Ineed with both of these questions. 1. find the length of side b to two decimal places. 2. find the length of side a to two decimal places.

1) b=14.34 units.

2) a=20.48 units

Step-by-step explanation:

since, the triangle is a right angled triangle so we can use the trignometric identity in order to find the values of a and b.

let the base be denoted by 'B'.

height or perpendicular side of the triangle be denoted by 'P'.

and hypotenuse of the triangle be denoted by 'H'.

then using sine and cosine trignometric identity we have:

and

Here x=35°

and H=25 units , P=b and B=a

Hence

as  

hence, b=14.3394 units.

also

and

Hence a=20.4788 units

In two decimal places we could represent it as:

a=20.48 units

and b=14.34 units.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

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