Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Elementary Technical Mathematics
Find each product: (t+10)2Find each product: (4y+5)(4y5)Find each product: (200+5)(2005)Find each product: (xy4)2Find each product: (x2+y)(x2y)Find each product: (ab+d)2Find each product: (ab+c)(abc)Find each product: (z11)2Find each product: (x3+8)(x38)Find each product: (st7)2Find each product: (w+14)(w14)Find each product: (x+y2)(xy2)Find each product: (1x)2Find each product: (x+5)2Find each product: (x6)2Find each product: (x+7)(x7)Find each product: (y12)(y+12)Find each product: (x3)2Find each product: (x+4)2Find each product: (ab+2)(ab2)Find each product: (m3)(m+3)Find each product: (x2+2)(x22)Find each product: (m+15)(m15)Find each product: (r15)2Find each product: (t+7a)2Find each product: (y35)2Find each product: (4x2)2Find each product: (10x)(10+x)Find each product: (ay23)(ay2+3)Factor completely. Check by multiplying the factors: a2+8a+16Factor completely. Check by multiplying the factors: b22b+1Factor completely. Check by multiplying the factors: b2c2Factor completely. Check by multiplying the factors: m21Factor completely. Check by multiplying the factors: x24x+4Factor completely. Check by multiplying the factors: 2c24c+2Factor completely. Check by multiplying the factors: 4x28EFactor completely. Check by multiplying the factors: y236Factor completely. Check by multiplying the factors: a264Factor completely. Check by multiplying the factors: 5a2+10a+5Factor completely. Check by multiplying the factors: 9x225Factor completely. Check by multiplying the factors: 181y2Factor completely. Check by multiplying the factors: 16x2100Factor completely. Check by multiplying the factors: 49a4Factor completely. Check by multiplying the factors: m22mn+n2Factor completely. Check by multiplying the factors: 49x264y2Factor completely. Check by multiplying the factors: x2y21Factor completely. Check by multiplying the factors: 1x2y2Factor completely. Check by multiplying the factors: c2d216Factor completely. Check by multiplying the factors: 4x212x+9Factor completely. Check by multiplying the factors: 16x21Factor completely. Check by multiplying the factors: R2r2Factor completely. Check by multiplying the factors: 36x212x+1Factor completely. Check by multiplying the factors: 49x225Factor completely. Check by multiplying the factors: 1100y2Factor completely. Check by multiplying the factors: y210y+25Factor completely. Check by multiplying the factors: x2+6x+9Factor completely. Check by multiplying the factors: b29Factor completely. Check by multiplying the factors: 16c2d2Factor completely. Check by multiplying the factors: m2+22m+121Factor completely. Check by multiplying the factors: n230n+225Factor completely. Check by multiplying the factors: 4m29Factor completely. Check by multiplying the factors: 16b281Factor completely. Check by multiplying the factors: 4x2+34x+36Factor completely. Check by multiplying the factors: 2y2+12y18Factor completely. Check by multiplying the factors: 27x33Factor completely. Check by multiplying the factors: 225x49x2Factor completely. Check by multiplying the factors: am214am+49aFactor completely. Check by multiplying the factors: bx212bx36bFactor completely: 5x22812Factor completely: 4x24x3Factor completely: 10x229x+21Factor completely: 4x2+4x+1Factor completely: 12x228x+15Factor completely: 9x236x+32Factor completely: 8x2+26x45Factor completely: 4x2+15x4Factor completely: 16x211x5Factor completely: 6x2+3x3Factor completely: 12x216x16Factor completely: 10x235x+15Factor completely: 15y2y6Factor completely: 6y2+y2Factor completely: 8m210m3Factor completely: 2m27m30Factor completely: 35a22a1Factor completely: 12a228a+15Factor completely: 16y28y+1Factor completely: 25y2+20y+4Factor completely: 3x2+20x63Factor completely: 4x2+7x15Factor completely: 12b2+5b2Factor completely: 10b27b12Factor completely: 15y214y8Factor completely: 5y2+11y+2Factor completely: 90+17c3c228EFactor completely: 6x213x+5Factor completely: 56229x+3Factor completely: 2y4+9y235Factor completely: 2y2+7y99Factor completely: 4b2+52b+169Factor completely: 6x219x+15Factor completely: 14x251x+40Factor completely: 42x413x240Factor completely: 28x3+140x2+175xFactor completely: 24x354x221xFactor completely: 10ab215ab175aFactor completely: 40bx272bx70b1RSolve for x:3x(x2)=0Solve each equation by factoring: x24=0Solve each equation by factoring: x2x=6Solve each equation by factoring: 5x26x=0Solve each equation by factoring: x23x28=0Solve each equation by factoring: x214x=45Solve each equation by factoring: x2183x=0Solve each equation by factoring: 3x2+20x+32=0Solve each equation using the quadratic formula (when necessary, round result to three significant digits): 3x216x12=0Solve each equation using the quadratic formula (when necessary, round result to three significant digits): x2+7x5=0Solve each equation using the quadratic formula (when necessary, round result to three significant digits): 2x2+x=15Solve each equation using the quadratic formula (when necessary, round result to three significant digits): x24x=2Solve each equation using the quadratic formula (when necessary, round result to three significant digits): 3x24x=5The area of a piece of plywood is 36 ft2. Its length is 5 ft more than its width. Find its length and width.A variable electric current is given by the formula i=t212t+36, where t is in s. At what times is the current i equal to a. 4 A? b. 0 A? c. 10 A?Draw the graph of each equation and label each vertex: y=x2x6Draw the graph of each equation and label each vertex: y=3x2+2Express each number in terms of j: 36Express each number in terms of j: 73Simplify: j12Simplify: j27Determine the nature of the roots of each quadratic equation without solving it: 9x2+30x+25=0Determine the nature of the roots of each quadratic equation without solving it: 3x22x+4=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): x24x+5=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 5x26x+4=0A solar-heated house has a rectangular heat collector with a length 1 ft more than three times its width. The area of the collector is 21.25 ft2. Find its length and width.A rectangular opening is 15 in. wide and 26 in. long. (See Illustration 1.) A strip of constant width Is to be removed from around the opening to increase the area to 672 in2. How wide must the strip be?Solve each equation: x2=64Solve each equation: x28x=0Solve each equation: x2+9x36=0Solve each equation: 12x2+4x=1Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 5x2+6x10=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 3x2=4x+97T8T9T10TDraw the graph of y=x28x15 and label the vertex.Draw the graph of y=2x2+8x+11 and label the vertex.Express each number in terms of j: 16Express each number in terms of j: 29Simplify: j9Simplify: j28Determine the nature of the roots of 3x2x+4=0 without solving it.One side of a rectangle is 5 cm more that another. Its area is 204 cm2. Find its length and width.Solve each equation: x2+x=12Solve each equation: x23x+2=0Solve each equation: x2+x20=04ESolve each equation: x22=xSolve each equation: x215x=54Solve each equation: x21=0Solve each equation: 16n2=49Solve each equation: x249=010ESolve each equation: w2+5w+6=0Solve each equation: x26x=013ESolve each equation: c2+2=3cSolve each equation: n26n60=0Solve each equation: x217x+16=0Solve each equation: 9m=m2Solve each equation: 6n215n=0Solve each equation: x2=108+3xSolve each equation: x2x=42Solve each equation: c2+6c=16Solve each equation: 4x2+4x3=0Solve each equation: 10x2+29x+10=0Solve each equation: 2x2=17x8Solve each equation: 4x2=25Solve each equation: 25x=x2Solve each equation: 9x2+16=24xSolve each equation: 24x2+10=31xSolve each equation: 3x2+9x=0A rectangle is 5 ft longer than it is wide. (See Illustration 1.) The area of the rectangle is 84 ft2. Use a quadratic equation to find the dimensions of the rectangle. ILLUSTRATION 1The area of a triangle is 66 m2, and its base is 1 m more than the height. (See Illustration 2.) Find the base and height of the triangle. (Use a quadratic equation.) ILLUSTRATION 2A rectangle is 9 ft longer than it is wide, and its area is 360 ft2. Use a quadratic equation to find its length and width.A heating duct has a rectangular cross section whose area is 40 in2. If it is 3 in. longer than it is wide, find its length and width.Find the value of a, b, and c in each equation: x27x+4=0Find the value of a, b, and c in each equation: 2x2+x3=0Find the value of a, b, and c in each equation: 3x2+4x+9=04EFind the value of a, b, and c in each equation: 3x2+4x+7=0Find the value of a, b, and c in each equation: 17x2x+34=0Find the value of a, b, and c in each equation: 3x214=0Find the value of a, b, and c in each equation: 2x2+7x=0Solve each equation using the quadratic formula. Check your solutions: x2+x6=0Solve each equation using the quadratic formula. Check your solutions: x24x21=0Solve each equation using the quadratic formula. Check your solutions: x2+8x9=0Solve each equation using the quadratic formula. Check your solutions: 2x2+5x12=0Solve each equation using the quadratic formula. Check your solutions: 5x2+2x=0Solve each equation using the quadratic formula. Check your solutions: 3x275=0Solve each equation using the quadratic formula. Check your solutions: 48x232x35=0Solve each equation using the quadratic formula. Check your solutions: 13x2+178x56=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 2x2+x5=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 3x2+2x+5=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 3x25x=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 7x2+9x+2=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 2x2+x+3=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 5x27x+2=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 6x2+9x+1=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 16x225=0Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 4x2=5x+1Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 9x2=21x10Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 3x2=17Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 8x2=11x3Solve each equation using the quadratic formula (when necessary, round results to three significant digits): x2=15x+7Solve each equation using the quadratic formula (when necessary, round results to three significant digits): x2+x=1Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 3x231=5xSolve each equation using the quadratic formula (when necessary, round results to three significant digits): 3x25=7x2Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 52.3x=23.8x2+11.8Solve each equation using the quadratic formula (when necessary, round results to three significant digits): 18.9x244.2x=21.5A variable voltage in an electrical circuit is given by V=t212t+40, where t is in seconds. Find the values of t when the voltage V equals a. 8 V, b. 25 V, c. 104 V.A variable electric current is given by i=t27t+12, where t is in seconds. At what times is the current i equal to a. 2 A? b. 0 A? c. 4 A?A rectangular piece of sheet metal is 4 ft longer than it is wide. (See Illustration 1.) The area of the piece of sheet metal is 21 ft2. Find its length and width. ILLUSTRATION 1A hole in the side of a large metal tank needs to be repaired. A piece of rectangular sheet metal of area 16 ft2 will patch the hole. If the length of the sheet metal must be 8 ft longer than its width, what will the dimensions of the sheet metal be?The area of the wings of a small Cessna is 175 ft2. If the length is 30 ft longer than the width, what are the dimensions of the wings? (This wing is one piece and goes along the top of the aircraft.)The perimeter of a rectangle is 46 cm, and its area is 120 cm2. Find its dimensions.The perimeter of a rectangle is 160 m, and its area is 1200 m2. Find its dimensions.A rectangular field is fenced in by using a river as one side. If 1800 m of fencing are used for the 385,000-m2 field, find its dimensions.The dimensions of a doorway are 3 ft by 7 ft 6 in. If the same amount is added to each dimension, the area is increased by 18 ft2. (See Illustration 2.) Find the dimensions of the new doorway. ILLUSTRATION 2A square, 4 in. on a side, is cut out of each corner of a square sheet of aluminum. (See Illustration 3.) The sides are folded up to form a rectangular container with no top. The volume of the resulting container is 400 in3. What was the size of the original sheet of aluminum? ILLUSTRATION 3A square is cut out of each corner of a rectangular sheet of aluminum that is 40 cm by 60 cm. (See Illustration 4.) The sides are folded up to form a rectangular container with no top. The area of the bottom of the container is 1500 cm2. a. What are the dimensions of each cut-out square? b. Find the volume of the container. (V=lwh) ILLUSTRATION 4The area of a rectangular lot 80 m by 100 m is to be increased by 4000 m2. (See Illustration 5.) The length and the width will be increased by the same amount. What are the dimensions of the larger lot? Find the percent increase for the length and width. ILLUSTRATION 513EA border of uniform width is printed on a page measuring 11 in. by 14 in. (See Illustration 7.) The area of the border is 66 in2. Find the width of the border . ILLUSTRATION 7A company needs to build a ware house with perimeter 300 ft. Find the dimensions to give maximum floor space. a. If the length is 10 ft, what is the area? b. If the length is 20 ft, what is the area? c. Write a formula (model) for the area in terms of the length. d. Complete the following table: Length (ft) 30 40 50 60 80 90 100 110 120 130 140 Area (ft2) e. Does one of these values give a maximum area? Explain. f. Graph the equation. g. Is there a different maximum?A 2000-ft2 storage building 9 ft high is needed to store yard maintenance equipment. What dimensions should be used to minimize the outside walls?A landscaper is laying sod in a rectangular front lawn that is 76 ft longer than it is wide. Its area is 9165 ft2. Find its dimensions.A rectangular forest plot contains 120 acres and is three times as long as it is wide. Find its dimensions.Draw the graph of each equation and label each vertex: y=2x2Draw the graph of each equation and label each vertex: y=2x2Draw the graph of each equation and label each vertex: y=12x2Draw the graph of each equation and label each vertex: y=12x2Draw the graph of each equation and label each vertex: y=x2+3Draw the graph of each equation and label each vertex: y=x24Draw the graph of each equation and label each vertex: y=2(x3)2Draw the graph of each equation and label each vertex: y=(x+2)2Draw the graph of each equation and label each vertex: y=x22x+1Draw the graph of each equation and label each vertex: y=2(x+1)23Draw the graph of each equation and label each vertex: y=2x25Draw the graph of each equation and label each vertex: y=3x22xDraw the graph of each equation and label each vertex: y=x22x5Draw the graph of each equation and label each vertex: y=3x2+6x+15Draw the graph of each equation and label each vertex: y=x22x15Draw the graph of each equation and label each vertex: y=2x2x15Draw the graph of each equation and label each vertex: y=4x25x+9Draw the graph of each equation and label each vertex: y=4x212x+9Draw the graph of each equation and label each vertex: y=15x225x+4Draw the graph of each equation and label each vertex: y=0.4x2+2.4x+0.7Express each number in terms of j (when necessary, round the result to three significant digits): 49Express each number in terms of j (when necessary, round the result to three significant digits): 64Express each number in terms of j (when necessary, round the result to three significant digits): 14Express each number in terms of j (when necessary, round the result to three significant digits): 5Express each number in terms of j (when necessary, round the result to three significant digits): 2Express each number in terms of j (when necessary, round the result to three significant digits): 3Express each number in terms of j (when necessary, round the result to three significant digits): 56Express each number in terms of j (when necessary, round the result to three significant digits): 121Express each number in terms of j (when necessary, round the result to three significant digits): 169Express each number in terms of j (when necessary, round the result to three significant digits): 60Express each number in terms of j (when necessary, round the result to three significant digits): 27Express each number in terms of j (when necessary, round the result to three significant digits): 40Simplify: j3Simplify: j6Simplify: j13Simplify: j16Simplify: j19Simplify: j31Simplify: j24Simplify: j26Simplify: j38Simplify: j81Simplify: 1jSimplify: 1j6Determine the natural of the roots of each quadratic equation without solving it: x2+3x10=0Determine the natural of the roots of each quadratic equation without solving it: 2x27x+3=0Determine the natural of the roots of each quadratic equation without solving it: 5x2+4x+1=0Determine the natural of the roots of each quadratic equation without solving it: 9x2+12x+4=0Determine the natural of the roots of each quadratic equation without solving it: 3x+1=2x2Determine the natural of the roots of each quadratic equation without solving it: 3x2=4x8Determine the natural of the roots of each quadratic equation without solving it: 2x2+6=xDetermine the natural of the roots of each quadratic equation without solving it: 2x2+7x=4Determine the natural of the roots of each quadratic equation without solving it: x2+25=0Determine the natural of the roots of each quadratic equation without solving it: x24=0Solve each quadratic equation using the quadratic formula (when necessary, round results to threes significant digits): x26x+10=0Solve each quadratic equation using the quadratic formula (when necessary, round results to threes significant digits): x2x+2=0Solve each quadratic equation using the quadratic formula (when necessary, round results to threes significant digits): x214x+53=0Solve each quadratic equation using the quadratic formula (when necessary, round results to threes significant digits): x2+10x+34=0Solve each quadratic equation using the quadratic formula (when necessary, round results to threes significant digits): x2+8x+41=0Solve each quadratic equation using the quadratic formula (when necessary, round results to threes significant digits): x26x+13=0