A'B' and AB are equal in length because a rotation does change the length of a line segment it only changes it's position on the graph.
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.
Answer: 6.8571 (Round as needed)
Hope this is correct
Step-by-step explanation:
This is a simple ratio problem
Using the similarity statement we can say 14:12, (ab:pq)
That is our ratio.
So we do 14/12 = 8/x, we solve this using algebra to get our answer.
Hope this is correct.
Answer:
y=2x+0
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
The first equation is in slope-intercept form, so you can see that the boundary line has a slope of -2 and goes through the point (x, y) = (0, -4). Since the comparison is "<", the line is dashed and shading is below it.
The second equation is that of a vertical boundary line at x=-3. It is solid, because the comparison includes the "equal" case. Shading is to the right of it, where x values are greater than -3.