State whether the system is consistent and independent, consistent and dependent or inconsistent. y = 0.5x 2y = x + 4 a. consistent and independent c. inconsistent

The correct option is c. The given system is inconsistent.

Step-by-step explanation:

Inconsistent system: If the given system has no solutions, then it is an inconsistent system.

Consistent and independent system: If the given system has only one solutions, then it is an consistent and independent system.

Consistent and dependent system: If the given system has many solutions, then it is an consistent and dependent system.

The given equations are

      ... (1)

Divide the second equation by 2, to rewrite the given equation in slope intercept form.

      ..... (2)

The slope intercept form of a line is

y = mx + b       ....(3)

Where, m is slope and b is y-intercept.

On comparing the (1), (2) and (3), we get the slope of first line is 0.5 and slope of second line is 0.5.

Since the slope of two parallel lines are same, therefore both the given equations are parallel and parallel equations have no solutions.

Therefore option c is correct.

b is the answer that makes most sense

step-by-step explanation:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.