(CMRJ 2014) - Question Medium of Mathematics

Consider the linear system below: 2x + 3y = 10 5x - 4y = -7 Transform this linear system into a matrix form using a matrix A and a column vector X, representing the unknowns. Write down the resulting matrix equation and inform what is the dimension of matrix A.

João is in a candy store and wants to buy a chocolate bar that costs R$3.50. He hands a R$10.00 bill to the cashier. What is the change amount that João should receive? Select the correct alternative.

In a civil engineering project, an architect needs to divide a rectangular plot of land into two equal parts for the construction of two semi-detached houses. The coordinates of the vertices of the land on the Cartesian plane are A(0, 0), B(30, 0), C(30, 20), and D(0, 20). Using concepts of analytic geometry, determine the coordinates of the point that represents the midpoint of side CD of the land, which will be the dividing point between the two new properties. Then, verify if the obtained midpoint point is indeed on segment CD, ensuring the accuracy of the project. Explain the reasoning used to determine the coordinates and to verify the positioning of the midpoint on the land.