Answer:
X = 5
Step-by-step explanation:
I know B is true, but i’m unsure for the other choices.
<h3>
Answer: 24 feet (Choice D)</h3>
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Explanation:
Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.
Focus on triangle BCD.
The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.
We know that he's 14 ft off the ground, which explains why AB = CD = 14.
The goal is to find BC = AD = x.
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Again, keep your focus on triangle BCD.
We'll use the tangent ratio to say
tan(angle) = opposite/adjacent
tan(B) = CD/BC
tan(30.26) = 14/x
x*tan(30.26) = 14
x = 14/tan(30.26)
x = 23.9965714046732
That value is approximate. Make sure your calculator is in degree mode.
That value rounds to 24 feet when rounding to the nearest whole foot.
You can use systems of equations for this one.
We are going to use 'q' as the number of quarters Rafael had,
and 'n' as the number of nickels Rafael had.
You can write the first equation like this:
3.50=0.05n+0.25q
This says that however many 5 cent nickels he had, and however many
25 cent quarters he had, all added up to value $3.50.
Our second equation is this:
q=n+8
This says that Rafael had 8 more nickels that he had quarters.
We can now use substitution to solve our system.
We can rewrite our first equation from:
3.50=0.05n+0.25q
to:
3.50=0.05n+0.25(n+8)
From here, simply solve using PEMDAS.
3.50=0.05n+0.25(n+8) --Distribute 0.25 to the n and the 8
3.50=0.05n+0.25n+2 --Subtract 2 from both sides
1.50=0.05n+0.25n --Combine like terms
1.50=0.30n --Divide both sides by 0.30
5=n --This is how many NICKELS Rafael has.
We now know how many nickels he has, but the question is asking us
how many quarters he has.
Simply substitute our now-known value of n into either of our previous
equations (3.50=0.05n+0.25q or q=n+8) and solve.
We now know that Rafael had 13 quarters.
To check, just substitute our known values for our variables and solve.
If both sides of our equations are equal, then you know that you have
yourself a correct answer.
Happy math-ing :)
First compute the perimeter of the pool:
(21+33)*2=108 foot.
Since the material cover 232 ft^2, then it is sufficient to divide the above number over the length of the border like this:
232/108=2.1
The trip can be 2.1 ft in wide.
