Determine whether the following sets are subspaces of r 3 under the operations of addition and scalar multiplication defined on r 3 . justify your answers. (a) w 1 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 = 3 a 2 and a 3 = − a 2 } (b) w 2 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 = a 3 + 2 } (c) w 3 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : 2 a 1 − 7 a 2 + a 3 = 0 } (d) w 4 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 − 4 a 2 − a 3 = 0 } (e) w 5 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : a 1 + 2 a 2 − 3 a 3 = 1 } (f) w 6 = { ( a 1 , a 2 , a 3 ) ∈ r 3 : 5 a 2 1 − 3 a 2 2 + 6 a 2 3 = 0 }

Angle xyz is formed by segments xy and yz on the coordinate grid below: a coordinate plane is shown. angle xyz has endpoints at 3 comma negative 1 and 6 negative 2 and 3 comma negative 3 and measures 36.87 degrees. angle xyz is rotated 270 degrees counterclockwise about the origin to form angle x′y′z′. which statement shows the measure of angle x′y′z′?

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match each division expression with the correct quotient.

Barbara has a good credit history and is able to purchase a car with a low-interest car loan. she co-signs a car loan for her friend jen, who has poor credit history. then, jen defaults on the loan. who will be held legally responsible by the finance company and why? select the best answer from the choices provided. a. barbara will be held legally responsible because she has a good credit history. b. jen will be held legally responsible because she drives the car. c. barbara will be held legally responsible because she is the co-signer. d. jen will be held legally responsible because she has a poor credit history. the answer is a