Mrs. Smith needs fabric pieces for an art project for her students. The pieces will be cut to two rectangular sizes. One has side lengths of x and (x + 5) cm. The other has side lengths of x and (x + 10) cm. Determine a simplified expression for the area of fabric needed if 12 students choose the first size and 14 students choose the second size. Show all of your work and use diagrams to help explain your thinking.

Of four points are collinear, they are also coplanar

17. a researcher measures three variables, x, y, and z for each individual in a sample of n = 20. the pearson correlations for this sample are rxy = 0.6, rxz = 0.4, and ryz = 0.7. a. find the partial correlation between x and y, holding z constant. b. find the partial correlation between x and z, holding y constant. (hint: simply switch the labels for the variables y and z to correspond with the labels in the equation.) gravetter, frederick j. statistics for the behavioral sciences (p. 526). cengage learning. kindle edition.

Which of the statements about the graph of the function y = 2x are true? check all of the boxes that apply. the domain is all real numbers x because the exponent of 2 can be any real number when the x-values increases by 1 unit, the y-value multiplies by 2. the y-intercept is (0, 1). the graph never goes below the x-axis because powers of 2 are never negative. the range is all real numbers.