Solving the system of inequalities :
-34
I wish I could but I’m not smart I feel the same way!
Answer: 20 oz of juice concentrate and 60 oz of water.
Explanation:
Translate the word statements into algebraic expressions to set a system of equations that you can solve.
1) Name the variables:
- j: parts of juice concentrate
- w: parts of water
2) Statement one, 2 parts juice concentrate to 6 parts water, translates into a proportion:
j / w = 2 / 6
3) Statement two, 80 oz of the drink, tanslates into an equality:
j + w = 80
4) Solve the system to find how many oz of juice concentrate and water Elena needs:
a) System:
j / w = 2 / 6
j + w = 80
b) Solve for w in the first equation: w = 6j / 2 = 3j
c) Substitute w in the second equation: j + 3j = 80
d) Combine like terms: 4j = 80
e) Use division property of equality: j = 20
f) Substitue in w = 3j: 3 = 3(20) = 60.
5) Solution: j = 20, w = 60.
6) Verify:
- j / w = 20 / 60 = 2 / 6 ⇒ right
- j + w = 20 + 60 = 80 ⇒ right
We have constructed two angles with angle measures, 30° and 50° respectively.
Recall the angle sum of a triangle is 180°; the formula for angle sum of any n-sided polygon is formulated by: 180(n - 2), where n is the number of sides.
Since we need the three angles to equal to 180, we can call the third angle x.
Hence, our equation becomes:
x + 30 + 50 = 180
x + 80 = 180
x = 100
Thus, our third angle is 100°
