Answer:
41
Step-by-step explanation:
Given:
Line a is perpendicular to line b
.
Line a passes through the points (1,-8) and (9,-12)
.
Line b passes through the point (-8, -16).
To find:
The equation of b.
Solution:
Line a passes through the points (1,-8) and (9,-12)
. So, slope of line a is
Product of slopes of two perpendicular lines is -1.



Slope of line b is 2.
If a line passing through a point
with slope m, then equation of line is

Line b passing through (-8,-16) with slope 2. So, equation of line b is



Subtract 16 from both sides.

Therefore, the equation of line b is
.
Answer:
(3, 2), (6, 4)
Step-by-step explanation:
Since one end (A) of the segment AB is at the origin, the required points will be 1/3 and 2/3 of the coordinates of B:
(1/3)(9, 6) = (3, 2)
(2/3)(9, 6) = (6, 4)
The answer is: 5,614 square inches.
The explanation is shown below:
1. The gift on the bottom is a rectangular prism. To calculate its surface area, you must apply the following formula:
![SA=2[(l)(w)+(l)(h)+(h)(w)]](https://tex.z-dn.net/?f=SA%3D2%5B%28l%29%28w%29%2B%28l%29%28h%29%2B%28h%29%28w%29%5D)
Where
is the length (20 inches),
is the width (42 inches) and
is the heigth (16 inches).
2. Substitute values:
![SA1=2[(20in)(42in)+(20in)(16in)+(16in)(42in)]=3,664in^{2](https://tex.z-dn.net/?f=SA1%3D2%5B%2820in%29%2842in%29%2B%2820in%29%2816in%29%2B%2816in%29%2842in%29%5D%3D3%2C664in%5E%7B2)
3. The surface area of the other gifts can be calculated with the formula for calculate the surface area of a cube:

Where
is the side.
4. The surface area of the bigger cube is:

5. The surface area of the smaller cube is:

6. The total surface area (the combined surface area of the three gifts) is:
