You have two 30-60-90 triangles, ADC and BDC.
The ratio of the lengths of the sides of a 30-60-90 triangle is
short leg : long leg : hypotenuse
1 : sqrt(3) : 2
Using triangle ADC, we can find length AC.
Using triangle BDC, we can find length BC.
Then AB = AC - BC
First, we find length AC.
Look at triangle ACD.
DC is the short leg opposite the 30-deg angle.
DC = 10sqrt(3)
AC = sqrt(3) * 10sqrt(3) = 3 * 10 = 30
Now, we find length BC.
Look at triangle BCD.
For triangle BCD, the long leg is DC and the short leg is BC.
BC = 10sqrt(3)/sqrt(3) = 10
AB = AC - BC = 30 - 10 = 20
The answer to this question would be: B. JK and LM meet at a right angle.
The reversed T symbol in this question means "perpendicular". That means the JK and LM line have 90-degree angle difference. A straight angle is 180 degree and right angle mean 90 degrees.
A perpendicular line should be in the same plane and intersect each other.
Answer:
The domain is (-∞ , ∞)
The domain is continuous
Step-by-step explanation:
Here, we want to identify the domain of the linear function
The domain in this case can be represented by the set of all real numbers.
When we talk of the domain of a function, we are simply referring to the the range of values between the smallest value on the x-axis and the largest number on the x-axis
Hence, mathematically, we are simply considering the smallest value of b up to the largest value of b in this case. Where b simply represents the number of books
Thus, the domain here will be (-∞ , ∞)
On if the domain is discrete or continuous, we can see that the domain is continuous.
The domain is continuous simply because, the domain we have contains all the values and not some in the set of real numbers. If it had contain only some, then it would have been discrete. But since it contains all, it is continuous
Answer: The average number of hours she danced per day is 1.9 hours (rounded to the nearest tenth)
Step-by-step explanation: We start by calculating how many hours she danced all together which can be derived as follows;
Summation = 3 +2 +2 + 1 + 1.5 + 2 = 11.5
The number of days she danced which is the observed data is 6 days (she did not dance at all on Wednesday).
The average (or mean) hours she danced each day can be calculated as
Average = ∑x ÷ x
Where ∑x is the summation of all data and x is number of observed data
Average = (3+2+2+1+1.5+2) ÷ 6
Average = 11.5 ÷ 6
Average = 1.9166
Approximately, average hours danced is 1.9 hours (to the nearest tenth)
Answer:
\sqrt(217)
Step-by-step explanation:
(19)^2=(12)^2
361 - 144 + 217
\sqrt(217)
