CPhill

The sum of the acute angles = 90°

Can you solve this now, NSS???

d =  sqrt [ ( -2 - 5)^2 + ( -4 - 7)^2 ]  = 

sqrt [ (-7)^2 + (-11)^2 ] =

sqrt [ 49 + 121 ] =

sqrt[ 170]  ≈  13.03

We know an angle and an opposite side.....and we are trying to find the adjacent side....the tangent seems logical, here

tan 63 = 24 / miles       rearrange as

miles =    24 / tan 63  ≈   12.2 

100 = k * (0.25)      divide both sides by 0.25

100/ 0.25  = k =  400

So

80  =  400 (x)    divide both sides by 400

80/ 400 =  x =  1/5 m =  0.2 meters

A

Remember that.....with inverse variation, the product of the variables is constant

So....x * y  =  5 * 12  =  60

So....

x * 32  =  60       divide both sides by 32

x = 60 / 32  =   15 / 8

312.50 = k * 25       divide both sides by 25

(312.50 / 25)  =  k = 12.5

So....the equation is

p = 12.5 h           where h is the number of hours worked 

Not an expert on this, NSS...I think the spring constant should be  " 0.3 N / m"

So

F =  (0.3 N/ m) (1.5 m)

F =  (0.3)(1.5)N =   0.45 N

Here's the second one

New point =

[ (1, 4) - (-3, 1) ] (2) + (-3, 1) = [ 4, 3 ](2) + (-3,1) = [ 8, 6] + (-3, 1) = ( 5, 7)

New point =

[ (2, 2) - (-3,1)](2) + (-3, 1) = [ 5,  1](2) + (-3, 1)  = [ 10,2] + (-3, 1) = (7, 3)

New point

[ (-3, 3) - (-3, 1)](2) + (-3,1) = [ 0, 2] (2) + (-3,1) = [ 0, 4] + (-3, 1) = (-3, 5)

Here's the image

See if you can do the last one....

We can do this with a "formula"

New point =  [ old point - center of dilation ] (scale factor) + center of dilation

First one

New point =  [ ( 2,4) - (0,0)] (1/2) + (0,0) =   [ 2,4](1/2) + (0,0) = (1,2)

New point  = [ ( -2, 8) - (0,0) ] (1/2) +  (0,0) = [ -2,8](1/2) + (0,0) = (-1, 4)

New point = [ (-4, 2) - (0,0)](1/2) + (0,0) = [-4,2](1/2) + (0,0) = (-2, 1)

Here's the graph: