What is the nature of triangle formed by the lines x+y=0 , 3x+y=0 , x+3y-4=0
1 answer:
Answer:
isosceles obtuse triangle
Step-by-step explanation:
The attached graph shows a plot of the three lines.
The triangle is an isosceles obtuse triangle in the 2nd quadrant.
_____
It is convenient to let a graphing calculator plot these lines. If you're going to plot them by hand, it usually works best to choose values of the variables for the variable that has the largest coefficient (3 in two of the equations). That way, you're not trying to plot coordinates that contain fractions.
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Answer:
C. The population must be normally distributed.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For us to apply the central limit theorem with a sample size of 14, the underlying population must be normally distributed.
So the correct answer is:
C. The population must be normally distributed.
The area of figure ABCDEF can be computed as the sum of the areas of trapezoid ACDF and triangle ABC, less the area of trangle DEF.
trapezoid ACDF area = (1/2)(AC +DF)·(CD) = (1/2)(8+5)(6) = 39
triangle ABC area = (1/2)(AC)(2) = 8
triangle DEF area = (1/2)(DF)(2) = 5
Area of ABCDEF = (ACDF area) + (ABC area) - (DEF area) = 39 +8 -5 = 42
The actual area of ABCDEF is 42 square units.
trapezoid ACDF area = (1/2)(AC +DF)·(CD) = (1/2)(8+5)(6) = 39
triangle ABC area = (1/2)(AC)(2) = 8
triangle DEF area = (1/2)(DF)(2) = 5
Area of ABCDEF = (ACDF area) + (ABC area) - (DEF area) = 39 +8 -5 = 42
The actual area of ABCDEF is 42 square units.