Answer:
x = 16
y = -24
Step-by-step explanation:
Recall that the addition of matrices is done when matrices are of the same dimension. In this case, you are in fact adding matrices of the same dimension (dimension 1x2). Recall as well that in the addition of matrices, the elements of each matrix combine only with the element located in the exact same position in the other matrix.
So for this case the first element of the first matrix "16" combines with the first element of the second matrix "0" resulting in an element of value16 + 0 =16 in the new matrix.
Equally, the second element of the first matrix "-24" combines with the second element of the second matrix, resulting in : -24 + 0 = -24.
Therefore, the matrix resultant from this addition is: [16 -24] (same form of the first matrix, which indicates that adding a zero matrix to an existing matrix will not change the first matrix.
Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.

Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:

The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.
Answer:
c
Step-by-step explanation:
you divide each side by four to get a=2.5 b=2.5 and c=3
From the given question we come to know of certain number of facts and they are:
At 1:00 PM the water level of the pond was = 13 inches
At 1:30 PM the water level of the pond was = 18 inches
At 2:30 PM the water level of the pond was = 28 inches
From the above given facts we can easily find the amount of water changing every half an hour.
Amount of increase in water from 1:00PM to 1:30 PM = (18 - 13) inches
= 5 inches
Amount of increase in water level from 1:30PM to 2:30PM = (28 -18) inches
= 10 inches
From the above two deductions we can come to the conclusion the the constant rate of change in water level is 5 inches for every half an hour.