Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 9x − 10 given ⇒ 2(x − 4) + 6x = 9x − 10
step 1 ⇒ 2x − 8 + 6x = 9x − 10
step 2 ⇒ 2x + 6x − 8 = 9x − 10
step 3 ⇒ 8x − 8 = 9x − 10
step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
step 5 ⇒ 0 − 8 = x − 10
step 6 ⇒ −8 = x − 10
step 7 ⇒ −8 + 10 = x − 10 + 10
step 8 ⇒ 2 = x + 0
step 9 ⇒ 2 = x
which step in solving this equation is justified by the distributive property?
a) step 1 ⇒ 2x − 8 + 6x = 9x − 10
b) step 2 ⇒ 2x + 6x − 8 = 9x − 10
c) step 3 ⇒ 8x − 8 = 9x − 10
d) step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10

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You will get 25 points an image of a rectangular prism is shown below: part a: a cross section of the prism is cut with a plane parallel to the base. what is the name of the shape created by the cross section? explain your answer. (5 points) part b: if a cross section of the prism is cut perpendicular to the base, what would be the shape of the resulting cross section? explain your answer. (5 points)

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Give the functions f(x) = |x + 2| - 3, what is the domain? a,b,c, or d all real numbers x > 2 x < -2 all real numbers and x cannot equal to 2