Ahandyman knows from experience that his 29-foot ladder rests in its most stable position when the distance of its base from a wall is 1 foot farther than the height it reaches up the wall. how far up a wall does this ladder reach?

This 29-foot ladder forms a triangle, with the height of the top of the ladder and the distance of the base of the ladder from the wall forming the shorter sides.  According to the Pythagorean Theorem, (base)^2 + (height)^2 = (29 ft)^2.  

But here we're told that (base) = (height) + 1 ft.

Substituting (height) + 1 ft for (base), we get:

(height)^2 + [(height) + (1 ft)]^2 = (29 ft)^2

Expanding  [(height) + (1 ft)]^2, we get:

(height)^2 + (height)^2 + 2(height) + (1 ft)^2 = (29 ft)^2, or

2(height)^2 + 2(height) + 1 ft^2 = 841 ft^2.  This equation has the form

2h^2 + 2h - 1 = 841, or 2h^2 + 2h - 842 = 0.  This is a quadratic equation with a = 2, b = 2 and c = -842.

The discriminant is b^2-4ac, or 4-4(2)(-842) = 4+6736, or 6740, and the sqrt of the discriminant is 82.1 ft.

Thus,

                 -2 plus or minus 82.1 ft

(height) =

                               2(2)

(height) =  [(height) + (1 ft)]^2 = 20.0 ft, or (height) = (-2 - 82.1)/4 = negative #

We must discard the negative root because it does not make sense in this situation.  Thus, the top of the ladder reaches the building 20 ft. above the ground.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

costs the what? what is the cost of the pants?

step-by-step explanation:

if it is $10, then the price is 14.

take 40% of the cost, and then add the cost.

40% of 10 = 4

4+10 = 14.