Triangle cat is translated using the rule (x, y)→(x−3, y+4) to create triangle c'a't'. if a line segment is drawn from point c to point c' and from point a to point a', which statement would best describe the line segments drawn? they share the same midpoints. they are diameters of concentric circles. they are perpendicular to each other. they are parallel and congruent.

option: d is correct. (they are parallel and congruent.)

step-by-step explanation:

let us consider a triangle cat such that the vertices have the coordinates (0,0), (4,0) and (2,0).

i.e. the coordinates of c are (0,0), coordinates of a are (4,0) and coordinates of t are (2,2).

now on transforming δcat to δc'a't' using the rule (x,y)→(x−3, y+4);

we get the coordinates of c' to be (0-3,0+4)=(-3,4)

coordinates of a' are: (4-3,0+4)=(1,4)

coordinates of t' are: (2-3,2+4)=(-1,6)

hence from the figure( attached to the answer) we could see this transformation.

now we join c to c' and a to a' and get that the two lines are parallel and congruent.

hence, option d is correct.

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west