112Work out the sum of 2/6 and 1/6Give your answer in its simplest form.
2 answers:
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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.
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<em>Check</em>
12 × 84% + 8 × 4% = 10.40 = 20 × 52%
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<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
Applying the trigonometric area formula, the amount of fabric she will need to make all the three triangles is: C. 417 square inches.
<h3>What is the Trigonometric Area Formula?</h3>The trigonometric area formula is expressed as: Area = 1/2 × ab × sin(C).
Find the area of one of the triangles:
a = 17 in.
b = 17 in.
C = 74°
Area = 1/2 × (17)(17) × sin(74) ≈ 139 sq. in.
Area of the three triangles = 3(139) = 417 square inches.
Learn more about the trigonometric area formula on:
#SPJ4
Answer:
x=3/2y−6
y=2/3x+4
Step-by-step explanation:
Let's solve for y.
12=−2x+3y
Step 1: Flip the equation.
−2x+3y=12
Step 2: Add 2x to both sides.
−2x+3y+2x=12+2x
3y=2x+12
Step 3: Divide both sides by 3.
3y/3=2x+12/3
