Answer:
A∩B=∅
Step-by-step explanation:
A intersect B have no elements in common - so we have the empty set.
<u>Answer:</u>
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<u>Step-by-step explanation:</u>
From the graph, we can see that y = -1 when x = 0.
So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.
1. y = cos(x + pi/2) = cos(0 + pi/2) = 0
2. y = cos(x+2pi) = cos(0+2pi) = 1
3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5
4. y = cos(x+pi) = cos(0+pi) = -1
Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.
Answer:
Step-by-step explanation:
If these 3 points are collinear, then we can find the slope of the linear function using any 2 of those points. Suppose we use (-4, 3) and (0, 1):
As we move from (-4, 3) to (0, 1), x increases by 4 and y decreases by 2. Hence, the slope of this lilne is m = rise/run = -2/4, or m = -1/2.
Using the slope-intercept formula y = mx + b and replacing y with 1, x with 0 and m with -1/2, we get:
1 = (-1/2)(0) + b, or b = 1. Then the desired equation is y = f(x) = (-1/2)x + 1
128.34
= 128+ 0.34
= 128+ 34/100
= 128+ (34/2) / (100/2)
= 128+ 17/50
= 128 17/50
128.34 written as a mixed number is 128 17/50~
Rates like $ per channel is a slope, "m". The added fee is a constant so it's the intercept "b".
y = mx + b
So for the first problem (9)
(a)
y = total cost in dollars
x = number of premium channels
y = 16x + 44
(b) when x = 3 channels
y = 16(3) + 44
y = 92 $
the second problem (10)
(a) every 4 years the tree grows by 12-9=3 ft
So the unit rate or slope will be 3 ft per 4 yrs, (3/4). You can see this also by solving for slope "m" using the given points (4,9) and (8,12).
x = number of years
y = height of tree in ft
y = (3/4)x + b
use one of the points to find the y-intercept "b".
9 = (3/4)(4) + b
9 = 3 + b
9 - 3 = b
6 = b
y = (3/4)x + 6
(b) when x = 16
y = (3/4)(16) + 6
y = 12 + 6
y = 18 ft
