determine which system below will produce infinitely many solutions.

2x + 5y = 24
2x + 5y = 42
3x − 2y = 15
6x + 5y = 11
4x − 3y = 9
−8x + 6y = −18
5x − 3y = 16
−2x + 3y = −7

The system of equations are

Equations (1) and (2) are same and these two given equations represents the same line.

Therefore the given system is consistent and  it has an infinite number of solutions, and also it is dependent

Step-by-step explanation:

Given system of equations is

To verify that the given system of equations have infinitely many solutions :

Equation (1) is

Equation (2) becomes

Dividing by (-2) on both sides we get

Therefore Equations (1) and (2) are same and these two given equations represents the same line.

Therefore the given system is consistent and  it has an infinite number of solutions, and also it is dependent

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12