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Math 125 EXAM 1 Determine whether the statement is true or false. 1) - 7 2 < 6 2 - 9 2 - 49 < 36 - 81 - 49 < - 45 True Decide if the statement is true or false. 2) - 11 - -13 -11 -13 True *Evaluate the expression for the given values. If necessary, round to the nearest tenth. 3) 7x 2 - 2y - x 2 - y3 x = -4, y = -3 7 -4 2 - 2 -3 - -4 2 - -3 3 7 16 + 6 - 16 - (-27) 112 - 10 + 27 129 State the phrase as a mathematical expression. Use x to represent the variable. 4) The quotient of a number less than four and twice a number 4-x 2x Provide an appropriate response 5) Give an example of an expression which includes the use of distributive property and at least one fraction. 3 x+ 1 2 6) Give an example of the inverse property of multiplication using a negative number, and identify the multiplicative inverse by its commonly used name. -4- 1 =1 4 - 1 is the reciprocal 4 Conplete the problem to illustrate the commutative property of addition. 7) 2 + (x + 7) = 2 + (7 + x) Tell whether the statement is true or false. If the statement is false, explain why and give an example of a number that makes it false. 8) Some integers are irrational numbers. False, no integer is irrational. ex. 5 9) Some real numbers are integers. True 1 *Identify the composite integer(s) from the set below. 10) {-2, 0, - .3, 5, -24, 7 1 26 , - 1 , 9.2, , 4, - 7, 1} 8 7 13 4 Find the measure of each marked angle. 11) (2x + 45)° (5x + 6)° 2x + 45 = 5x + 6 39 = 3x 13 = x 2 13 + 45 26 + 45 71 both angles are 71° Find each unit cost to two decimal places. Tell which brand is the better buy. 12) Brand A 24 oz for $18.96 Brand B 21 oz for $15.96 Brand A $18.96 = $ .79/oz 24oz Brand B $15.96 = $ .76/oz 21oz Simplify the expression. 4 1 7 1 3 y+2 13) - (z + 12) - z - y - 6 + 3 6 9 12 8 - 4 1 28 3 19 z - 16 - z y-6+ y+ 3 6 36 36 8 - 8 1 25 19 z - 22 - z y+ 6 6 36 8 - 9 176 25 19 zy+ 6 8 36 8 - 3 157 25 zy 2 8 36 Solve the equation. If it is an identity or contradiction, then indicate so. 14) 6(x + 2) - (6x + 12) = 0 6x + 12 - 6x - 12 = 0 0=0 , ) identity 2 15) - - 1 3 1 y - (y - ) = ( y - 4) 3 8 72 1 3 1 1 y-y+ = y3 8 72 18 72 - 1 3 1 1 y - y+ y72 = 3 8 72 18 - 24y - 72y + 27 = y - 4 -96y + 27 = y - 4 31 = 97y 31 =y 97 16) 5 3x + 10 = 2 7x 5 7x = 2 3x + 10 35x = 6x + 20 29x = 20 20 x= 29 Use a proportion to solve the following problem. 17) A tree casts a shadow 28 m long. At the same time, the shadow cast by a 61-cm tall statue is 92 cm long. Find the height of the tree. Round results to the nearest unit. 28m 92cm = xm 61cm 92x = 61 28 1708 x= 92 x 19m Write an equation and use it to solve the problem. 18) Find the measure of an angle, if its supplement measures 41° more than twice its complement. 180 - x = 2 90 - x + 41 180 - x = 180 - 2x + 41 x = 41 19) A square plywood platform has a perimeter which is 10 times the length of a side, decreased by 42. Find the perimeter. 4x = 10x - 42 -6x = - 42 x=7 P = 4(7) = 28 20) A bag of fertilizer covers 500 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 310 feet by 140 feet. (think carefully about your final answer.) 500sqft 310 140 = 1 bag x bags 500x = 43400 x = 86.8 87 bags 3 21) In a chemistry class, 8 liters of a 4% silver iodide solution must be mixed with a 12% solution to get a 6% solution. How many liters of the 12% solution are needed? round answer to the nearest tenth, if necessary. 8 .04 + .12x = .06 x + 8 .32 + .12x = .06x + .48 .06x = .16 x 2.7 liters 22) A paint mixture contains 29 gallons of base for every gallon of color. In 1470 gallons of paint, how many gallons of color are there? base + color = paint mixture 29c + c = 1470 30c = 1470 c = 49 gallons 23) Roberto invested some money at 8%, and then invested $2000 more than twice this amount at 11%. His total annual income from the two investments was $3520. How much was invested at 11%? .08x + .11 2x + 2000 = 3520 .08x + .22x + 220 = 3520 .30x = 3300 x = 11,000 2 11,000 + 2000 22,000 + 2000 $24,000 24) From a point on a straight road, John and Fred ride bicycles in opposite directions. John rides 32 miles in the same amount of time that Fred rides 48 miles. John rides 4 miles per hour slower than Fred. Find John's rate. John Fred 32 = r - 4 t 32 =t r- 4 48 = rt 48 =t r 32 48 = r- 4 r 32r = 48 r - 4 32r = 48r - 192 192 = 16r r = 12 12 - 4 = 8mph is John's rate Bonus. Write an equation and use it to solve the problem. (10 points) 25) If three times the smaller of two consecutive integers is added to four times the larger, the result is 46. Find the smaller integer. 3x + 4 x + 1 = 46 3x + 4x + 4 = 46 7x = 42 x=6 4