Answer: w=12, y=6√3
Step-by-step explanation:
Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.
In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.
The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.
x√2=8
x=8/√2
x=5.7 or 6 [Let's use 6 so that it is easier to work with a whole number]
Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.
w=2x
w=2(6)
w=12
We know the leg opposite of 60° is x√3. We can plug in x.
y=6√3
The assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
Important assumptions in regression model analysis are
- There should be a linear and additive relationship between dependent (response) variable and independent (predictor) variable(s).
- There should be no correlation between the residual (error) terms. Absence of this phenomenon is known as auto correlation.
- The independent variables should not be correlated. Absence of this phenomenon is known as multi col-linearity.
- The error terms must have constant variance. This phenomenon is known as homoskedasticity. The presence of non-constant variance is referred to heteroskedasticity.
- The error terms must be normally distributed.
Hence we can conclude that the assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
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S=i(n-1)+2*(n-1)+1 perhaps
(f o g)(x)
g(x) = x + 2
Since it’s telling you to use g(x), you use (x + 2) as your new x value for function f.
f(x + 2) = 5(x + 2) + 5
= 5x + 10 + 5
= 5x + 15
