Add 9 to both sides to form a perfect square trinomial:
x² + 6x = 7
x² + 6x + 9 = 16
x² + 2•x•3 + 3² = 16
(x + 3)² = 16
(recall that (a + b)² = a² + 2ab + b²)
Now solve for x. Taking square roots on both sides, we get
x + 3 = ± √16
x + 3 = ± 4
x = -3 ± 4
so the two solutions are x = -7 and x = 1.
In this sequence a=7
d=11.5-7=4.5
So 46th term = a+45d
=7+45(4.5)
=7+202.5
=209.5
There are also 6 possibilities because the die has six sides with 1 different number on each.
Answer:
see explanation
Step-by-step explanation:
the vertices of S under the translation
are
(2, 3 ) → (2, 0 )
(6, 3 ) → (6, 0 )
(4, 5 ) → (4, 2 )
Under an anticlockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) then the above coordinates become
(2, 0 ) → (0, 2 )
(6, 0 ) → (0, 6 )
(4, 2 ) → (- 2, 4 )
which are the coordinates of the vertices of the image T
then the rotation is 90° anticlockwise about the origin , point (0, 0 )