Answer:
a) x = 60. b) b = 110. c) x = 20. d) x = 30.
Explanation:
For question a, 2x and 120° are opposite (vertical) angles so they must be the same measure according to the vertical angle theorem by definition, given they are angles formed by the transversal cutting two parallel lines. 2x = 120, so x = 60.
For question b, 130° and b + 20 are corresponding angles of the transversal cutting parallel lines, so they must be the same measure according to corresponding angle theorem(same side, one angle inner, and the other exterior of that) by definition. Given that they are both pairs of the same angle, they must be corresponding angles. 130° = b + 20, b = 110.
For question c, 120° and 2x + 20 are same side interior angles so they must be supplementary(add up to 180°) by definition. This is on the *same side* of the transversal inside the two parallel lines cut by it. 120° + 2x + 20° = 180°, x = 20°.
For question d, They are also on the same side but on the left so the same property of corresponding angles applies, so 3x + 10, and 100° must be the same measure. Therefore 3x + 10 = 100°, and x = 30.
Answer:
Step-by-step explanation:
Given that:
A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data.
To obtain the geometric mean of the untransformed data,
X = set of numbers
N = number of observations
Arithmetic mean if transformed data = 1.65
Log(Xi).... = transformed data
Arithmetic mean = transformed data/ N
Log(Xi) / N = 1.65
(Πx)^(1/N), we obtain the antilog of the aritmétic mean simply by raising 10 to the power of the Arithmetic mean of the transformed data.
10^1.65 = 44.668359
Answer:
(1, 3)
Step-by-step explanation:
A 90° clockwise rotation about the origin maps every point
(x, y)→(y, -x).
The coordinates of X are (-3, 1); using this transformation, we have
(-3, 1)→(1, 3).