3+ x, 9 + 3x, 13 + 4x, is an arithmetic sequence for some real number x.
b. find the 10th term of the sequence.

The 10th term is 19

Step-by-step explanation:

For a sequence to be an arithmetic sequence, then there exist a common difference.

How do we calculate common difference?

Common difference is calculated by subtracting the first term from the second term, subtracting the second term from the third term and so on.

From the sequence given , 3 + x, 9 + 3x, 13 + 4x, .. , calculating common difference implies

(9+3x) – ( 3 +x) = 13 + 4x – ( 9 + 3x)

Expanding, we have

9 + 3x – 3 – x = 13 + 4x – 9 – 3x

⇒9 – 3+3x –x = 13 – 9 +4x – 3x

⇒6 + 2x = 4 + x

Collecting the like terms  , we have

2x – x = 4 – 6

which gives X = -2

Since the value of x is gotten now , we can get what the given sequence looks like by substituting the value of x into each term given, the sequence becomes:

3 + (-2), 9 + 3(-2), 13 + 4(-2) +...

Which gives

1 , 3 ,5, …

We can therefore note that the common difference is 2

check: 3 - 1 = 5 -3 = 2

(b) To calculate the tenth term , we use the general formula for calculating nth term , which is given as

= a + (n-1)d

Where n is the number of terms , a is the first term and d is the common difference,  

Therefore, = 1 + ( 10-1)x2

= 1 + 18

= 19

Therefore the 10th term is 19

∠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.