Answer: After matching each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion that proves the relationship the matched pairs are as follows:

1 . AB = XY ,BC = YZ and ∠B ≅ ∠Y ⇒ ΔABC ≅ ΔXYZ by SAS criterion.

2 . AB = XY and ∠A ≅ ∠X and ∠B ≅ ∠Y⇒ ΔABC ≅ ΔXYZ by ASA criterion.

3 . ∠A=∠X,∠B=∠Y and ∠C=∠Z⇒ ΔABC and ΔXYZ are not necessarily congruent.[by AAA similarity criteria both triangles are similar but may not congruent ∵ every congruent triangles have equal sides and equal angles]

4 . AB = XY, BC = YZ and CA = ZX ⇒ ΔABC ≅ ΔXYZ by the SSS criterion.

4 0

3 years ago

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If x/0.5 + y/0.2 = 18, where x and y are positive integers, then what is the value of x ?

dem82 [27]

An equation without exponents and two variables, is typically a straight line. All the points on the line with integer coordinates are solutions of the equation. Since x and y have to be positive as well, there aren't that many solutions.

Let's see where the line crosses the x-axis, it is where y=0:

x/0.5 + 0 = 18, so x=9 at the intercept. y=0 there, so this is a point on the line, but not a solution to the question (y was supposed to be positive).

Possible values for x are thus limited to 1,2,3,4,5,6 and 7. You can try them all (ie., solve the equation with them) and see for which x values the y is also positive and integer.

You will find that x=4, y=2 is the only pair that satisfies these conditions.

7 0

2 years ago