Answer:
22 lawns could be mowed as it takes 1.5 hours per lawn.
If they sold six lizards they would earn $71.82
The answer is: {4, 1} .
________________________________________________________
Explanation:
________________________________________
Given the equations:
________________________________________
"12x = 54 −<span> 6y ;
"-17x = -62 </span>− 6y ;
_________________________________________
Multiply the second equation (both sides) by "-1" ;
___________________________________________
-1*{-17x = -62 − 6y} ;
to get:
17x = 62 + 6y ;
___________________________________________
{Note: The reason we do this is that we notice the TWO "-6y" values; and by multiplying one of the entire equations by "-1" ; we can change said equation to an equation with a "(+6y)" value; and the "(+6y)" and the "(-6y)" values cancel out to "zero" ; providing an opportunity to isolate "x"; and to solve for "x".}.
___________________________________________
Now, rewrite the two equations:
___________________________________________
12x = 54 − 6y ;
17x = 62 + 6y ;
___________________________________________
↔ Rewrite; and then add the two together:
6y + 62 = 17x
-6y + 54 = 12x
____________________
0 + 116 = 29x ;
↔ 29x = 116 ;
Divide EACH SIDE of the equation by "29" ; to isolate "x" on one side of the <span>equation ; and</span> to solve for "x" ;
________________________________________________
29x / 29 = 116 / 29 ;
________________________________________________
to get:
________________________________________________
x = 4 .
______________________________________________
Now that we have the value for "x" , which is "4" ; let us plug in "4" for "x" for either of the original two equations, to solve for "y". In fact, let us try substituing "4" for "x" ; for BOTH of the two original equations; to see if the value is correct.
_____________________________________________
Our original two given equations are:
_____________________________________________
"12x = 54 − 6y ;
"-17x = -62 − 6y ;
_____________________________________________
Let us start with the first equation:
________________________
" 12x = 54 − 6y " ;
__________________________________
When "x = 4" ; what does "y" equal ?
Plug in "4" for "x" ; to solve for "y" ;
12(4) = 54 − 6y ;
→ 48 = 54 − 6y ;
Subtract "54" from EACH SIDE of the equation;
→ 48 − 54 = 54 − 6y − 54 ;
to get:
→ -6 = -6y ;
→ Divide EACH side of the equation by "-6" ; to isolate "y" on one side of the <span>equation ; and</span> to solve for "y" ;
→ -6/-6 = -6y / -6 ;
to get:
1 = y ; ↔ y = 1 ; So, we have: x = 4, y = 1 ; or, {4, 1}.
______________________________________________
Let us check to see, if the second (orginal equation) holds true when "x = 4" and "y = 1 " ;
______________________________________________
The second "original equation" given is:
______________________________________________
" -17x = -62 − 6y " ;
______________________________________________
→ -17(4) = ? -62 − 6(1) ?
→ -68 = ? -62 − 6 ?
→ -68 = ? -68 ? Yes!
________________________________________________________
The answer is: {4, 1} .
________________________________________________________
Answer:
Hexagon AGHBGHCGHDGHEGHFGH coincides with hexagon ABCDEF when GH passes through the midpoints of opposite sides; that is, it is a perpendicular bisector of the two sides. HexagonAGHBGHCGHDGHEGHFGH also coincides with hexagon ABCDEF when the line of reflection joins a pair of vertices opposite one another on the hexagon. There are three perpendicular bisectors and three pairs of opposite vertices. In all, there are six lines of reflection that will map the hexagon back onto itself.
Step-by-step explanation:
I mean it would be A and D because I don't know why they are both the same answer. If 10 books were sold yesterday, at LEAST 20 are needed to make the goal.
