Given that \tan\theta =\frac{9}{40}tanθ= 40 9 ​ and that angle \thetaθ terminates in quadrant \text{III}III, then what is the value of \sin\thetasinθ?

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

question says to graph a triangle (xyz) and reflect it over the line y=x to create triangle x'y'z'.

we know that line y=x has both coordinates equal like (1,1), (5,5) etc so we can easily graph that reflecting line.

description of transformation:

we can see that x and y coordinate gets switched after transformation like (2,8) changed to (8,2)

what do you notice about the two line segments you drew:

we see that line segments xp and x'p are of same length and perpendicular to the reflecting line y=x.

do you think you would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line? :

yes, i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line.

how do you know? :

by measuring the length of yk and y'k.

as given ,→planes t and x are parallel.

→plane t contains line a.

→plane x contains line b.

as we know by definition of line , if we take any two points on a plane the line should completely lie on it i. pass through these two points.

out of the four options given it seems that two possibilities might be true.

1. they may be skew lines , so they will never intersect.

2.if lines a and b are parallel, so again they will not intersect.

other two seems incorrect

because if a and b are perpendicular to the plane ,

1. either they will join each other to form a unique line or2. they will never intersect.

there is no possibility that they will intersect at two points.