A triangle is formed with edges along the line y = 2/3*x + 5, the x-axis, and the line x = k. If the area of the triangle is less than 50, find the sum of all possible integral values of k.

Guest Feb 15, 2022

#1**+2 **

You can make the equation: \({(x+7.5)}{({2\over3}x+5)}<100\)

The second term is the height of the triangle, and the first term is the base.

When you solve the equation, you find that \(x\leq4.74\).

This means that the possible ranges are: \(-7\leq x\leq4\).

Of the values, \(-4\leq x \leq4\) cancel out, making the sum: \(\color{brown}\boxed{-15}\)

BuilderBoi Feb 15, 2022

#1**+2 **

Best Answer

You can make the equation: \({(x+7.5)}{({2\over3}x+5)}<100\)

The second term is the height of the triangle, and the first term is the base.

When you solve the equation, you find that \(x\leq4.74\).

This means that the possible ranges are: \(-7\leq x\leq4\).

Of the values, \(-4\leq x \leq4\) cancel out, making the sum: \(\color{brown}\boxed{-15}\)

BuilderBoi Feb 15, 2022