From the law of sines, we have:

,
where x and y are the sides opposite to angles X and Y, respectively.
Substituting the known values, we have:

, thus

.
Using a calculator, we can find that arcsin(0.31)=18 degrees, approximately.
We know that sine of (180-18)=162 degrees is also 0.31. But 162 and 51 degrees add up to more than 180 degrees.
Thus, there is only one triangle that can be formed under these conditions.
Answer:
Statement A is correct about Sam's box and whisker plot.
Step-by-step explanation:
We have been given a box plot and we are asked to find out true statement according to the box plot.
Since we know data represented by box plot is divided in four equal parts.
Upon looking at our box plot we can see that our data is symmetric. It's median is 15, which means half the math assignments have less than 15 problems and half of the math assignments have more than 15 problems.
Interquartile range represents 50% values of data and it is the difference between upper quartile and lower quartile. IQR is not affected by outliers.

Upon substituting given values from box plot we get,

From IQR we can conclude that half of the assignments contained 15 problems or fewer.Therefore, option A is the correct choice.
Answer:
ΔDCE by ASA
Step-by-step explanation:
The marks on the diagram show AE ≅ DE. We know vertical angles AEB and DEC are congruent, and we know alternate interior angles BAE and CDE are congruent. The congruent angles we have identified are on either end of the congruent segment, so the ASA theorem applies.
Matching corresponding vertices, we can declare ΔABE ≅ ΔDCE.
Answer:
6.4
Step-by-step explanation:
Answer:
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