A jewelry company prints a hidden logo watermark. The watermark is a chord that is 0.8 cm from the center of a circular ring that has a r = 3 cm radius. What is the length of the chord to the nearest tenth?

5.8 cm

Step-by-step explanation:

Let's call the length of the chord 'c'.

To find the length of the chord, we can use the Pythagoras' theorem in the triangle ABC as shown in the image attached.

r^2 = (c/2)^2 + 0.8^2

9 = c^2/4 + 0.64

c^2/4 = 8.36

c^2 = 33.44

c = 5.78 cm

Rounding to nearest tenth, we have that the length of the chord is c = 5.8 cm.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,