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<p>E. coli is a type of bacteria that can cause dangerous health problems. It doubles every 20 min. The initial population of a sample of E. coli is 400.</p><p>a) Copy and complete this table.</p><img src="/qimages/22266" /><p>b) Construct a graph of population versus time. Use a smooth curve to connect the points. Describe the shape of the graph.</p><p>c) What will the population be after</p> <ul> <li><p>5 h?</p></li> <li><p>8 h?</p></li> </ul>
Similar Question 2
<p>Use tiles to model each algebraic expression.</p><p><code class='latex inline'>3x^2-4x</code></p>
Similar Question 3
<p>Winson is building a dock at his cottage. The length of the dock is twice the width, plus 3 m.</p><p>a) Draw a diagram of the dock and label the width and length with algebraic expressions.</p><p>b) Find a simplified algebraic expression for the perimeter of the dock.</p><p>c) Find an algebraic expression for the area of the dock.</p><p>d) If the width of the dock is 2 m, find the perimeter and area of the dock.</p>
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Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
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<p>A soccer team gives each player a bonus on top of his or her base salary for every goal the player scores. Data for some of the team’s players are given.</p><img src="/qimages/22221" /><p>a) Find a simplified expression for the total earnings for these three players if b represents the bonus, in dollars.</p><p>b) Find the total earnings for these three players when b = $300</p> <p>Judy is training for an Ironman triathlon race. During her training program, she finds that she can swim at 1.5 km/h, cycle at 30 km/h, and run at 12 km/h. To estimate her time for an upcoming race, Judy rearranges the formula did <code class='latex inline'>distance = speed\times time</code> to find that <code class='latex inline'>time = \dfrac{distance}{speed}</code>.</p><p>a) Choose a variable to represent the distance travelled for each part of the race. For example, choose 6 for cycle.</p><p>b) Copy and complete the table. The second row is done for you.</p><img src="/qimages/22208" /><p>c) Write a trinomial to model Judy’s time.</p><p>d) The upcoming Ironman race is a triathlon composed of a 3.8-km swim, a 180.2-km cycle, and a full marathon run of 42.2 km. Using your expression from part c), calculate how long it will take Judy to finish the race.</p> <p>Elizabeth has a summer job at a camera store. She earns a$10 bonus for each gold membership and a $5 bonus for each silver membership.</p><p>a) Write a polynomial expression that describes Elizabeth’s total bonus.</p><p>b) Identify the variable and the coefficient of each term and explain what they mean.</p><p>c) How much will Elizabeth’s bonus be if she sells 20 gold memberships and 30 silver memberships?</p> <p>Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Ursula walked an unknown distance,</p><p>three times.</p> <p>Use tiles to model each algebraic expression.</p><p><code class='latex inline'>x^2-5x-3</code></p> <p>Each unit tile represents 1 m that Jacinth walked on a hike. Find each distance.</p><img src="/qimages/22203" /> <p>A rectangular cake has dimensions 4x by 3x+2. Find a simplified expression for its perimeter.</p> <p>A swimming pool manufacturer installs rectangular pools whose length is twice the width, plus 5 m.</p><p>How much coping is required if the width of the pool is 6 m?</p> <p>The students at Northdale High School sell coupon books to raise money for a school trip. The school receives 45% of the money paid for the coupon books.</p><p>a) Choose a variable to represent the money paid for the coupon books.</p><p>b) Using your variable from part a), write the expression for the amount of money the school will receive.</p><p>c) Shannon sold one coupon book to her grandmother for$20. Calculate the amount of money the school receives on this sale.</p><p>d) The sum of all coupon book orders was $14 000. Use your formula to calculate how much the school will receive for this fundraiser.</p> <p>Write the algebraic expression represented by each model.</p><img src="/qimages/22198" /> <p>Use algebra tiles to represent each area.</p><p>4 square units</p> <p>On a multiple-choice test, you earn 1 point for each correct answer and lose 2 points for each incorrect answer.</p><p>a) Write an expression for a student’s total score.</p><p>b) Tim answered 22 questions correctly and 3 incorrectly. Find Tim’s score.</p> <p>Write the algebraic expression represented by each model.</p><img src="/qimages/22197" /> <p>Write the algebraic expression represented by each model.</p><img src="/qimages/22196" /> <p>Use tiles to model each algebraic expression.</p><p><code class='latex inline'>x^2+5x</code></p> <p>Use tiles to model each algebraic expression.</p><p><code class='latex inline'>2x^2+3x+4</code></p> <p>In a hockey tournament, teams are awarded 4 points for a win and 2 points for an overtime win.</p><p>a) Write an expression that describes the number of points a team has.</p><p>b) Use your expression to find the number of points earned by a team that has five wins and two overtime wins.</p> <p>a) Build a volume model to represent a cube with side length <code class='latex inline'>\displaystyle 4 \mathrm{~cm} . </code> Sketch the model and label the length,</p><p>width, and height.</p><p>b) What is the volume of the cube?</p><p>Write this as a power.</p><p>c) Write an expression for the area of</p><p>one face of the cube as a power.</p><p>Evaluate the area of one face.</p><p>d) Write an expression for the surface</p><p>area of the cube. Evaluate the surface</p><p>area of the cube.</p> <p>Each unit tile represents 1 m that Jacinth walked on a hike. Find each distance.</p><img src="/qimages/22202" /> <p>A soccer team earns 2 points for a win and 1 point for a tie. Let <code class='latex inline'>w</code> represent the number of wins and <code class='latex inline'>t</code> represent the number of ties. Write an expression that describes the team’s total points.</p> <p>E. coli is a type of bacteria that can cause dangerous health problems. It doubles every 20 min. The initial population of a sample of E. coli is 400.</p><p>a) Copy and complete this table.</p><img src="/qimages/22266" /><p>b) Construct a graph of population versus time. Use a smooth curve to connect the points. Describe the shape of the graph.</p><p>c) What will the population be after</p> <ul> <li><p>5 h?</p></li> <li><p>8 h?</p></li> </ul> <p>Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Tasnia drove <code class='latex inline'>\displaystyle 5 \mathrm{~km} </code> plus an unknown distance.</p> <p>Each unit tile represents 1 m that Jacinth walked on a hike. Find each distance.</p><img src="/qimages/22199" /> <p>Use tiles to model each algebraic expression.</p><p><code class='latex inline'>3x^2-4x</code></p> <p>A swimming pool manufacturer installs rectangular pools whose length is twice the width, plus 5 m.</p><p>Draw a diagram of the pool and label the width and length with algebraic expressions.</p> <p>A group of employees at a shoe store are paid a yearly salary according to the following rate, where n is the amount of sales.</p><img src="/qimages/22222" /><p>a) Write a simplified expression for the total amount paid to the group of employees.</p><p>b) This table shows the sales achievement levels for the company.</p><img src="/qimages/22223" /><p>Determine the total annual salary for the group if their sales achievement level</p> <ul> <li><p>reaches silver status</p></li> <li><p>reaches gold status</p></li> <li><p>reaches platinum status</p></li> </ul> <p>c) Which employee makes the highest salary at each achievement level?</p> <p>Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Sheila swam <code class='latex inline'>\displaystyle 5 \mathrm{~km} </code>.</p> <p>Write the algebraic expression represented by each model.</p><img src="/qimages/22195" /> <p>Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Susu read a book twice.</p> <p>Each unit tile represents 1 m that Jacinth walked on a hike. Find each distance.</p><img src="/qimages/22200" /> <p>Each unit tile represents 1 m that Jacinth walked on a hike. Find each distance.</p><img src="/qimages/22201" /> <p>A theatre charges$80 for orchestra seats, $50 for dress circle seats, and$25 for balcony seats.</p><p>a) Write an expression that describes the total earnings from seat sales.</p><p>b) Identify the variable and the coefficient of each term and explain what they mean.</p><p>c) How much will the theatre earn if it sells 100 orchestra seats, 200 dress circle seats, and 150 balcony seats?</p><p>d) How much with the theatre earn if it sells 80 orchestra seats, 250 dress circle seats, and 200 balcony seats?</p>
<p>Protect-a-Boat Insurance Company charges $400 for liability, plus 15% of the value of the boat, plus$200 per passenger.</p><p>a) Write an expression to model the insurance cost.</p><p>b) Find the cost of insurance tor a \$120 000 boat that can carry 60 passengers.</p>
<p>In a basketball game, each player on the team receives 2 points for a basket and 1 point for a free throw.</p><p>3) Write an expression to represent a player’s total score for the game.</p><p>b) In the game, Mohamed scored six baskets and five free throws. Use your expression to find Mohamed’s total score.</p>
<p>Use algebra tiles to represent each area.</p><p>9 square units</p>
<p>Winson is building a dock at his cottage. The length of the dock is twice the width, plus 3 m.</p><p>a) Draw a diagram of the dock and label the width and length with algebraic expressions.</p><p>b) Find a simplified algebraic expression for the perimeter of the dock.</p><p>c) Find an algebraic expression for the area of the dock.</p><p>d) If the width of the dock is 2 m, find the perimeter and area of the dock.</p>
<p>The length of a rectangular garden is five times its width.</p><p>a) Write an expression for the perimeter of the garden.</p><p>b) Find the perimeter if the garden is 20 m wide.</p><p>c) Find the length and width if the perimeter is 180 m.</p><p>d) Write an expression for the area of the garden.</p><p>e) Find the area if the garden is 30 m wide.</p><p>f) Find the length and width if the area is 500 m<code class='latex inline'>^2</code>.</p>
<p>Use algebra tiles to represent each area.</p><p>2x<code class='latex inline'>^2</code> square units</p>
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