take the positive root  of both sides

16  = radius  [in cm ]

Circumference  =  2 * pi * radius   =  2 * pi * 16cm   =   32pi   cm