Answer:
Point B is
Step-by-step explanation:
Given: A triangle ABC was rotated 90 degrees counterclockwise
To find: coordinates of the point B
Solution:
A triangle is three - dimensional figure that has three sides, three vertices and three angles.
Counterclockwise refers to the direction opposite to the direction of movement of hands of the clock.
As triangle ABC was rotated 90 degrees counterclockwise about the origin, point B is
Answer:
x >= -7 ................(1a)
x >= 3 ...............(2a1)
Step-by-step explanation:
f(x) = .............(0)
find the domain.
To find the (real) domain, we need to ensure that each term remains a real number.
which means the following conditions must be met
x+7 >= 0 .....................(1)
AND
x^2+2x-15 >= 0 ..........(2)
To satisfy (1), x >= -7 .....................(1a) by transposition of (1)
To satisfy (2), we need first to find the roots of (2)
factor (2)
(x+5)(x-3) >= 0
This implis
(x+5) >= 0 AND (x-3) >= 0.....................(2a)
OR
(x+5) <= 0 AND (x-3) <= 0 ...................(2b)
(2a) is satisfied with x >= 3 ...............(2a1)
(2b) is satisfied with x <= -5 ................(2b1)
Combine the conditions (1a), (2a1), and (2b1),
x >= -7 ................(1a)
AND
(
x >= 3 ...............(2a1)
OR
x <= -5 ................(2b1)
)
which expands to
(1a) and (2a1) OR (1a) and (2b1)
( x >= -7 and x >= 3 ) OR ( x >= -7 and x <= -5 )
Simplifying, we have
x >= 3 OR ( -7 <= x <= -5 )
Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.
