Two datasets arranged in descending order are; {8, x, 4,1} and {9, y, 5,2}. If the medians of
the two given datasets are equal, what is the value of (y − x)
2
?

Step-by-step explanation:

A data arranged in descending order is a data arranged from the biggest to the smallest. The medisn of the data sets is the value at the middle of the dataset after rearrangment.

For the dataset {8, x, 4,1}, the median will be x and 4. Since we have two median values, we will take their average as shown

Median(1) = ... 1

Simialrly for dataset {9, y, 5,2}, the median will be y and 5.

Median(2) = ...2

Since the medians of  the two given datasets are equal, we will equate equation 1 and 2 and calculate for y-x as shown;

Therefore y-x = -1

(y-x)² = (-1)²

= 1

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.