Question 1125864
1. Rearrange the following formula to make {{{y}}} the subject of the equation.

a. 
{{{d=7y-4}}}
{{{d+4=7y}}}
{{{y=(d+4)/7}}}

b.  

{{{k=-3y+5+6y}}}
{{{k=5+3y}}}
{{{k-5=3y}}}
{{{y=(k-5)/3}}}

c.

{{{t=-8(y-1)^2}}}
{{{t/(-8)=(y-1)^2}}}
{{{-t/8=(y-1)^2}}}
{{{-sqrt(t/8)=sqrt((y-1)^2)}}}
{{{-sqrt(t)/sqrt(2^2*2)=y-1}}}
{{{-sqrt(t)/2sqrt(2)=y-1}}}
{{{y=1-sqrt(t)/2sqrt(2)}}}
{{{y=1-(sqrt(t)sqrt(2))/(2sqrt(2)sqrt(2))}}}
{{{y=1-(sqrt(t)sqrt(2))/(2*2)}}}
{{{y=1-(sqrt(t)sqrt(2))/4}}}


2.
{{{3t -6 = -2t + 6}}}

Solve for{{{ t}}}.
{{{3t +2t = 6 + 6}}}
{{{5t = 12}}}
{{{t = 12/5}}}

Prove your solution is correct.
{{{3t -6 = -2t + 6}}}....substitute {{{t}}}
{{{3(12/5) -6 = -2(12/5) + 6}}}
{{{36/5 -(6*5)/5 = -24/5 + (6*5)/5}}}
{{{36/5 -30/5 = -24/5 + 30/5}}}
{{{6/5 =6/5}}}


3. 

The area {{{A}}} of a circle is given by the equation: 
{{{A= pi* r^2}}} where {{{pi}}} is a constant approximately equal to {{{3.14}}} and {{{r }}}is the radius of the circle. 

What is the radius of a circle if it has an area of {{{616cm^2}}}?

{{{616cm^2= pi* r^2}}}

{{{616cm^2/3.14= r^2}}}

{{{r=sqrt(616cm^2/3.14)}}}

{{{r=14.01cm}}}



4. 

Find the gradient and the intercept of the following two lines:

first arrange the line’s equation into slope-intercept form which is {{{y = mx + b}}}
 If {{{y}}} is alone on the left side, then {{{m}}} is the slope of line, and {{{b}}} will just be the y-intercept of that line

a. 
{{{y=2x+4}}}... already in slope-intercept form
so, {{{m=2}}} and y-intercept {{{b=4}}}

b. 
{{{2y-2x=4}}}
{{{2y=2x+4}}}
{{{y=2x/2+4/2}}}
{{{y=x+2}}}
so, {{{m=1}}} and y-intercept {{{b=2}}}

c. Are these two lines parallel? Justify your answer.

these lines are {{{not}}} parallel because parallel lines have {{{same}}} slopes
as we can see one line has a slope {{{m=2}}} and other line {{{m=1}}}

here is the graph:

{{{ graph( 600, 600, -10, 10, -10, 10, 2x+4, x+2) }}}


a. Expand the following {{{3x(y -x^2 - 2x)}}}
 {{{3xy -3x*x^2 - 3x*2x)}}}
{{{3xy -3x^3 - 6x^2)}}}

b. Factorize the following expression: {{{4a3b + 6ab^2 }}}

{{{4a^3*b + 6ab^2=2ab(2a^2+3b) }}}