Math - Elementar Algebra Final Eam, Fall Name: Date: Score: / Show the necessar work on the test cop. For an of the graphs use a straightedge to receive full credit. Place our answers in the blanks provided to the right of the problem. The points for each problem are to the right of the blank.. Write the following phrase as an algebraic epression and simplif if possible. Let n represent the unknown number. Three times the sum of a number and, subtracted from. () (simplified) (). Solve each equation. (a) + = () (b) + ( ) = () (c).( + ) =.( ) +. (). Solve A = P + PRT for R. R = ()
. A small plane can fl against the wind, blowing at a rate of miles per hour, a distance of miles in hours. What would be the speed of the plane in still air?. Solve. + =. Find last ear s salar and the dollar amount of the pa raise if after a % increase this ear s salar is $,. Last ear s salar: () Dollar amount of pa raise: () 7. An architect is planning the laout of a new office building, measuring sqft. Building code requires sqft for hallwas and fire-escapes, and offices have to measure at least sqft. How man offices can the architect design into the building? Epress the situation as an inequalit and then solve it. Inequalit: () Solution: ()
8. Solve the compound inequalit. (a) Write the solution in interval notation and (b) graph the solution set. 7 + < 7 (a) Interval: () -. -. -. -. -....... (b) Graph: () 9. Graph the linear equation b finding and plotting its intercepts. + = Intercepts: () Graph: () - - - - - - - - - - - -. Graph the linear equation and find the slope of the line. Write N if the slope is not defined. = Slope: () Graph: () - - - - - - - - - - - -
. Find the slope and the -intercept of the line. Use them to graph the equation. + = Slope: () -Intercept: () Graph: - - - - - - - - - - - -. (a) Find the slope-intercept form of the line given b = +. (b) Is the line given b this equation parallel, perpendicular, or neither to the line given b the equation = +? (a) () (b) (). Find an equation of the line that passes through (-,7) and (,-). Your answer should use function notation, that is, f() = a + b.
. Given f = {(, ), (, ), (, ), (, )}. State the domain. Domain: () State the range. Range: () Is the relation a function? (Y/N): (). Given the function G(t) = t t. Find G( ). (). Graph the nonlinear function f() =. State the domain and the range of the function. - - - - - - - - - - - - Graph: Domain: () Range: () 7. Graph the solution of the sstem of linear inequalities. { + >
Graph: () - - - - - - - - - - - - 8. Solve the sstem of equations b using a method of our choice. Write an ordered pair if there is one solution; otherwise, write N if there is no solution or I if there are infinitel man solutions. { = = 7 () 9. Suppose ou work in a lab. You need liters of an 8% acid solution for a certain test, but our supplier onl ships a % solution and a % solution. You decide to make the 8% solution ourself b miing the two available solutions. How man liters of % solution and % solution should ou order? Use a sstem of equations where represents the amount of the % acid and represents the mount of the % acid needed. Sstem of equations: (I) () (II) () Solution:
. Convert from scientific to standard notation:.7. (). Evaluate the epression without converting dividend and divisor into standard notation. Present the quotient in scientific notation. (. 7 ) ( ) (). Simplif the following epressions, and write the results using positive eponents. (a) ( )( ) () (b) a (b ) 8ab (c) ( w w ) 7
. Perform the indicated operations. (a) ( + 8) ( + 7 + ) () (b) 9a b(a a b + ab ) () (c) ( )( + ) () (d) (m n mn + m ) (mn ) () (e) + +. Factor the following polnomials completel. (a) + () 8
(b) 7a a a + (c) b + 9b (d) 8p q 8q (). Solve the following polnomial equations. (a) v(v + ) = (b) w = 8w 9