<h3>
Answer: x = 61</h3>
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Explanation:
The angle x and the 29 degree angle combine to form a 90 degree angle. This is because the square maker on the left has that angle at 90 degrees, and all of the angles combine to form 180. So 180-90 = 90 is the left over amount.
Add up x and 29 to get 90
x+29 = 90
Solve for x by subtracting 29 from both sides
x+29-29 = 90-29
x+0 = 61
x = 61
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An alternative is to solve the equation below for x
x+29+90 = 180 ... see note below
x+119 = 180
x+119-119 = 180-119 ... subtract 119 from both sides
x = 61
we get the same answer
note: this equation turns into x+29 = 90 if you subtracted 90 from both sides
Tanα=y/x
y=xtanα, we are told that x=25ft and α=30°
y=25tan30° ft
y≈14.43 ft (to nearest hundredth of a foot)
Since their home is 20 feet from the base of the tree, it poses no risk right now.
<h3>
Answer: p = 0.12*(1.02)^t</h3>
Explanation:
The general exponential growth equation is
p = A*B^t
where t is the number of years that have gone by after 2008, A is the starting amount, B is the growth multiplier, and p is the price t years after 2008
We know that A = 0.12 is the starting price
The value of B is B = 1.02 which is in the form 1+r since 1.02 = 1 + 0.02 = 1+r
The r value is r = 0.02 and it is positive to represent growth. Keep in mind that 2% = 2/100 = 0.02
So we go from
p = A*B^t
to
p = 0.12*(1.02)^t
I really hate these algebra problems pretending to be geometry.
Anyway angles B and D are congruent in a parallelogram. Geometry part done.
4n - 2 = 2n + 32
2n = 34
n = 17
Answer: 17, which is the 3rd choice
