Which equations have one solution
1 answer:
Answer: C and F
Step-by-step explanation:
Remember that for two equations to have the same solutions they need to have the different slopes and different y intercepts or they could have the same y-intercepts but different slopes.
First we will simply each of the equations
A. reduces to .
Since this have the same slopes and same y-intercept they have infinitely many solutions
B. x +3 + 3x = -3 +4x +6 reduces to 4x + 3 = 4x +3 This also have the same slopes and same y-intercepts which means it also have infinitely many solutions.
C. 2(1/5 + 1/4x) -2x = x -1 reduces to -3/2x +2/5 = x -1 This have different slopes and different y intercepts so they have One solution.
D . 4.3x + 2.5 -2.2x + 2.2 -2.1x = 0 reduces to 4.7 = 0 which means that this equation have no solution because 4.7 does not equal 0.
E. 2(4x +3) + 2x= 5(2x + 3) reduces to 10x + 6 = 10x + 15 which means this also have No solution because they have the same slopes but different y-intercepts.
F. 2/5x + 10 + 3/5x = 2x + 5 reduces to 1x + 10 = 2x + 5 This also have 1 solution because they have different slopes and different y intercepts.
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Answer:
As you can see Rectangle L M NO and Rectangle L'M'N'O' are such that
1. Size of Rectangle L M NO > Size of Rectangle L'M'N'O'
2. Sides of, means length and breadth of Rectangle L M N O is not in proportion to Rectangle L'M'N'O'. i.e
3. Out of four possibilities given :
, Reflection and Rotation is not possible because in all the three cases Pre-image and image are not congruent or similar.
As in,Rectangle LMNO →when length and breadth get reduced by scale of 2 and 0 and Dilation by scale factor of< 1 we get Rectangle L'M'N'O'.Centre of dilation may be other than origin.
So, Stretching of preimage i.e Rectangle L M NO→ means Shrinking has taken place to get image Rectangle L'M'N'O'.As shrinking is not an option.
So, Dilation by a factor less than 1, center of dilation other than origin has taken place.