Mr. Austin is driving 390 miles to visit the Gateway Arch in St. Louis, Missouri. He dries at an average rate of 65 miles per ho
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Answer:
Irrational numbers are not closed under addition.
Step-by-step explanation:
Irrational numbers are the numbers that cannot be expressed in the form of a fraction . In other words we can say that irrational number,s decimal expantion does not cease to end.
The closure property of addition in irrational numbers say that sum of two irrational number is always a rational number, But this is not true. It is not necessary that the sum is always irrational some time it may be rational.
This can be understood with the help of an example:
let (2+√2) and (-√2) be two irrational number. Their sum is (2+√2)+(-√2) = 2, which is clearly a rational number.
Hence, irrational numbers are not closed under addition.
Answer:
Here is your answer:
Step-by-step explanation:
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