A circular flower bed is 24 m in diameter and has a circular sidewalk around it 3 m wide. Find the area of the sidewalk in square meters

120.105m^2

Step-by-step explanation:

Given data

Diameter of circular bed=  24+3m = 27m

radius= 27/2= 13.5 m

Diameter of side walk = 12

radius= 24= 12 m

Hence the area of the sidewalk is

Area= area of circular bed- area of side walk

Area=πR^2-πr^2

Area=π(R^2-r^2)

Area=π(13.5^2-12^2)

Area= 3.14(182.25-144)

Area= 3.14(38.25)

Area=120.105m^2

Hence the area of the side walk is 120.105m^2

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

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