Answer: 
12.5
Step-by-step explanation: The triangle ABC and its altitude 
is represented in the figure below.
<u>Altitude</u> is a segment of line that link a vertex and the opposite side, forming a right angle.
So, because of , now we have two similar triangles, which means that ratios of corresponding sides are equal:
(1)
This is always true for a right triangle and a altitude drawn to the hypotenuse.
Triangle BDC is also right triangle. So, we can use Pythagorean theorem to determine the missing side.
(2)
Substituting (2) into (1):
We want to find f, so:
f = 7.5
The length of 
is
The length of the hypotenuse of triangle ABC is 12.5 units.
Answer:
- 12 gallons 84%
- 8 gallons 4%
Step-by-step explanation:
I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.
Here, that means the ratio of 84% solution to 4% solution is ...
48 : 32 = 12 : 8
Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)
Mary must use ...
- 12 gallons of 84% acid solution
- 8 gallons of 4% acid solution
You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.
_____
<em>Check</em>
12 × 84% + 8 × 4% = 10.40 = 20 × 52%
_____
<em>Usual Solution</em>
A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...
0.84x + 0.04(20 -x) = 0.52(20)
0.80x + 0.8 = 10.4 . . . . simplify
0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8
x = 9.6/0.8 = 12 . . . . gallons of 84% acid
20-x = 8 . . . . . . . . . . gallons of 4% acid
Answer: Part A = 12 candles per hour
Step-by-step explanation:
48/4 = 12
Answer:
The jetski is 2.28 dB loud when the person is 41 feet away.
Step-by-step explanation:
Loudness (L) ∝ 1 / Distance² (d²)
Introduce a constant 'K'
L = K (1/d²)
L = K/d²
K = Ld²
Find the K from a previously known information: If a person 8 feet from a jetski hears 60 decibels loud
∴ d = 8 ft , L = 60 db
K = 60(8²) = <em>3840</em>
How loud is the jetski when the person is 41 feet away?
Distance is now 41 ft
since: L = K/d²
∴ L = 3840 / 41²
L = 3840 / 1681
L = 2.28 db
