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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.

Feb 15, 2022

#1
+2432
+1

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: $$\color{brown}\boxed{-15}$$

Feb 15, 2022

#1
+2432
+1

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