Triangle pqr is dilated by a scale factor of 1.5 to form triangle p′q′r′. this triangle is then dilated by a scale factor of 2 to form triangle p″q″r″. if vertex p is at (3, -4) and vertex q is at (5, -1), what are the coordinates of vertices p″ and q″? p″(4.5, -6) and q″(7.5, 1.5) p″(4.5, -6) and q″(7.5, -1.5) p″(-9, 12) and q″(15, -3) p″(9, -12) and q″(15, -3) p"(-9, -12) and q"(-15, -3)

P″(9, -12) and Q″(15, -3)

Step-by-step explanation:

When a figure with coordinate (x,y) dilated by scale factor k , then the coordinates of the image is given by :-

Given : The coordinates of vertex P is (3, -4) and Q is (5, -1) .

Triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′.

Then, the co-ordinates of P' and Q' are given by:-

Triangle P′Q′R′ is then dilated by a scale factor of 2 to form triangle P″Q″R″.

Then, the co-ordinates of P" and Q" are given by:-

Hence, the coordinates of vertices P″ and Q″ are P″(9, -12) and Q″(15, -3).

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.