Answer:
The ones that give a rational number answer are:
C+D
A*B
C*D
A*A
Step-by-step explanation:
A+B does not give a rational number answer; √3+2√3 = 3√3
C+D is a rational number; √25=5 and √16=4; 5+4=9.
A+D is not a rational number; √3+√16 = √3+4
A*B is a rational number; √3*2√3 = 2√9 = 2*3 = 6
B*D is not a rational number; 2√3*√16 = 2√3*4 = 8√3
C*D is a rational number; √25*√16 = 5*4 = 20
A*A is a rational number; √3*√3 = √9 = 3
Answer:
Step-by-step explanation:
2x - 3y = 9
-5x - 3y = 30
For simplicity, let's eliminate the y variable in this system by multiplying the second equation by -1:
-1·(-5x - 3y = 30)
==> -1·-5x - -1·3y = -1·30
==> 5x + 3y = -30
Add this equation to the first original equation:
2x - 3y = 9
+ 5x + 3y = -30
__________________
2x + 5x - 3y + 3y = 9 + -30 ==> 7x + 0y = -21 ==> 7x = -21
7x = -21
7x/7 = -21/7 ==> x = -3
Plug this value for x into either of the original equations from the system (I will use the first equation) to solve for y:
2x - 3y = 9
2·(-3) - 3y = 9
-6 - 3y = 9
Add 6 to both sides of the equation:
-6 + 6 - 3y = 9 + 6
-3y = 15
Divide both sides of the equation by -3:
-/-3 = 15/-3
y = -5
<h2>
Option C is the correct answer.</h2>
Step-by-step explanation:
Diameter, D = 42 feet
Circumference = πD = π x 42 = 131.95 feet
Number of rotations per minute = 3
Total time = 5 minutes
Total rotations = 5 x 3 = 15
Distance traveled per rotation = 131.95 feet
Distance traveled in 15 rotations = 15 x 131.95 = 1978 feet
Option C is the correct answer.