Answer:
Only D,F, and G are perfect cubes.
Step-by-step explanation:
A) Technically not a perfect cube.
B) Not a perfect cube
C) Not a perfect cube
D) Yes. 3*3=9
E) Not a perfect cube
F) Yes. 8*8=64
G) Yes. 10*10=100
H) Not a perfect cube
Answer:
28
Step-by-step explanation:
-2+9 (4)=7(4)=28
Answer: <span><span>{x|x ∈ U and 2x is prime} is an empty set.
</span>Justification:
</span>
U = {x|x is a positive integer greater than 1} = {2, 3, 4, 5, 6, ...}<span>
1) {x|x ∈ U and (1/2) x is prime}
Take x = 4 => (1/2) 4 = 4 / 2 = 2 = prime, so this is not empty.
{x|x ∈ U and 2x is prime}
2) 2x = {4, 6, 8, 10, 12, } so none of them is prime, hence this is an empty set.
3) {x|x ∈ U and (1/2) x can be written as a fraction}
Take any x that is odd. For example x = 3
=> (1/2)x = (1/2)3 = 3/2 which is a fraction, so this is not an empty set.
2) {x|x ∈ U and 2x can be written as a fraction}
Take any value of x, for example x = 7 => 2 = 14, and 14 = 28 / 2 so this is not an empty set.
</span>
Answer:
ththe answer is written in the picture.
Answer: speed of plane is 720 km/h
Speed of wind is 80km/h
Step-by-step explanation:
Let x represent the speed of the plane.
Let y represent the speed of the wind.
The plane flies from Atlanta to los Angeles and against the wind in 5hrs and the distance between Atlanta and los Angeles is 3200 km.
Since it flew against the wind, the speed would be x-y km/hour
Distance = speed × time. Therefore
3200 = 5(x - y )
3200 = 5x - 5y - - - - - - - - - 1
the return trip back to Atlanta with the wind only 4 hr. This means that the speed is x+y km/hour. Therefore
3200 = 4(x+y)
3200 = 4x + 4y - - - - - - - - 2
Multiplying equation 1 by 4 and equation 2 by 5, it becomes
12800 = 20x - 20y
16000 = 20x - 20y
Adding both equations, it becomes
28800 = 40x
x = 28800/40 = 720
Substituting x = 720 into 3200 = 5(x - y )
x - y = 3200/5 = 640
y = 720 - 640 = 80
