MAT 090 Midterm Answer Key

92 MAT 090 Beginning Algebra Midterm NAME: KEY 1. State whether the following statements are TRUE or FALSE. No explanation is needed. DA3 26 = 5 15 FALSE B)-3-9 TRUE 2+4x-6x NOT LIKE TERMS FALSE 3.2 5 ک -3.3 -9 32. Translate the following math statement into a verbal statement: 2x-5 Many right an ankness- HERE IS NE: DOUBLE A NUMBER MINUS FIVE. 3. Use the commutative law of multiplication to write an equivalent expression for (x+3)(x+5) (X+5) (x+3) 24. Use the associative law of addition to write an equivalent expression for (2x+3y)+5 2x + (3y +5) 5. Use PRIME FACTORIZATION to help you simplify the following fractions: 30 5.9 533 3 45 3.10 3.2.8 2 = 6. Perform the indicated operations below. Answers should be in lowest terms (you do not need to use prime factorization). SHOW YOUR WORK. 1 LED 12 A) 2 4 3 92 + 4 3 3.9 5.1 414 4.3 3 1 27 D) 60+3(-4) 20(-4) 12 E)(-2)-2(-2)(3)-32 4-2(-6)-9 -80 4+12-9 16-9 3 C)-12-(-6)-4+(-2) -12+6+(-4)+(-2) -6+(-6) -12 7 4-(-12)-9 29 3 7. Simplify the following expression: 16 8. Solve the following equations. To receive full credit, you must show your work. 3 A) 2x-5-3x+9 -3 +5-3x+5 -X = 14 X = -14 C) 5(x+1)-(x-5)=2x+2(x+5) 5x+5-x+5 = 2x+2x+10 4x +10 4x+10 IDENTITY x= all real H's 3 X= 19 9. Solve the following formulas for the indicated variable. Please show your work. (3) x+y A) A=+ solve for x 3 3A=3(4) 3A = x+y X=3A-y 3 B) 2x+3y=6 solve for y. -2x -2x 3-2 = 3 y=-x+2 10. Solve the following inequality. Put your final answer in interval notation. A) 4-5x2x48 -457x -() -(-x) ->x X 00) (-00,-314) 31 11. SET UP and SOLVE the following problems. To receive full credit, you need to clearly label your unknown(s) and set up an equation(s). A) In a recent survey, seven students said that they loved the Dodgers. This represented 35% of the students in the survey. How many students participated in the survey? PACT = 35 35 35 70035T 205 TOTAL 100 700= 35T 20 =T B) In planning for a wedding, Kathleen and Gabe have to stay within a budget of $3,500 for food. Algebra Catering Services costs $500 to use their services and then they charge $15 per plate. How many people can Kathleen and Gabe invite to their wedding dinner? 500+15P=3500 -500 500 P=200 200 PEOP 150 = 3000 C) The perimeter of a rectangular lot is 210 feet. The width of this lot is 25 feet longer than its length. Find the dimensions of this rectangular lot. W=L+25 210=2L+2(L+25) 210=2L+21+520 L= 40 F P=2L+20 210=4L+50 W=40+2 210=2L+20 -50 -50 W=65- 100=4 12. SET UP ONLY the following word problems. Define and label your unknowns, and set up the equation(s) you would use to solve the word problem. You do not need to solve your equations. SET UP ONLY. A) Double the difference of a number and three is the quotient of that number and five increased by six. 2(x-3) = +6 B) Find the base of a triangle whose area is 44 ft² and whose height is three more than double the base. A=BH A=2B+3 44=2BH C) A hospital nutritionist put a meal together for a patient. There were 640 total calories in the meal. The calories from carbohydratesser 100 more than the calorics from protein. The calories from that were one-fifth the amount of the calories from protein. How many calories came from fats, carbohydrates, and protein? FAT F+C+P=640 C=P+100 F=P CAMBS