The figure shows two triangles on a coordinate grid: The image is pinned 1)A translation 5 units up followed by a 180-degree counterclockwise rotation about the origin

2) A translation 5 units up followed by a 270-degree counterclockwise rotation about the origin

3) A 180-degree counterclockwise rotation about the origin followed by a translation 5 units to the left

4) A 270-degree counterclockwise rotation about the origin followed by a translation 5 units to the left

Use addition and subtraction to simplify the following polynomials. a. add polynomials: (3 – 4x + 8x^2) + (–6 + 2x – 5x^2) step 1: rewrite the polynomials without the parentheses. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial. b. subtract polynomials: (3x – 5 – 7x^2) – (–2 + 6x^2 – 5x) step 1: rewrite the polynomials without the parentheses. remember to multiply each term in the second parentheses by –1. show your work. step 2: write the polynomial in descending order and use parentheses around like terms. step 3: add the like terms identified in step 2 to simplify the polynomial.

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

Michelle is planting flowers in her garden. she wants the ratio of daises to carnations to be 3 to 2. michelle wants to plant a total of 35 flowers. how many daises should she plant?