2. A packaging box for a

metal rod is 7.5 inches

along a diagonal of the

base. The height of the

box is 18 inches. What

is the length of a

diagonal of the box?

19.5 inches

Step-by-step explanation:

See attachment for the figure, where two diagonals are added with labels.

Given:

length of BC 'b'= 7.5 inches

length of AC 'a'= 18 inches

Required:

length of diagonal= length of BA=?

Also, angle BCA is forming a right angle triangle. So we'll apply the Pythagoras theorem in order to find hypotenuse 'c' i.e the length of BA

c = √a²+b² => √7.5²+18²

c= 19.5

Therefore, the length of a  diagonal of the box is 19.5 inches

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(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180