f(x) = 3x + 1
y = 3x + 1
y - 1 = 3x + 1 - 1
y - 1 = 3x
3 3
¹/₃y - ¹/₃ = x
y = ¹/₃x - ¹/₃
f⁻¹(x) = ¹/₃x - ¹/₃
f⁻¹(10) = ¹/₃(10) - ¹/₃
f⁻¹(10) = 3¹/₃ - ¹/₃
f⁻¹(10) = 3
It is equal too (10, 3).
Begin at the leftmost digit
Ten thousands; then thousands; then hundreds; then tens; then ones; then tenths; then hundreths; then thousandths,
Answer:
"Rotation" refers to the action of turning about a central point: The distance from this center to any part of the shape remains constant. Each point traces out a circular path around the center.
Figure 2 was derived from figure 1. Among all the proposed options, those relevant for the transformation being classified as a rotation are:
A) The line connecting the center of rotation, C, to a point in the original image (figure 1) has the same length as the line connecting the center to the corresponding point in the new image (figure 2).
(B) The transformation maintains rigidity.
(C) Every point in figure 1 rotates through an identical angle around the center of rotation, C, to form figure 2.
(E) If figure 1 undergoes a 360° rotation about point C, it will align with itself.
Thus, options A, B, C, and E are valid.
The sine, cosine, and tangent functions for 60 degrees are equivalent to those for 120, 240, and 300 degrees. Angles of 30 degrees, 45 degrees, and 60 degrees can be paired with corresponding angles from different quadrants. The angles that possess unique sine, cosine, and tangent values are 90, 180, 270, and 360 degrees. The radian measure of π/4 can be calculated using the formula:
π/4 * 180/π.
The two π values will cancel, leading to:
180/4, which yields the degree measure. This same calculation can also be applied to π/6. Additionally, you can determine radians from degrees by multiplying the degree value by π/180 and then simplifying the fraction or radian as needed. The π will remain in your final result.
According to the definition, isometric refers to having equal measurements. Therefore, a rigid transformation ensures that all dimensions of the original figure (the one being transformed) remain identical in the resulting figure after the transformation.
This means you can confirm a transformation is rigid by comparing the sizes of both the original and transformed figures: only if the dimensions match exactly can the transformation be considered rigid.
