Describe all the situations in which the following statements are true.
a. two vertical angles are also complementary
b. a linear pair is also supplementary
c. 2 supplementary angles are also a linear pair
d. two vertical angles are also a linear pair

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."

  d. △abc is congruent to △fde

step-by-step explanation:

triangle abc is reflected across the x-axis. the corresponding vertices are

the names of the triangles in the congruence statement must have corresponding vertices in the same order. that is, △abc is congruent to △fde.