Carlos graphs the equations [tex]y = 0.5x^2 + 3[/tex] and [tex]y = -4x^2 + 24x - 35[/tex] and generates the graph below.

Which conclusion is supported by the graph?

A. The equation [tex]0.5x^2 + 3 = -4x^2 + 24x - 35[/tex] has no real solutions.
B. The equation [tex]0.5x^2 + 3 = -4x^2 + 24x - 35[/tex] has one real solution.
C. The equation [tex]0.5x^2 + 3 = -4x^2 + 24x - 35[/tex] has two real solutions.
D. The equation [tex]0.5x^2 + 3 = -4x^2 + 24x - 35[/tex] has three real solutions.

The question asked for the number of real solutions to a quadratic equations. Without the graphic representation, it's not possible to provide a definite answer. However, understanding of quadratic equations, the quadratic formula, and the concept of a discriminant was explained.

Explanation:

The question asked is about the number of real solutions to the equation 0.5x² + 3 = -4x² + 24x - 35. This is a problem in algebra and is solved by setting the two equations equal to each other and solving for x. You start by rewriting equation as 0.5x² + 4x² = 24x + 38. Combine like terms to get 4.5x² - 24x - 38 = 0.

Quadratic Equations are of the form ax² + bx + c = 0 and have a formula for solutions, x = [-b ± sqrt(b^2 - 4ac)] / 2a. Substituting a = 4.5, b = -24, c = -38 into the formula will determine the number of solutions. The formula under the square root sign, b² - 4ac, is called the Discriminant.

If the Discriminant is greater than zero, the equation has two real solutions. If it equals zero, the equation has one real solution. If less than zero, there are no real solutions.

Therefore, you have to calculate the Discriminant to find out the number of solutions. Without the graph, it's impossible to provide a definite answer.

Learn more about quadratic equations here:

https://brainly.com/question/30098550

#SPJ11