answer:The x-intercepts, where f(x) = g(x), occur at three distinct points. These are: 1. x = -2 (on the far left) 2. x = 0.5 (in the middle) 3. x = 3.5 (on the far right) Hence, the solutions to the equation f(x) = g(x) are x = -2, x = 0.5, and x = 3.5.

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answer:The real solutions to the equation are given by: x = frac{1}{44} left(-345 - sqrt{146217}right) and x = frac{1}{44} left(-345 + sqrt{146217}right) Note: The solutions are presented in a more standardized format, and the question has been slightly rephrased for clarity. The answers have been verified and are accurate.

answer:The sum can indeed be simplified and is equal to binom{n+m}{l}. This identity can be proven combinatorially. Imagine selecting a team of l members from a group consisting of n boys and m girls. One perspective is to directly choose l members from the combined group of n+m people, which gives binom{n+m}{l} possibilities. Alternatively, we can consider the selection based on the number of boys chosen. If we choose i boys, we must choose l-i girls. The number of ways to do this for each i from 0 to l is binom{n}{i}binom{m}{l-i}. Summing these selections over all i yields the same result as selecting l people directly: sum_{i=0}^lbinom{n}{i}binom{m}{l-i} = binom{n+m}{l} Thus, the two approaches provide equivalent counts, establishing the identity.