A circular mirror is surrounded by a square metal frame. The radius of the mirror is 7x.
The side length of the metal frame is 21x. What is the area of the metal frame?
The area of the frame is square units.

The area of the frame is 287.14x² square units

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the given information,

radius = 7x

Therefore, area of the circular mirror is

3.14 × (7x)² = 153.86x² square units

The formula for determining the area of a square is expressed as

Area = L²

From the information given,

L = 21x

Area of the total square metal frame is

(21x)² = 441x²

Therefore, area of the metal frame is total area of the square - area of the mirror. It becomes

441x² - 153.86x² = 287.14x² square units

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true