Question 1133112


1. Factor completely: 

{{{3x^2 - 75 }}}
{{{3x^2 - 3*25 }}}
{{{3(x^2 - 25 )}}}
{{{3(x^2 - 5^2 )}}}
{{{3(x - 5 )(x+5)}}}


2. A car travels for {{{2}}}{{{1/2}}}={{{2.5}}} hours and covers a distance of {{{125}}} miles. What was the car’s average speed? 


{{{distance= speed*time}}}

given:

{{{distance=125mil}}}
{{{time =2.5h}}}

{{{125mil= speed*2.5h}}}

{{{speed=125mil/2.5h}}}

{{{speed=50(mil/h)}}}



3. If {{{f(x) = 2x - 3}}},{{{ g(x) = x^2}}}, and {{{h(x) = 3x}}}, find {{{(g f h )(2)}}}.=> I guess you have product here

{{{ (g f h )(x)=g(x)*f(x) *h(x)}}}

{{{ (g f h )(x)=x^2*(2x - 3) *3x}}}

{{{(g f h )(x)=3x^3*(2x - 3) }}}

{{{(g f h )(x)=6x^4 - 9x^3}}}

if {{{x=2}}}, we have 

{{{(g f h )(2)=6*2^4 - 9*2^3}}}

{{{(g f h )(2)=6*16 - 9*8}}}

{{{(g f h )(2)=96 - 72}}}

{{{(g f h )(2)=24}}}


4. Factor: 

{{{15x^2 + 7x - 36}}} ..........write {{{7x}}} as {{{27x-20x}}}

{{{15x^2 +27x-20x-36}}}.....group

{{{(15x^2 -20x)+(27x-36)}}}

{{{5x(3x -4)+9(3x-4)}}

{{{(3 x - 4) (5 x + 9)}}}


5. Find the zeros of the polynomial function {{{f(x) = 15x^2 + 7x - 36}}}.

=>{{{f(x) =0}}}

{{{0 = 15x^2 + 7x - 36}}}....use already factored form above

{{{ 0=(3 x - 4) (5 x + 9)}}}

solutions:

if {{{0=(3 x - 4) }}}=>{{{3x=4}}} =>{{{ x=4/3}}}

if {{{0= (5 x + 9)}}} =>{{{5x=-9}}} =>{{{ x=-9/5}}}



6. If {{{g(x) = 5x + 6}}}, find {{{g^ -1(x) }}}solved for{{{ y}}}.


{{{g(x) = 5x + 6}}}..........since {{{g(x) =y}}}

{{{y = 5x + 6}}}..........swap {{{x}}} and {{{y}}} variables

{{{x= 5y + 6}}}.........solve for {{{y}}}

{{{x-6= 5y }}}

{{{y=(x-6)/5}}}

{{{y=(1/5)(x-6)}}}

=>{{{g^ -1(x)=(1/5)(x-6)}}}