What is the length of line segment LJ?9 units12 units15 units18 units
2 answers:
Answer: LJ = 15 units
Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle. The length of K M is 6 and the length of M J is 3. What is the length of line segment LJ? 9 units 12 units 15 units 18 units
Step-by-step explanation:
See attached image for more information about the question.
Given;
JM = 3
KM = 6
Using Pythagoras theorem, we can solve for JK
JK^2 = JM^2 + KM^2
JK^2 = 3^2 + 6^2
JK = √(9+36)
JK = √45 = 3√5
Secondly, let x represent angle KJM
cosine = adjacent/hypothenus
cosx = JM/JK = JK/JL
JM/JK = JK/JL
Substituting the values
3/3√5 = 3√5/JL
JL = 3√5 × 3√5/3
JL = 3√5 × √5
JL = 15
JL = LJ = 15 units
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Answer:
15 ft
Step-by-step explanation:
This problem can be represented by a right angle triangle, shown in the diagram below.
The distance between Jin and Zoe is the hypotenuse of the triangle, x.
According to Pythagoras theorem,
hyp² = opp² + adj²
Where opp is the opposite side and adjacent is the adjacent side to any angle of consideration (which is not important in this case)
Hence:
x² = 12² + 9²
x² = 144 + 81
x² = 225
Finding the square root:
x = 15 ft
Jin and Zoe are 15 ft apart.
Answer:
For this case the 95% confidence interval is given (63.5 , 74.4) and we want to conclude about the result. For this case we can say that the true mean of heights for male students would be between 63.5 and 74.4. And the best answer would be:
b. The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches.
Step-by-step explanation:
Notation
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the mean and the sample deviation we can use the following formulas:
(2)
(3)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
For this case the 95% confidence interval is given (63.5 , 74.4) and we want to conclude about the result. For this case we can say that the true mean of heights for male students would be between 63.5 and 74.4. And the best answer would be:
b. The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches.