Answer:
The system is consistent; it has one solution ⇒ D
Step-by-step explanation:
A consistent system of equations has at least one solution
- The consistent independent system has exactly 1 solution
- The consistent dependent system has infinitely many solutions
An inconsistent system has no solution
In the system of equations ax + by = c and dx + ey = f, if
- a = d, b = e, and c = f, then the system is consistent dependent and has infinitely many solutions
- a = d, b = e, and c ≠ f, then the system is inconsistent and has no solution
- a ≠ d, and/or b ≠ e, and/or c ≠ f, then the system is consistent independent and has exactly one solution
In the given system of equations
∵ -2y + 2x = 3 ⇒ (1)
∵ -5y + 5x = 12 ⇒ (2)
→ By comparing equations (1) and (2)
∵ -2 ≠ -5
∵ 2 ≠ 5
∵ 3 ≠ 12
→ By using the 3rd rule above
∴ The system is consistent independent and has exactly one solution
∴ The system is consistent; it has one solution
Answer:
The18th term of the given sequence is -128
Explanation:
To find the 18th term of the sequence:
42, 32, 22, 12, ..., we need to find the nth term of the sequence first.
The nth term of a sequence is given be the formula:

Where a is the first term, and d is the common difference.
Here, a = 42, d = 32 - 42 = -10

To find the 18th terem, substitute n = 18 into the nth term
The cheetah runs 2 meters/sec faster than the gazelle. Eventually the cheetah will overcome the gazelle. Since distance = rate times time, time = distance/rate.
Thus,
300 meters / (2 meters/sec) = 150 sec = 2 min 30 sec
Answer
The measurement of the missing sides are 4 cm on each side
Step-by-step explanation:
multiply 5 times 2 (5x2=10) take away the 10 and 18 and the answer for it is the answer for the whole thing.
Answer:
Large baking dish of cylinder, cone and sphere.
Step-by-step explanation:
When we compute the volume of each of the small and large baking dish taking
=3.14, we get
Volume of cylinder (small dish)=
(r^2)(h)
=3.14(
)^2*3
= 
= 21.195
Volume of cylinder (large dish)=
(r)^2(h)= 3.14*(3)^2(3)
=84.78
Similarly, volume of cone (smaller dish)= 
= 7.065
Volume of cone (larger dish)= 84.78
Volume of sphere(smaller dish)= 
= 14.13
Volume of sphere (larger dish) = 85.17 (approx)
Hence, we get that larger baking dish have approximately same volume.
Therefore, large baking dish of cylinder, cone, sphere will be chosen.