Answer:
15.
16. 10 ml of 20% saline and 40 ml of 10% saline
Step-by-step explanation:
A chemist takes x ml of 20% saline and y ml of 10% saline. In total, he takes
x + y ml that is 50 ml, so
There are ml of salt in x ml of 20% saline and
ml of salt in 10% saline. There are
ml of salt in 50 ml of 12% saline. Thus,
15. We get the system of two equations:
16. Solve this system. From the first equation:
Substitute it into the second equation:
If ΔACB is an isosceles triangle, then ∠A ≅ ∠B and AC ≅ CB
Since ∠C = 120° and ∠A + ∠B + ∠C = 180°, then ∠A = 30° and ∠B = 30°
Next, look at ΔADB. ∠A + ∠D + ∠B = 180°, so ∠A + 90° + 30° = 180° ⇒ ∠A = 30°
Now look at ΔADC. Since ∠A = 30° in ΔACB, and ∠A = 60° in ΔADB, then ∠A = 30° in ΔADC <em>per angle addition postulate.</em>
Now that we have shown that ΔADB and ΔADC are 30-60-90 triangles, we can use that formula to calculate the side lengths.
CD = 4 cm (given) so AC = 2(4 cm) = 8 cm
Since AC ≅ BC, then BC = 8 cm. Therefore, BD = 4 + 8 = 12 <em>by segment addition postulate.</em>
Lastly, look at ΔBHD. Since ∠B = 30° and ∠H = 90°, then ∠D = 60°. So, ΔBHD is also a 30-60-90 triangle.
BD = 12 cm, so HD = = 6 cm
Answer: 6 cm