Sophia’s math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test?

There are 30 questions worth 3 points and 10 questions worth 4 points.

Step-by-step explanation:

If you try to plug in some numbers, you can try 20 questions for 4 and 20 questions for 3. That would add up to 140 questions. That means that the questions worth 4 points will have to be reduced that the ones worth 3 will have to increase. If you try 30 times 3, it will equal 90. You then try 10 times 4 and that equals 40. If you add 90 and 40, then you get 130. Therefore, there are 30 questions worth 3 points and 10 questions worth 4 points. :D

45

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: