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All Textbook Solutions for High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
The given expression represents the area. Find the side length of the square. 16s2+104s+169Error Analysis Describe and correct the error made in factoring the expression at the right.Factor each expression. 26.m249Factor each expression. c2100Factor each expression. p216Factor each expression. 4a225Factor each expression. 64n21Factor each expression. 31.25x2144Factor each expression. 50g28Factor each expression. 8d28Factor each expression. 34.27x248Factor each expression. 35.24e254Factor each expression. 245k220Factor each expression. 37.112h263Factor each expression. 48x2+72x+27Factor each expression. 8b2+80b+200Factor each expression. 40.48w2+48w+12Factor each expression. 41.45s2210s+245Factor each expression. 42.45t272t+24Factor each expression. 100z2120z+36Writing Explain how to recognize a perfect-square trinomial.a. Open-Ended Write an expression that shows the factored form of a difference of two squares. b. Explain how you know that your expression is a difference of two squares.Factor each expression. 46.36s860s4+25Factor each expression. c1030c5d2+225d4Factor each expression. 25n6+40n3+16Mental Math For Exercises 49-51, find a pair of factors for each number by using the difference of two squares. 24Mental Math For Exercises 49-51, find a pair of factors for each number by using the difference of two squares. 28Mental Math for Exercises 49-51, find a pair of factors for each number by using the difference of two squares. 72Reasoning Explain how reversing the rules for multiplying squares of binomials can help you factor a perfect-square trinomial.Writing The area of a square parking lot is 49p484p2+36. Explain how you would find the length of the parking lot.For Exercises 16, choose the correct letter: What is the factored form of q212q+36? A. (q+6)(q6) B. (q6)(q6) C. (q9)(q+4) D. (q+4)(q+9)For Exercises i -6, choose the correct letter. What is the factored form of 9x2+12x+4? F. (3x+2)2 G. (3x+3)2 H. (3x2)2 I. (3x3)2For Exercises I6, choose the correct letter. What is the factored form of x2196? A. (x14)2 B. (x+14)2 C. (x28)(4x+7) D. (x14)(x+14)For Exercises I6, choose the correct letter. What is the factored form of 9x264? F. (3x8)2 G. (3x+8)2 H. (3x8)(3x+8) I. (9x8)(x+8)For Exercises 16, choose the correct letter. What is the factored form of 12m275? A. 3(2m5)2 B. 3(2m+5)(2m5) C. 3(2m+5)2 D. (6m25)(2m+3)For Exercises 16, choose the correct letter. What is the factored form of 49x256x+16? F. (7x4)2 G. (7x+4)(7x4) H. (7x+4)2 I. (7x8)2A four-sided building has an area of 36x2+48x+16. Explain how to find a possible length and width of the building. What is a possible shape of the building?Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 1.12x3+3x2+20x+5Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 2.6v3+42v2+5v+35Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 8t3+36t2+2t+9Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 10s3+35s2+6s+21Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 9m36m2+12m8Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 8w3+6w228w21Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 7r3+16r29r72Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. 21x328x26x+8Factor each expression. 8j3+4j2+10j+5Factor each expression. 2m3+8m2+9m+36Factor each expression. 11.10s3+25s2+8s+20Factor each expression. 6x3+9x2+2x+3Factor each expression. 21x3+6x228x8Factor each expression. 8w3+12w2+10w+15Factor each expression. 18r312r2+21r14Factor each expression. 36n327n28n+6Factor each expression. 17.110b3+77b260b42Factor each expression. 64d340d224d+15Factor each expression. 19.10s3+80s27s56Factor each expression. 20.25j3+15j25j3Factor each expression. 21.24c384c2+10c35Factor each expression. 27f3+9f224f8Factor completely. 32x3+8x2+48x+12Factor completely. 45w436w3+15w212wFactor completely. 25.32k416k3+12k26kFactor completely. 6g3+18g2+60g+180Factor completely. 30b445b310b2+15bFactor completely. 28.32m3+72m280m180Factor completely. 29.63j4+84j318j224jFactor completely. 96n3240n2168n+420Factor completely. 12e4+18e3+36e2+54eFactor completely. 60a572a4210a3+252a2Find linear expressions for the possible dimensions of each rectangular prism.Find linear expressions for the possible dimensions of each rectangular prism.Find linear expressions for the possible dimensions of each rectangular prism.Find linear expressions for the possible dimensions of each rectangular prism.A shipping box in the shape of a rectangular prism has a volume of 12x3+32x2+20x. What linear expressions can represent possible dimensions of the box?Error Analysis Describe and correct the error made in factoring completely.Open-Ended Write a 3 -term expression for the volume of a rectangular prism that you can factor by grouping. Factor your polynomial.For Exercises 15, choose the correct letter. What is the GCF of the first two terms of the polynomial 4y3+8y2+5y+10? A. 4y B. 4y2 C. 4y3 D. 4For Exercises 15, choose the correct letter. What is the factored form of 4x3+3x2+8x+6? F. 2x2+3(2x+3) G. 2x2+2(2x+3) H. x2+2(2x+3) I. x2+2(4x+3)For Exercises 15, choose the correct letter. What is the factored form of 9x46x3+18x212x? A. 3xx22x(x4) B. 3xx22(3x+2) C. 3xx2+2(3x2) D. 3x3x22x(6x4)For Exercises 15, choose the correct letter. What is the factored form of 20p3+40p2+15p+30? F. 52p2+3(p+2) G. 52p2+6(p+4) H. 54p2+3(p+2) I. 54p2+8p(3p+6)For Exercises 15, choose the correct letter. A box in the shape of a rectangular prism has a volume of 9x3+24x2+12x. Which is not one of the possible dimensions? (Its dimensions are all linear expressions with integer coefficients.) A. 2x+3 B. 3x+2 C. 3x D. x+2The polynomial 3x3+24x2+48x represents the volume of a cylinder. The formula for the volume of a cylinder with radius r and height h is V=r2h. a. Factor 3x3+24x2+48x. b. Write a linear expression for a possible radius of the cylinder. Explain.Identify the vertex of each graph. Tell whether it is a minimum or a maximum.Identity the vertex of each graph. Tell whether it is a minimum or a maximum.Identify the vertex of each graph. Tell whether it is a minimum or a maximum.Graph each function. f(x)=3x2Graph each function. f(x)=2.5x2Graph each function. f(x)=15x2Order each group of quadratic function from widest to narrowest graph. y=3x2,y=5x2,y=1x2Order each group of quadratic functions from widest to narrowest graph. y=4x2,y=2x2,y=6x2Order each group of quadratic function from widest to narrowest graph. y=x2,y=13x2,y=2x2Order each group of quadratic functions from widest to narrowest graph. y=16x2,y=14x2,y=12x2Graph each function. f(x)=x2+1Graph each function. f(x)=x22Graph each functions. f(x)=2x2+1Graph each functions. f(x)=12x2+5Graph each function. f(x)=3x24Graph each function. f(x)=5x210For a physics experiment, the class drops a golf ball off a bridge towards the pavement below. The bridge is 75 feet high. The function h=16t2+75 gives the golf balls height h above the pavement (in feet) after t second. Graph the function. How many seconds does it take for the golf ball to hit the pavement?A relief organization flew over a village and dropped a package of food and medicine. The plane is flying at 1000 feet. The function h=16t2+1000 gives the packages height h above the ground (in feet) after t second. Graph the function. How many seconds does it take for the package to hit the ground?Identify the domain and range of each function. y=5x25Identify the domain and range of each function. y=12x2+3Identify the domain and range of each function. y=34x22Identify the domain and range of each function. f(x)=9x2+1Use a graphing calculator to graph each function. Identify the vertex and axis of symmetry. y=2.75x2+3Use a graphing calculator to graph each function. Identify the vertex and axis of symmetry. y=13x28Use a graphing calculator to graph each function. Identify the vertex and axis of symmetry. y=2x2+7Writing Discuss how the function y=x2+4 differs from the graph y=x2.Writing Explain how you can determine if the parabola opens up or down by simply examining the equation.For Exercises 1-4, choose the correct letter. What is the vertex of the parabola shown at the right? (1,0) (1,4) (0,3) (3,0)For Exercises 1-4, choose the correct letter. Which of the following has a graph that is wider than the graph of y=3x2+2? F. y=3x2+3 H. y=4x21 G. y=0.5x+1 I. y=4x2+1For Exercises 1-4, choose the correct letter. Which graph represents the function y=2x5?For Exercises 1-4, choose the correct letter. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=10x2,f(x)=2x2, and f(x)=0.5x2? F. f(x)=10x2,f(x)2x2, and f(x)=0.5x2 G. f(x)=10x2, f(x)10x2, and f(x)=0.5x2 H. f(x)=0.5x2,f(x)=2x2, and f(x)=10x2 I. f(x)=0.5x2,f(x)=10x2, and f(x)=2x2A ball fell off a cliff into the river from a height of 25 feet. The function h=30t2+25 gives the balls height h above water after t seconds. Graph the function. How much time does it take for the ball to hit the water?Find the equation of the axis of symmetry and the coordinate of the vertex of the graph of each function. y=4x22Find the equation of the axis of symmetry and the coordinate of the vertex of the graph of each function. y=x2+4x6Find the equation of the axis of symmetry and the coordinates of the vertex and the graph of each function. y=x2+4x+5Find the equation of the axis of symmetry and the coordinates of the vertex and the graph of each function. y=x28x+12Find the equation of the axis of symmetry and the coordinates of the vertex and the graph of each function. y=6x2+3Find the equation of the axis of symmetry and the coordinates of the vertex and the graph of each function. y=3x2+12x7Find the equation of the axis of symmetry and the coordinates of the vertex and the graph of each function. y=2x2+x14Find the equation of the axis of symmetry and the coordinates of the vertex and the graph of each function. y=6x28x+10Find the equation of the axis of symmetry and the coordinates of the vertex and the graph of each function. y=2x2+3x+6Graph each function. Label the axis of symmetry and the vertex. f(x)=x22x1Graph each function. Label the axis of symmetry and the vertex. f(x)=2x2+8x10Graph each function. Label the axis of symmetry and the vertex. f(x)=2x212x+19Graph each function. Label the axis of symmetry and the vertex. f(x)=3x26x8Graph each function. Label the axis of symmetry and the vertex. f(x)=2x2+2x+1Graph each function. Label the axis of symmetry and the vertex. f(x)=2x2+12x2A punter kicked the football into the air with an upward velocity of 62 ft/s. Its height h in feet after t seconds is given by the function h=16t2+62t+2. What is the maximum height the ball reaches? How long will it take the football to reach the maximum height? How long does it take for the ball to hit the ground?A disc is thrown into the air with an upward velocity of 20 ft/s. Its height h in feet after t seconds is given by the function h=16t2+20t+6. What is the maximum height the disc reaches? How long will it take the disc to reach the maximum height? How long does it take the disc to be caught 3 feet off the ground?Graph each function. Label the axis of symmetry and the vertex. f(x)=32x2+6x+2Graph each function. Label the axis of symmetry and the vertex. f(x)=23x2+8x+5Graph each function. Label the axis of symmetry and the vertex. f(x)=14x2+4x10Graph each function. Label the axis of symmetry and the vertex. f(x)=12x212x+11Graph each function. Label the axis of symmetry and the vertex. f(x)=34+2x+3Graph each function. Label the axis of symmetry and the vertex. f(x)=54x24x+1Open-Ended For Exercises 24-26, given an example of a quadratic function with the given characteristic (s). Its graph opens up and has its vertex at (0,3).Open-Ended For Exercises 24-26, given an example of a quadratic function with the given characteristic (s). Its graph lies entirely below the x axis.Open-Ended For Exercises 24-26, given an example of a quadratic function with the given characteristic (s). Its vertex lies on the x-axis and the graph opens down.A fountain that is 5 feet tall sprays water into the air with an upward velocity for 22 ft/s. What function gives the height h of the water in feet t seconds after it is sprayed upward? What is the maximum height of the water?The parabola shown at the right is of the form xy=ax2+bx+c. What is the y -intercept? What is the axis of symmetry? Use the formula x=b2a to find b . What is the equation of the parabola?For Exercises 1-5, choose the correct letter. Which equation represents the axis of symmetry of the function y=2x2+4x6? y=1 B. x=1 C. x=3 D. x=3For Exercises 1-5, choose the correct letter. What are the coordinates of the vertex of the graph of the function y=x2+6x11? F. (3,2) G. (3,16) H. (3,29) I. (3,29)For Exercises 1-5, choose the correct letter. What are the coordinates of the vertex of the graph of the function y=3x212x+3? (2,29) B. (2,15) C. (2,9) D. (3,6)For Exercises 1-5, choose the correct letter.For Exercises 1-5, choose the correct letter. Which equation matches the graph shown at the right? y=8x2+2x5 y=8x2+2x+5 y=2x2+8x+5 y=2x2+8x5A golf ball is driven in the air toward the hole from an elevated tee with an upward velocity of 160 ft/s. Its height h in feet after t second is given by the function h=16t2+160t+18. How long will it take for the golf ball to reach its maximum height? What is the balls maximum height?Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. x216=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. x2+12=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 2x218=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 7x2=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 12x22=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. x2+49=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. x215=15Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 4x236=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. x2+36=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. t2=25Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. k2=484Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. z2256=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. d214=50Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 9y216=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 2g232=32Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 4a2=36Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 7x2+28=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 6n254=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 81c2=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 16x249=0Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. 64+j2=0Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth. Find the side length of a square with an area of 196ft2.Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth. Find the radius of a circle with an area of 100 in2.Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth. Find the side length of a square with an area of 50 cm2.Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth. The square tarp you are raking leaves onto has an area of 150 ft2. What is the side length of the tarp? Round your answer to the nearest of a foot if necessary.Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth. There is enough mulch to spread over a flower bed an area of 85 m2. What is the radius of the largest circular bed that can be covered by the mulch? Round your answer to the nearest tenth of a meter if necessary.Mental Math Tell how many solutions each equation has. q222=22Mental Math Tell how many solutions each equation has. m2+15=0Mental Math Tell how many solutions each equation has. b212=12Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth. 3.35z2+2.75=14Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth. 100t2+36=100Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth. 5a21125=0Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth. 13h212=0Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth. 12m2+5=10Solve each equation by finding square roots. If the equation has no real-number solution, write no solution. If a solution is irrational, round to the nearest tenth. 11x20.75=3.21Find the value of n such that the equation x2n=0 has 24 and 24 as solutions.Find the value of x for the square and triangle. If necessary, round to the nearest tenth.Find the value of x for the square and triangle. If necessary, round to the nearest tenth.Writing Explain how the number of solutions for a quadratic equation relates to the graph of the function.For Exercises 1-7, choose the correct letter. What is the solution of n249=0? 7 7 7 no solutionFor Exercises 1-7, choose the correct letter. What is the solution of x2+64=0? F. 5 G. 8 H. 8 I. no solutionFor Exercises 1-7, choose the correct letter. What is the solution of a2+17=42? A. 5 B. 5 C. 5 D. no solutionFor Exercises 1-7, choose the correct letter. What is the side length of a square with an area of 144x2? F. 12 G. 12x H. 12x I. no solutionFor Exercises 1-7, choose the correct letter. What is the value of b in the triangle shown at the right? A. 4in. B. 4 in. C. 4in. D. no solutionFor Exercises 1-7, choose the correct letter. What is the radius of a sphere whose surface area is 100 square centimetres? Use the formula for determining the surface area of a sphere, s=4r2, and 3.14 for . Round your answer to the nearest hundredth. F. 2.82 cm G. 5 cm H. 5.64 cm I. 125,600 cmFor Exercises 1-7, choose the correct letter. What is the value of z so that 9 and 9 are both solutions of x2+z=103? A. 22 B. 3 C. 22 D. 184A ball is dropped from the top of a building that is 250 feet tall. The height h of the ball in feet after t seconds is modeled by the function h=16t2+250 h = 1612 + 250. Round to the nearest tenth if necessary. a. How long will it take for the ball to reach the ground? Show your work. b. How long will it take for the ball to reach a height of 75 feet? Show your work.Use the Zero-Product Property to solve each equation. (y+6)(y4)=0Use the Zero-Product Property to solve each equation. (3f+2)(f5)=0Use the Zero-Product Property to solve each equation. (2x7)(4x+10)=0Use the Zero-Product Property to solve each equation. (8t7)(3t+5)=0Use the Zero-Product Property to solve each equation. d(d8)=0Use the Zero-Product Property to solve each equation. 3m(2m+9)=0Solve by factoring. n2+2n15=0Solve by factoring. a215a+56=0Solve by factoring. z210z+24=0Solve by factoring. 8x2+10x+3=0Solve by factoring. 3b2+7b6=0Solve by factoring. 5p29p2=0Solve by factoring. w2+w=12Solve by factoring. s2+12s=32Solve by factoring. d2=5dSolve by factoring. 3j220j=12Solve by factoring. 12y2+40y=7Solve by factoring. 27r2+69r=8Use the Zero-Product Property to solve each equation. Write your solutions as a set in roster form. k211k+30=0Use the Zero-Product Property to solve each equation. Write your solutions as a set in roster form. x26x7=0Use the Zero-Product Property to solve each equation. Write your solutions as a set in roster form. n2+17n+72=0The volume of a sandbox shaped like a rectangular prims is 48 ft3. The height of the sandbox is 2 feet. The width is w feet and the length is w+2 feet. Use the formula V=twh to find the value of w.The area of the rubber coating for a flat roof was 96 ft2. The rectangular frame the carpenter built for the flat roof has dimensions such that the length is 4 feet longer than the width. What are the dimensions of the frame?Ling is cutting carpet for a rectangular room. The area of the room is 324 ft2. The length of the room is 3 feet longer than twice the width. What should the dimensions of the carpet be?Write each equation in standard form. Then solve. 21x2+5x35=3x24xWrite each equation in standard form. Then solve. 3n22n+1=3n2+9n+11Find the value of x as it relates to each rectangle or triangle. Area -60 cm2Find the value of x as it relates to each rectangle or triangle.Find the value of x as it relates to each rectangle or triangle. Area = 20 in.2Find the value of x as it relates to each rectangle or triangle. Area =150 m2Reasoning For each equation, find k and the value of any missing solutions. x2kx16=0 where 2 in one solution of the equation.Reasoning For each equation, find k and the value of any missing solutions. x6x=k where 10 is one solution of the equation.Reasoning For each equation, find k and the value of any missing solutions. kx213x=5 where 13 is one solution of the equation.Writing Explain how you solve a quadratic equation by factoring.Solve each exercise and enter your answer on the grid provided. What is the positive solution of 3x210x8=0?Solve each exercise and enter your answer on the grid provided. A triangular-shaped wall has a base of 2x+4 and a height of x+3. The area of the triangle is 56 in2. What is the value of x?Solve each exercise and enter your answer on the grid provided. The product of two consecutive integers, n and n+1, is 42. What is the positive integer that satisfies the situation?Solve each exercise and enter your answer on the grid provided. One more rectangular-shaped piece of metal siding needs to be cut to cover the exterior of a pole barn. The area of the piece is 30 ft2. The length is 1 less than 3 times the width. How wide should the mental piece be? Round to the nearest hundredth of a foot.Solve each exercise and enter your answer on the grid provided. What solution do 2x213x+21=0 and 2x2+9x56=0 have in common? Round your answer to the nearest tenth if necessary.Find the value of c such that each expression is a perfect-square trinomial. x2+4x+cFind the value of c such that each expression is a perfect-square trinomial. b2+12b+cFind the value of c such that each expression is a perfect-square trinomial. g220g+cFind the value of c such that each expression is a perfect-square trinomial. a27a+cFind the value of c such that each expression is a perfect-square trinomial. w2+18w+cFind the value of c such that each expression is a perfect-square trinomial. n29n+cSolve each equation by completing the square. If necessary, round to the nearest hundredth. z219z=66Solve each equation by completing the square. If necessary, round to the nearest hundredth. p25p=4Solve each equation by completing the square. If necessary, round to the nearest hundredth. b2+6b=16Solve each equation by completing the square. If necessary, round to the nearest hundredth. c24c=21Solve each equation by completing the square. If necessary, round to the nearest hundredth. a22a=15Solve each equation by completing the square. If necessary, round to the nearest hundredth. v2+8v=15Solve each equation by completing the square. If necessary, round to the nearest hundredth. y2+16y=17Solve each equation by completing the square. If necessary, round to the nearest hundredth. x2+4x+3=0Solve each equation by completing the square. If necessary, round to the nearest hundredth. h2+4h=1Solve each equation by completing the square. If necessary, round to the nearest hundredth. r2+8r+13=0Solve each equation by completing the square. If necessary, round to the nearest hundredth. d22d4=0Solve each equation by completing the square. If necessary, round to the nearest hundredth. m224m+44=0Solve each equation by completing the square. If necessary, round to the nearest hundredth. 3y2+5y=12Solve each equation by completing the square. If necessary, round to the nearest hundredth. 2h25h=1Solve each equation by completing the square. If necessary, round to the nearest hundredth. 4k2+4k=5Solve each equation by completing the square. If necessary, round to the nearest hundredth. 2c2+7c+3=0Solve each equation by completing the square. If necessary, round to the nearest hundredth. 3f22f=1Solve each equation by completing the square. If necessary, round to the nearest hundredth. 9x242x+49=0The rectangle shown at the right has an area of 56 m2. What is the value of x?What are all of the values of c that will make x2+cx+49 a perfect square?What are all of the values of c that will make x2+cx+121 a perfect square?Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. k224k+4=2Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. 4x220x25=0Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. 2b2+10b+15=3Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. p2+3p+2=1Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. 5m2+10m80=75Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. 2a23a+4=0Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. 5a212a+28=0Solve each equation. If necessary, round to the nearest hundredth. If there is no solution, write no solution. 5t26t=35Writing Discuss the strategies of graphing, factoring, and completing the square for solving the quadratic equation x2+4x6=0.The height of a triangle is 4x inches and the base is (5x+1) inches. The area of the triangle is 500 square inches. What are the dimensions of the base and height of the triangle?The formula for finding the volume of a rectangular prism is V=lwh. The height h of a rectangular prism is 12 centimeters. The prism has a volume of 10,800 cubic centimeters. The prisms length t is modelled by 3x centimeters and its width w by (2x+1) centimeters. What is the value of x? What are the dimensions of the length and the width?Writing In order to solve a quadratic equation by completing the square, what does the coefficient of the squared term need to be? If the coefficient is not equal to this, what does your first step need to be to complete the square?For Exercises 1-6, choose the correct letter. What is the value of n such that the expression x2+11x+n is a perfect square trinomial? 11 B. 25 C. 30.25 D. 36For Exercises 1-6, choose the correct letter. What is a solution of x2+6x=5? F. x=6 G. x=1 H. x=1 I. x=6For Exercises 1-6, choose the correct letter. Which of the following is a solution of x2+4x1=0? If necessary, round to the nearest hundredth. A. x=0.24. B. x=4.24 C. x=4.24 D. no solutionFor Exercises 1-6, choose the correct letter. Which of the following is a solution of x2+14x+112=0? round to the nearest hundredth. F. x=0.94 G. x=14.94 H. x=14.94 I. no solutionFor Exercises 1-6, choose the correct letter. The rectangular poster shown at the right has an area of 5400 cm2. What is the value of w? A. 45 cm B. 45 cm C. 60 cm D. 90 cmFor Exercises 1-6, choose the correct letter. A box shaped like a rectangular prism has a height of 17 in. and a volume of 2720 in3. The length is 4 inches greater than twice the width. What is the width of the box? F. 10 in. H. 20 in. G. 0 in. I. 40 in.The area of a rectangular television screen is 3456 in2. The width of the screen in 24 inches longer than the length. What is a quadratic equation that represents the area of the screen? What are the dimensions of the screen?Use the quadratic formula to solve each equation. 7c2+8c+1=0Use the quadratic formula to solve each equation. 2w228w=98Use the quadratic formula to solve each equation. 2j23j=1Use the quadratic formula to solve each equation. 2x26x+4=0Use the quadratic formula to solve each equation. 2n26n=8Use the quadratic formula to solve each equation. 7d2+2d+9=0Use the quadratic formula to solve each equation. 2a2+4a6=0Use the quadratic formula to solve each equation. 3p2+17p=20Use the quadratic formula to solve each equation. 4d28d+3=0Use the quadratic formula to solve each equation. Round answers to the nearest hundredth. h22h2=0Use the quadratic formula to solve each equation. Round answers to the nearest hundredth. 5x2+3x=1Use the quadratic formula to solve each equation. Round answers to the nearest hundredth. z24z=2Use the quadratic formula to solve each equation. Round answers to the nearest hundredth. t2+10t=22Use the quadratic formula to solve each equation. Round answers to the nearest hundredth. 3n2+10n=5Use the quadratic formula to solve each equation. Round answers to the nearest hundredth. s210s+14=0A basketball is passed through the air. The height h of the ball in the feet after the distance d in feet the ball travels horizontally is given by h=d2+10d+5. How far horizontally from the player passing the ball land on the ground?Which method (s) would you choose to solve each equation? Justify your reasoning. h2+4h+7=0Which method (s) would you choose to solve each equation? Justify your reasoning. a24a12=0Which method (s) would you choose to solve each equation? Justify your reasoning. 24y211y14=0Which method (s) would you choose to solve each equation? Justify your reasoning. 2p27p4=0