# Mathematics Help

1. Perform the indicated operation and simplify. You must show all work. =8/(2m^2-7m-4)+7/(10m^2+3m-1)-4/(5m^2-21m+4)
2. Find complex number solutions. Solution: 2/(t+3)-3t/(t-3)=5/(t^2-9)
3. Simplify the complex rational expression.(4/(x^2+3x-18)+2/(x^2+4x-21))/(4/(x^2+13x+42)+2/(x^2+2x-15))
4. divide and simplify. (x^3-8)/(x^2+2x+4)÷(x^2-2^2)/(x^2+6x+8)
5. Multiply and simplify. f(a)=(110ab+110b)(30a-100)/(3a^2-10a)(11a^2 b-11b)
6. Solve the rational equation. f(x)=(x^2-8xy+16y^2)/(x^2-4xy)
7. Simplify right hand side f(x)=(16x^2-9)/(512x^3+216)
8. Find the domain of rational function f(x)=(x-7)/(x^3-〖7x〗^2-100x-700)
9. The function f(x) = 2.9√x + 20.1 models the median height, f(x), in inches, of boys who are x months of age. The graph of f is shown below.
10. Graph the standard quadratic function, f(x) = x^2. Then use transformations of this graph to graph the function h(x) = 〖(x - 2)〗^2 + 1. Using the coordinate template below, draw the graph of h(x).
11. Use the graph of y = f(x) to graph the function g(x) = f(2x). Use the coordinate template below to draw the graph of g(x)
12. Use the graph of y = f(x) to graph the function g(x)=f(x+1)+ 2. Use the coordinate template below to draw the graph of g(x).
13. The bar graph below shows that as costs changed over the decades, Americans devoted less of their budget to groceries and more to health care.
14. Write an equation in slope-intercept form of a linear function f whose graph satisfies the following conditions. The graph of f passes through (-6, 4) and is perpendicular to the line that has an x-intercept of 2 and a y-intercept of -4.
15. Find the average rate of change of the function f(x)=x^2+2x from x_1 =3 to x_2 = 5.
16. Write an equation for line L in point-slope form and slope-intercept form.
17. Using the graph below, list the slopes m1, m2, m3, and m4 in order of decreasing size.
18. Give the slope and y-intercept of the line whose equation is f(x)= 3/4 x-2. Then graph the linear function. Use the coordinate template below to draw the graph of f(x).
19. Using the coordinate template below, draw a graph with the square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Once the functions are graphed, describe how the graph of g is related to the graph
20. (2 Points) Use transformations of f(x)= 1/x or f(x)= 1/x^2 to graph the rational function (x)=1/〖(x+2)〗^2 .
21. (1 Point) Find the horizontal asymptote, if there is one, of the graph of the rational function g(x)=(12x^2)/(〖3x〗^2+1). Describe the steps to complete this and provide your answers. Horizontal Asymptote:
22. (1 Point) Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the rational function g(x)=(x-3)/(x^2-9) . Describe the steps to complete this and provide your answers. Vertical Asymptotes: Holes at x =
23. Question 12: (1 Point) Refer to the graph of the rational function for Exercises 15-20 on page 427 and complete the following statements.
24. (1 Point) Refer to the diagram of the rectangular box for Exercise #52 on Page 393. Use synthetic division to show that 2 is a solution of the polynomial equation (show your work) 2h^3+14h^2-72
25. Question 10: (1 Point) Describe the steps for dividing the following two polynomials using synthetic division. State the quotient, q(x), and the remainder, r(x).
26. Question 9: (1 Point) Describe the steps for dividing the following two polynomials using long division. State the quotient, q(x), and the remainder, r(x).
27. (2 Points) Refer to the graphs and description for Application Exercise #73 on Page 379. Then provide the following information
28. (2 Points) For the polynomial function f(x)=-x^4+4x^2
29. (1 Point) Using the Leading Coefficient Test, what is the end behavior of the graph of the polynomial function (x)=-5x^4+7x^2-x+9 ?
30. (1 Point) Which function is a polynomial function with degree 5?
31. (2 Points) A ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), in feet, can be modeled by f(x)=〖-0.8x〗^2+2.4x+6 , where x is the ball’s horizontal distance, in feet, from where it was thrown.
32. Solve this (2 Points) For the quadratic function f(x)=4-(〖x-1)〗^2
33. (1 Point) Find the coordinates of the vertex for the parabola defined by the quadratic function. The vertex is at x = _____ and y = _____