Question 536033
1) For what value or values of x is (check image) undefined ?
x=0

2) If (check image) , express y in terms of x
y=x+1

3) A motorist gets 3 more kilometers per liter when he drives along a highway than when he drives along a city road. Recently he drove 120km on a highway and 180km on a city road and used exactly 23 liters of gasoline. How many kilometers per liter did he get when he drove along the city road ?
let him get x km/l on city road
He gets (x+3)km/l on highway
120/(x+3)+180/x= 23
LCD = x(x+3). Multiply by LCD
120x+180(x+3)=23x(x+3)
120x+180x+540=23x^2+69x
300x+540=23x^2+69x
23x^2-231x-540=0
Find the roots of the equation by quadratic formula						
						
a=23,b=	-231c-540	
						
b^2-4ac=	53361	-	49680			
b^2-4ac=	103041					
{{{sqrt(	103041	)}}}=	321			
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}						
{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}						
x1=(231	+321)/46	
x1=	12					
x2=(	231	-321	) /	46		
x2= 	-1.957					
Ignore negative value						
speed	=	12	mph	on city road
15 on highway		




4) If (check image) , find x given that k = 3/4
x=k/(k-x)
kx-x^2=k
x^2=kx-k
x^2=k(x-1)
x^2=3/4(x-1)
multiply by 4
4x^2=3x-3
4x^2-3x+3=0
a=	4	,b=	-3	c	3
					
b^2-4ac=	9		-48		
b^2-4ac=	-39				
{{{sqrt(	-39	)}}}=	6.244998i
x1= (3+6.244998i)/8	
x1= 0.375 + 0.78062475 i
x2= 0.375 - 0.78062475 i



5) Mang Andok can finish a job in 6 hours while Mang Bok can finish the same job in 8 hours . They decided to work together , but they stop to talk and sometimes they argue . Assume that each man's work rate decreases by the same percent. If they complete the job in 5 hours , what is the percent decrease in the men's work rates?

6) Let a and b be distinct real numbers such that (check image)


7) If a nonzero number n increased by 4 times its reciprocal is equal to a real number constant r what is the sum of all possible values of n ?

Sorry too many questions