Answer:
The line passes through (4, -7) and (5, -10).
Step-by-step explanation:
When x = 4, y = 5 - 3(4), or 5 - 12, or -7. Thus the point (4, -7) lies on the graph. Similarly y = 5 - 3(5) = -10 when x = 5. Thus, the line also goes through (5, -10). Plot these two points and draw a line through them. Doing this will result in the desired graph.
Answer:
The student assumed he was asked to factor
(a^2 - b^2)
Which is equal to
= (a+b)*(a-b) (His response)
But, he was asked to simplify
(a^2 + b^2)
Which has imaginary roots, and can be factored as:
(b +ai)(b-ai)
Answer:
addition property of equality
Step-by-step explanation:
This is because the addition property of equality means
if 
then 
So if, 
then 
2:4:2.....added = 8
2/8 (56) = 112/8 = 14
4/8 (56) = 224/8 = 28
2/8 (56) = 112/8 = 14
14:28:14
tan²(<em>θ</em>) - sin²(<em>θ</em>) = sin²(<em>θ</em>)/cos²(<em>θ</em>) - sin²(<em>θ</em>)
-- because tan(<em>θ</em>) = sin(<em>θ</em>)/cos(<em>θ</em>) by definition of tangent --
… = sin²(<em>θ</em>) (1/cos²(<em>θ</em>) - 1)
-- we pull out the common factor of sin²(<em>θ</em>) from both terms --
… = sin²(<em>θ</em>) (1/cos²(<em>θ</em>) - cos²(<em>θ</em>)/cos²(<em>θ</em>))
-- because <em>x</em>/<em>x</em> = 1 (so long as <em>x</em> ≠ 0) --
… = sin²(<em>θ</em>) ((1 - cos²(<em>θ</em>))/cos²(<em>θ</em>))
-- we simply combine the fractions, which we can do because of the common denominator of cos²(<em>θ</em>) --
… = sin²(<em>θ</em>) (sin²(<em>θ</em>)/cos²(<em>θ</em>))
-- due to the Pythagorean identity, sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1 --
… = sin²(<em>θ</em>) tan²(<em>θ</em>)
-- again, by definition of tan(<em>θ</em>) --
