Solve the equation. check your solution. √2x + 7 = √5x - 8

Find a number such that if you add 8 and divide the result by 4 you will get the same answer as if you subtracted 3 from the original number and divided by 2

Which approach to the theory-and-research cycle does the following sequence reflect: (1) specific observations suggest generalizations, (2) generalizations produce a tentative theory, (3) the theory is tested through the formation of hypotheses, and (4) hypotheses may provide suggestions for additional observations?

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe