Which statements are true regarding the system of equations? check all that apply.

8 x + 10 y = 30. 12 x + 15 y = 60.
the lines coincide.
the lines are parallel.
the slopes are equal.
the y-intercepts are different.
the system has one solution.
the system has an infinite number of solutions.
the system has no solution.

Step-by-step explanation:

If the first equation is multiplied by 1.5, it will be transformed into the dependent equation

  12x +15y = 45

This is different from the second given equation, so that 2nd equation is not dependent upon the first. Rather it is the equation of a line parallel to the first. (See below for a graph.)

  The lines are parallel.

  The slopes are equal.

  The y-intercepts are different.

  The system has no solution.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).