3m
1 answer:
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Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
• If m > 0, then the line slopes upwards from left to right ( increases )
• If m < 0, then the line slopes downwards from left to right ( decreases )
(a)
y + x = 3 ( subtract x from both sides )
y = - x + 3 ← in slope-intercept form
with m = - 1 ⇒ decreasing from left to right
(c)
y = 4x + 8 ← is in slope-intercept form
with m = 4 ⇒ increasing from left to right
the equation of a line in the form x = c represents a vertical line, where c is the value of the x-coordinates the line passes through
(b)
x - 5 = 0 ( add 5 to both sides )
x = 5 ← is a vertical line
the equation of a line in the form y = c represents a horizontal line, where c is the value of the y-coordinates the line passes through
(d)
= - 6 ( multiply both sides by 4 )
y = - 24 ← is a horizontal line
Answer:
15 is the total number of animals for which (p ∨ q) ∧ r true.
Step-by-step explanation:
From the diagram it is clear that
p contains {2, 5, 8, 9}
q contains {2, 4, 7, 5}
r contains {2, 4, 6, 9}
p ∨ q is the union of p and q which include all the animals which are in p, in q, or in both p and q.
Note: p ∨ q can not have duplicate animals
So,
p ∨ q = {2, 4, 5, 7, 8, 9}
(p ∨ q) ∧ r contains the animals which need to be common in both (p ∨ q) and r.
As
p ∨ q = {2, 4, 5, 7, 8, 9}
r = {2, 4, 6, 9}
So,
(p ∨ q) ∧ r = {2, 4, 9}
As
Therefore, 15 is the total number of animals for which (p ∨ q) ∧ r true.
Keywords: union, and operation, or operation
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