Use what you know about special right triangles to find the missing measures. Show all calculations that lead to your final results. Please show calculations as well.

a) a=22, b=11

b) m=7, n=

Step-by-step explanation:

You should use trigonometry ratios as required and then you should use pythagoras theorem

In a) cosine(30°)= base/hypotenuse,

where 11√3 is the base

"a" is hypotenuse and

"b" is perpendicular

from this you can find the value of perpendicular then you should use pythagoras theorem to find the value of hypotenuse

pythagoras theorem is

base²+perpendicular²= hypotenuse²

Same is applied on (b) right triangle as, sine(45°)=perpendicular/hypotenuse

step-by-step explanation:

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