Let $f(m,1) = f(1,n) = 1$ for $m \geq 1, n \geq 1,$ and let $f(m, n) = f(m-1,n) + f(m, n-1) + f(m-1,n-1)$ for $m > 1$ and $n > 1.$ also, let $$s(k) = \sum_{a+b=k} f(a, b), \text{ for } a \geq 1, b \geq 1.$$note: the summation notation means to sum over all positive integers $a, b$ such that $a+b=k.$ given that $$s(k+2) = ps(k+1) + qs(k) \text{ for all } k \geq 2,$$for some constants $p$ and $q$, find $pq.$

s

step-by-step explanation:

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation:

answer: they are supplementary angles

step-by-step explanation: 161+19=180. supplementary angles equal 180 degrees

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.