[User]
Considering the functions f(x) = ax and g(x) = px^2 + qx, where a, p, q can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 1 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}

dataset: MATH


[User]
If a, b, p are integers between 1 and 5 inclusive, how many different combinations of these values make the functions f(x) = asin(bπx) + 2 and g(x) = px intersect at least 6 times in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p, q from 1 to 5, how many combinations can we have so that the function f(x) = ax^2 + bx and g(x) = px^2 + qx have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p, q from 1 to 5, how many combinations can we have so that the function f(x) = asin(bπx) and g(x) = pcos(qπx) - 3 have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
If a, b, p are integers between 1 and 5 inclusive, how many different combinations of these values make the functions f(x) = ax^2 + bx and g(x) = px + 3 intersect at least 1 times in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p from 1 to 5, how many combinations can we have so that the function f(x) = ax^2 + bx and g(x) = px have at least 2 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Considering the functions f(x) = asin(bπx) and g(x) = psin(qπx), where a, b, p, q can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 7 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p, q from 1 to 5, how many combinations can we have so that the function f(x) = ax^2 + bx and g(x) = px^2 + qx - 2 have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p from 1 to 5, how many combinations can we have so that the function f(x) = ax^2 + bx and g(x) = px have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Considering the functions f(x) = ax and g(x) = px + 3, where a, p can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 1 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, p, q from 1 to 5, how many combinations can we have so that the function f(x) = ax and g(x) = px^2 + qx have at least 2 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
If a, b, p, q are integers between 1 and 5 inclusive, how many different combinations of these values make the functions f(x) = acos(bπx) and g(x) = psin(qπx) intersect at least 2 times in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
If a, b, p, q are integers between 1 and 5 inclusive, how many different combinations of these values make the functions f(x) = ax^2 + bx and g(x) = pcos(qπx) intersect at least 1 times in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p, q from 1 to 5, how many combinations can we have so that the function f(x) = asin(bπx) and g(x) = pcos(qπx) have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, p, q from 1 to 5, how many combinations can we have so that the function f(x) = ax and g(x) = px^2 + qx have at least 3 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Considering the functions f(x) = ax^2 + bx and g(x) = px^2 + qx, where a, b, p, q can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 1 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p from 1 to 5, how many combinations can we have so that the function f(x) = ax^2 + bx and g(x) = px have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Considering the functions f(x) = acos(bπx) and g(x) = pcos(qπx) - 2, where a, b, p, q can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 5 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Considering the functions f(x) = ax^2 + bx and g(x) = px^2 + qx, where a, b, p, q can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 1 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, p, q from 1 to 5, how many combinations can we have so that the function f(x) = ax + 1 and g(x) = px^2 + qx have at least 3 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p, q from 1 to 5, how many combinations can we have so that the function f(x) = acos(bπx) and g(x) = pcos(qπx) + 2 have at least 7 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Considering the functions f(x) = ax^2 + bx + 3 and g(x) = px^2 + qx, where a, b, p, q can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 1 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p, q from 1 to 5, how many combinations can we have so that the function f(x) = ax^2 + bx and g(x) = px^2 + qx - 5 have at least 2 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
If a, b, p, q are integers between 1 and 5 inclusive, how many different combinations of these values make the functions f(x) = ax^2 + bx and g(x) = px^2 + qx intersect at least 3 times in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
If a, p are integers between 1 and 5 inclusive, how many different combinations of these values make the functions f(x) = ax and g(x) = px intersect at least 2 times in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, b, p, q from 1 to 5, how many combinations can we have so that the function f(x) = acos(bπx) - 1 and g(x) = psin(qπx) - 1 have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, p, q from 1 to 5, how many combinations can we have so that the function f(x) = ax - 5 and g(x) = px^2 + qx - 1 have at least 1 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Pick values for a, p from 1 to 5, how many combinations can we have so that the function f(x) = ax and g(x) = px have at least 3 intersections in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
If a, b, p, q are integers between 1 and 5 inclusive, how many different combinations of these values make the functions f(x) = ax^2 + bx and g(x) = px^2 + qx intersect at least 1 times in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Considering the functions f(x) = ax^2 + bx - 3 and g(x) = px^2 + qx, where a, b, p, q can each take integer values from 1 to 5, how many different combinations of parameter values result in at least 1 intersection points in the range [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}