Answer:
large triangle:
base = 6.64 cm
hypotenuse = 8.31 cm
small triangle:
base = 4 cm
Step-by-step explanation:
large triangle:
tan 37 = 5/base
0.7536 = 5/base
base = 6.64 cm
using the Pythagorean theorem:
hypotenuse² = 5² + 6.64²
hypotenuse² = 25 = 44.02 = 69.02
hypotenuse = 8.31 cm
small triangle:
using the Pythagorean theorem:
base² = 5² - 3²
base² = 25 - 9 = 16
base = 4 cm
If you round it to the nearest hundredths the answer is .21
Answer:
- 273 mL of 5%
- 117 mL of 15%
Step-by-step explanation:
Let q represent the quantity of 15% dressing used. Then the amount of 5% dressing is (390 -q). The amount of vinegar in the mix is ...
0.15q + 0.05(390 -q) = 0.08(390)
0.10q = 31.2 -19.5 = 11.7 . . . . . . subtract 0.05(390) and simplify
q = 117 . . . . . . . . . . . . . . . . . . multiply by 10
390-q = 273
The chef should use 273 mL of the first brand (5% vinegar) and 117 mL of the second brand (15% vinegar).
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<em>Additional comment</em>
You may have noticed that the value of q is (0.08 -0.05)/(0.10 -0.05)×390. The fraction of the mix that is the highest contributor is the ratio of the difference between the mix value and least contributor, divided by the difference between the contributors: (8-5)/(15-5) = 3/10, the fraction that is 15% vinegar. This is the generic solution to mixture problems.
To first find the answer to this, let's find a common denominator between each fraction. The denominator is the bottom number of a fraction.
To find the common denominator, let's factor out each of our denominators 5 times to see if they have a common number.
4: 4, 8, 12, 16, 20
2: 2, 4, 6, 8, 10
They both appear to have the smallest common denominator of 4, so let's use 4.
We already have 1/4 with a denominator of 4, but not 1/2.
2 x 2 = 4, so multiply the numerator and the denominator of 1/2 by 2.
1 x 2 = 2
2 x 2 = 4
Your new fraction is 2/4.
Our expression now is:
-2 1/4 + 5 2/4
or (in simpler terms)
5 2/4 - 2 1/4
Subtract the fractions first.
2/4 - 1/4 = 1/4
Now subtract the whole numbers.
5 - 2 = 3
You are left with:
3 1/4
I hope this helps!
Answer:
Don't lisen to that the anwer is 0.3125
Step-by-step explanation:
