Let's first take a look at function G. From the first to second row, the x-value increases by 2, and the y-value increases by 8.
Thus, function G has a rate of change of
, or 4.
In function H, there is a "2" before the "x", which means function H has a rate of change of 2.
Thus, the statement that is true is:
- Function G has a rate of change of 4, and function H has a rate of change of 2
Let me know if you need any clarifications, thanks!
~ Padoru
From the setup of the problem, the "length of the top of the bookcase, measured along the attic ceiling" will be the hypotenuse of a right triangle, the length "AB". We have both the angle between AB and AC and the length of AC (3.24 meters), so we can use trigonometric identities.
The cosine of the 40 degree angle between AB and AC is equivalent to the length of AC divided by the length of AB. Equivalently, we have:

where "h", the hypotenuse, is the length we want. Rearranging the formula to solve for h we have that

which is 4.2295... meters. Converting to centimeters (multiplying by 100) we have that h = 422.95... centimeters, or if we round the value, h = 423 centimeters.
4(4/5) + √(4/5) + 0.2 - 5(4/5)
= 16/5 + (2√5/5) + (1/5) - 4
= (16 + 2√5 + 1 - 20)/5
= (2√5 - 3)/5 or 0.29442719