This type of problem can be decided by looking at whether the function is positive or negative in the vicinity of the zeros. There are three roots: -12, -6, and 2 at which the function is clearly 0. Look at the four intervals the x axis:
interval x<-12: function is negative (just test using a number <-12, say, -13)
interval (-12,-6): function is positive
interval (-6, 2): function is negative
interval x>2: positive
From the above you deduce that at the roots the function must be crossing the x-axis (as opposed to just touching it) because the function value changes its sign every time.
Let's say the length of the ladder is "d". Since the distance from the bottom of the ladder to the building is 16 feet less than the length, we can write this as d - 16.
The distance from the ground to the top of the ladder is 2 feet less than the length of the ladder, so we can denote this as
d - 2.
The shape made by the ground, ladder, and side of the building is a right triangle, and we just found its legs. We can use the Pythagorean Theorem to solve for "d" and find how far up the side of the building the ladder is:
(d - 16)^2 + (d - 2)^2 = d^2
(d^2 - 32d + 256) + (d^2 - 4d + 4) = d^2
2d^2 - 36d + 260 = d^2
d^2 - 36d + 260 = 0
(d - 26) * (d - 10) = 0
d = 26 or d = 10
The answer d = 10 does not fit in this case because it isn't possible to have 16 feet less of 10 feet; it would be negative!
So, d = 26. The top of the ladder to the ground is 2 less than d, so we do 26 - 2 = 24 feet.
The answer is 24 feet.
Answer:
answers!
for the problem: 36 + 8 = 44 (keep in mind)
Step-by-step explanation:
1st one: 4 × (9 + 2) = 54
9 + 2 = 11
4 x 11 = 44
2nd: 4 x 11 = 44
This equals 180.
1 and 3 are corresponding angles which means they are the same. 1+2=180 therefore 2+3= 180
