Image included: a sequence of transformations maps ∆abc to ∆a′b′c′. the sequence of transformations that maps ∆abc to ∆a′b′c′ is a reflection across the followed by a translation
first box is a-(x-axis) b- (y-axis) c-(line y=x) or d-(line y=-x)
second box is a-(8 units to the right 10 units up) b- (8 units to the right 4 units up) c-(10 units to the right 2 units up) or d-(10 units to the right 4 units up)

The answer is (1) y = x and (2) 10 units to the right and 4 units up.

Step-by-step explanation:

A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units to the right and 4 units up.

The first is a reflection across a line and second is a translation.

We can see that the co-ordinates of point C are (-4, -2).

After reflection from the line y = x, the co-ordinates becomes (2, -4).

And the coordinates of point C' are (12, 0). So, to reach point C' from point C, we have to add 10 units to the x-coordinate and 4 units to the y-coordinate.

That makes a translation of 10 units right and 4 units up.

7

step-by-step explanation:

the answer would be 7

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841