Choose the correct solution and graph for the inequality.
3x -4 < -22 or 3x +2 > 17
The correct solution for the inequality is:
3x - 4 < -22
To solve this inequality, we need to isolate the variable x.
Adding 4 to both sides of the inequality, we get:
3x < -18
Dividing both sides of the inequality by 3, we get:
x < -6
The correct solution for the inequality 3x - 4 < -22 is x < -6.
The correct graph for the inequality x < -6 is an open circle on -6 on the number line, and a shaded region to the left of -6, indicating all values less than -6.
For the second inequality:
3x + 2 > 17
We need to isolate the variable x.
Subtracting 2 from both sides of the inequality, we get:
3x > 15
Dividing both sides of the inequality by 3, we get:
x > 5
The correct solution for the inequality 3x + 2 > 17 is x > 5.
The correct graph for the inequality x > 5 is an open circle on 5 on the number line, and a shaded region to the right of 5, indicating all values greater than 5.
Therefore, the correct solution and graph for the inequality are:
x < -6 or x > 5
Graph:
___________________________________________
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
O--------------------------> O--------------->
(-∞,-6) (5, ∞)
Start from 200 feet away, a person on a tractor rides towards a barn and then passes it. The rider is traveling at a constant rate of 8 feet per second. The distance between the tractor and the barn is given by the equation
d = |200 - 8t|. At what times is the tractor 20 feet away from the barn?
To find the times when the tractor is 20 feet away from the barn, we need to set the distance between the tractor and the barn equal to 20 and solve for t.
The distance is given by the equation d = |200 - 8t|. Setting this equal to 20, we have:
|200 - 8t| = 20
Now, we can solve for t by considering two cases:
1. When 200 - 8t is positive: 200 - 8t = 20
2. When 200 - 8t is negative: -(200 - 8t) = 20
Solving Case 1:
200 - 8t = 20
Subtracting 200 from both sides, we get:
-8t = -180
Dividing both sides by -8, we get:
t = 22.5
Solving Case 2:
-(200 - 8t) = 20
Expanding the negative sign, we get:
-200 + 8t = 20
Adding 200 to both sides, we get:
8t = 220
Dividing both sides by 8, we get:
t = 27.5
Therefore, the tractor is 20 feet away from the barn at times t = 22.5 seconds and t = 27.5 seconds.
If N is the set of natural numbers that are factors of 15, choose the selection below that correctly shows this set in roster form.
The set of natural numbers that are factors of 15 can be expressed in roster form as:
N = {1, 3, 5, 15}
Suppose R = {2, 4, 6, 8, 10, 12, 14} and D = {3, 6, 9, 12, 15, 18, 21}.
What is R^D
In set theory, the exponentiation of two sets represents the set of all possible ordered pairs where the first element comes from the first set and the second element comes from the second set.
In this case, R^D represents the set of all possible ordered pairs where the first element comes from the set R and the second element comes from the set D.
So, R^D = {(2, 3), (2, 6), (2, 9), (2, 12), (2, 15), (2, 18), (2, 21), (4, 3), (4, 6), (4, 9), (4, 12), (4, 15), (4, 18), (4, 21), (6, 3), (6, 6), (6, 9), (6, 12), (6, 15), (6, 18), (6, 21), (8, 3), (8, 6), (8, 9), (8, 12), (8, 15), (8, 18), (8, 21), (10, 3), (10, 6), (10, 9), (10, 12), (10, 15), (10, 18), (10, 21), (12, 3), (12, 6), (12, 9), (12, 12), (12, 15), (12, 18), (12, 21), (14, 3), (14, 6), (14, 9), (14, 12), (14, 15), (14, 18), (14, 21)}
Therefore, the set R^D is {(2, 3), (2, 6), (2, 9), (2, 12), (2, 15), (2, 18), (2, 21), (4, 3), (4, 6), (4, 9), (4, 12), (4, 15), (4, 18), (4, 21), (6, 3), (6, 6), (6, 9), (6, 12), (6, 15), (6, 18), (6, 21), (8, 3), (8, 6), (8, 9), (8, 12), (8, 15), (8, 18), (8, 21), (10, 3), (10, 6), (10, 9), (10, 12), (10, 15), (10, 18), (10, 21), (12, 3), (12, 6), (12, 9), (12, 12), (12, 15), (12, 18), (12, 21), (14, 3), (14, 6), (14, 9), (14, 12), (14, 15), (14, 18), (14, 21)}
Suppose R = {2, 4, 6, 8, 10, 12, 14} and D = {3, 6, 9, 12, 15, 18, 21}.
What is R half circle D
The term "R half circle D" is not a standard notation in set theory. It seems like you may be referring to the concept of the intersection and union of sets.
The intersection of two sets, denoted by the symbol ∩, represents the elements that are common to both sets. The union of two sets, denoted by the symbol ∪, represents all the elements that belong to either set or both sets.
Given the sets R = {2, 4, 6, 8, 10, 12, 14} and D = {3, 6, 9, 12, 15, 18, 21}, we can look at their intersection and union.
Intersection (R ∩ D):
The intersection of R and D is the set of elements that are present in both sets.
R ∩ D = {6, 12}
Union (R ∪ D):
The union of R and D is the set of elements that are present in either set or both sets.
R ∪ D = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 18, 21}
Therefore, there is no specific meaning or operation associated with "R half circle D". Instead, we can look at the intersection or union of the two sets, depending on what you are trying to find or express.