Determine the perimeter and area of the red portion of the 2 dimensional figure below, given the circle diameter of 7 cm and the perimeter of the entire figure is 42 cm. Round if necessary

Perimeter = 20cm ; area = 59.5cm

Step-by-step explanation:

Given the following :

Perimeter of entire figure = 42cm

Diameter of circle (d) = 7cm

Find the perimeter of the circle :

The perimeter (p) of a circle equals :

2πr

Where r = radius of circle

r = diameter /2 = 7/2 = 3.5cm

Therefore,

P = 2 * (22/7) * 3.5

P = 22 cm

Looking at the figure, we only take the semicircle :

Therefore perimeter of each semicircle =

22cm / 2 = 11cm

Therefore, perimeter of the red shaded region =

(42 - 22)cm = 20cm

Area of Circle = πr^2

(22/7) * 3.5^2 = 38.5 cm

Area of each semicircle = 38.5/2 = 19.25cm

Total area of semicircle = (19.25 +19.25) = 38.50cm

To find sides of rectangle :

Perimeter of the rectangle :

width = diameter of circle = 7cm

2(l + w) = 42

2(l + 7) = 42

2l + 14 = 42

2l = 42 - 14

2l = 28

l = 28/2

length (l) = 14cm

Therefore, area of rectangle :

Length * width

14 * 7 = 98cm

Area of red portion:

Area of rectangle - (area of the 2 semicircles)

98cm - 38.50cm

= 59.50cm

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

1. supplementary angles

2. acd and bcd

step-by-step explanation: