Two lines defined by the equations $y = mx + 4$ and $y = 3x + b$, where $m$ and $b$ are constants, intersect at the point $(6, 10)$. What is the value of $b + m$?

-7

Step-by-step explanation:

The two lines intersect at the point (6,10), so this point belongs to both lines. This means that if we use the value of x = 6 in the lines, we will find y = 10

So we can use this point to find the values of b and m:

y = mx + 4

10 = 6m + 4

6m = 6

m = 1

y = 3x + b

10 = 3*6 + b

b = 10 - 18 = -8

So the value of b + m is -8 + 1 = -7

∠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.