Point A(–4, 2) is reflected over the line x = 3 to create the point A'. What are the coordinates of A'?
2 answers:
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Answer:
The area of the quadrilateral B-H-G-E is 7
Step-by-step explanation:
The area of the parallelogram = 60
It can be shown that ΔG-D-F = 3/10 × Area of the parallelogram S = 3/10×S
Because the diagonal B-D shares A-F into the ratio 1:2, the ΔH-D-A = 2/3×ΔD-B_A where ΔD-B_A = 1/2·S, therefore, ΔD-B_A = 2/3×1/2×S = 1/3×S
ΔB-F-H is similar to ΔD-B_A scaled to 1/2,
Therefore;
The area of ΔB-F-H = 1/4×Area of ΔD-B_A = 1/4×1/3×S = 1/12×S,
ΔF-C-D = 1/4×S
ΔE-A-D = 1/4×S
The area of the quadrilateral B_H_G_E found as follows;
Area B_H_G_E = S - (ΔF-C-D + ΔG-D-F +ΔE-A-D +ΔB-F-H)
Area B_H_G_E = S - (1/4×S + 1/10×S +1/4×S +1/12×S) = S - 53/60×S = 7/60×S
Whereby we are given that the area, S of the parallelogram AB-CD = 60 we have;
Area B_H G_E = 7/60×60 = 7
Answer:
Both the variables are important for the regression analysis and cannot be deleted.
Step-by-step explanation:
(1)
The hypothesis for for the testing of coefficient β₁ are:
<em>H</em>₀: β₁ = 0 vs. <em>H</em>ₐ: β₁ ≠ 0
The test statistic is:
It is provided that H₀ is rejected if <em>t</em> > 2.042.
The test statistic value, <em>t</em> = 3.753 > 2.042.
Thus, the null hypothesis is rejected.
<u>Conclusion:</u>
There is a significant relationship between the regression variable and the dependent variable.
(2)
The hypothesis for for the testing of coefficient β₂ are:
<em>H</em>₀: β₂ = 0 vs. <em>H</em>ₐ: β₂ ≠ 0
The test statistic is:
It is provided that H₀ is rejected if <em>t</em> < -2.042.
The test statistic value, <em>t</em> = -3.046 < -2.042.
Thus, the null hypothesis is rejected.
<u>Conclusion:</u>
There is a significant relationship between the regression variable and the dependent variable.
Thus, both the variables are important for the regression analysis and cannot be deleted.