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Similar Question 1
<p>The total number of graphing calculators and scientific calculators in Carly&#39;s classroom is 14. </p><p>a) State how you will assign variables. </p><p>b) Write an equation to represent this situation. Then, write an equivalent linear equation. </p>
Similar Question 2
<p>A projectile is propelled upward at various angles from the ground (known as angles of elevation), with initial velocity of 10 m/s. Use graphing technology to compare the maximum heights of the projectiles with the angles of elevation shown in the table.</p><img src="/qimages/6053" />
Similar Question 3
<p>A hockey 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. </p><p>Which expression can be used to describe the total points?</p> <ul> <li><strong>A.</strong> <code class='latex inline'>2w + 1</code></li> <li><strong>B.</strong> <code class='latex inline'>w + t</code></li> <li><strong>C.</strong> <code class='latex inline'>2w + 1t</code></li> <li><strong>D.</strong> <code class='latex inline'>2w + t</code></li> </ul>
Similar Questions
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>In a TV trivia show, a contestant receives 500 points for a correct answer and loses 200 points for an incorrect answer. Let <code class='latex inline'>c</code> represent the number of correct answers and <code class='latex inline'>i</code> represent the number of incorrect answers. Which expression describes a contestant&#39;s total points.</p><p>A. <code class='latex inline'>500c + 200i</code></p><p>B. <code class='latex inline'>500c - 200i</code></p><p>C. <code class='latex inline'>500i + 200c</code></p><p>D. <code class='latex inline'>500i - 200c</code></p>
<img src="/qimages/42621" /><p>MODELING WITH MATHEMATICS Write and solve an equation to find the month when you would pay the same total amount for each Internet service.\cline { 2 - 3 } \multicolumn{1}{c|} {} &amp; Installation fee &amp; Price per month \Company A &amp; <code class='latex inline'>\displaystyle \$60.00 </code> &amp; <code class='latex inline'>\displaystyle \$ 42.95 </code></p><p>Company B &amp; <code class='latex inline'>\displaystyle \$25.00 </code> &amp; <code class='latex inline'>\displaystyle \$ 49.95 </code></p>
<img src="/qimages/24505" /><p>\multicolumn{1}{|c|} { Country } &amp; 1997 Population (billions) &amp; Projected Percent of Increase for 2050 \China &amp; <code class='latex inline'>\displaystyle 1.24 </code> &amp; <code class='latex inline'>\displaystyle 22.6 \% </code> \India &amp; <code class='latex inline'>\displaystyle 0.97 </code> &amp; <code class='latex inline'>\displaystyle 57.8 \% </code> \United States &amp; <code class='latex inline'>\displaystyle 0.27 </code> &amp; <code class='latex inline'>\displaystyle 44.4 \% </code></p><p>Which of these three countries is projected to be the most populous in 2050?</p>
<p>Tickets to a college swim meet cost <code class='latex inline'> \$10 </code> for general admission and <code class='latex inline'> \$ 5 </code> for students. There were <code class='latex inline'> x </code> general admission tickets and <code class='latex inline'> y </code> student tickets sold. Write algebraic expressions for</p><p>c) the revenue, in dollars, from the student tickets</p>
<p>A projectile is propelled upward at various angles from the ground (known as angles of elevation), with initial velocity of 10 m/s. Use graphing technology to compare the maximum heights of the projectiles with the angles of elevation shown in the table.</p><img src="/qimages/6053" />
<p>Edgar Rice Burroughs is the author of the Tarzan of the Apes stories. He published his first Tarzan story in 1912. Some years later, the town in southern California where he lived was named Tarzana.</p><p>The town was named in 1928. Write an equation to represent the situation.</p>
<p>In science lab, Devin and his classmates are asked to determine how many grams of hydrogen and how many grams of oxygen are in 477 grams of water. Devin used what he learned in class to determine that for every 8 grams of oxygen in water, there is 1 gram of hydrogen.</p><p>Write an equation to represent the situation.</p>
<p>Akira bought one new book for <code class='latex inline'>\displaystyle \$20 </code> and three used books for <code class='latex inline'>\displaystyle \$ 4.95 </code> each. Write and evaluate an expression to find how much money the books cost.</p>
<p>Traci invested <code class='latex inline'> \$x </code> at <code class='latex inline'> 7 \% </code> and <code class='latex inline'> \$ y </code> at <code class='latex inline'> 6 \% </code> . Write algebraic expressions for</p><p>d) the total revenue from all the tickets</p>
<p>A plane flies at <code class='latex inline'> x </code> kilometres per hour in still air. The wind speed is <code class='latex inline'> y </code> kilometres per hour. Write algebraic expressions for the speed of the plane when it is flying</p><p>a) into the wind</p>
<p>James and Sylvie need to paint the line around the outside of a soccer field. To know how much paint to buy, they must find the perimeter of the field.</p><p>James claims, “I can calculate the perimeter of the field by using the formula <code class='latex inline'>P = 2(l + w)</code>.”</p><p>Sylvie replies, “That’s not right, James. The correct formula is P =2l+ 2w.”</p> <ul> <li> Who is correct? Is it possible for both to be right? Provide evidence to support your answer.</li> </ul>
<p>The total of three cousins’ ages is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?</p>
<p>DVD A company that replicates DVDs spends <code class='latex inline'>\displaystyle \$1500 </code> per day in building overhead plus <code class='latex inline'>\displaystyle \$ 0.80 </code> per DVD in supplies and labor. If the DVDs sell for <code class='latex inline'>\displaystyle \$1.59 </code> per disk, how many DVDs must the company sell each day before it makes a profit?</p> <p>The total number of dimes and quarters in Mary&#39;s piggy bank is 82. </p><p>a) State how you will assign variables. </p><p>b) Write an equation to represent this situation. Then, write an equivalent linear equation. </p> <p>Traci invested <code class='latex inline'> \$ x </code> at <code class='latex inline'> 7 \% </code> and <code class='latex inline'> \$y </code> at <code class='latex inline'> 6 \% </code> . Write algebraic expressions for</p><p>c) the revenue, in dollars, from the student tickets</p> <p>Write an equation for each problem. Then solve the equation.</p><p>Two fifths of a number equals -􏰁24. Find the number.</p> <p>Determine whether the following statement is sometimes, always, or never true.</p><p>&quot;The sum of two consecutive even numbers equals the sum of two consecutive odd numbers.&quot;</p> <p>The volume <code class='latex inline'>V</code> of a sphere is four-thirds times 􏰉<code class='latex inline'>\pi</code> times the radius <code class='latex inline'>r</code> of the sphere cubed.</p><p>Write a formula for the volume of a sphere.</p> <p>If <code class='latex inline'>r</code> represents rate, <code class='latex inline'>t</code> represents time, and <code class='latex inline'>d</code> represents distance, then <code class='latex inline'>rt=d</code>. Write the formula in words.</p> <img src="/qimages/12377" /><p>Reasoning Use the table to decide whether <code class='latex inline'>\displaystyle 49 n+0.75 </code> or <code class='latex inline'>\displaystyle 49+0.75 n </code> represents the total cost to rent a truck that you drive <code class='latex inline'>\displaystyle n </code> miles.</p><p> Truck Rental Fees Number of Miles &amp; Cost \1 &amp; <code class='latex inline'>\displaystyle \$ 49+(\$.75 \times 1) </code> \2 &amp; <code class='latex inline'>\displaystyle \$ 49+(\$.75 \times 2) </code> \3 &amp; <code class='latex inline'>\displaystyle \$ 49+(\$.75 \times 3) </code> \<code class='latex inline'>\displaystyle n </code> &amp; <code class='latex inline'>\displaystyle \mid </code></p> <p>A computer store has certain software on sale at 3 for$20.00, with a limit of 3 at the sale price. Additional software is available at the regular price of $9.95 each.</p><p>How much would 5 software packages cost?</p> <p>Write an equation for each problem. Then solve the equation.</p><p>Two and one half times a number equals one and one fifth. Find the number.</p> <p>A rectangle is cut from the corner of a 10-inch by 10-inch of paper. The area of the remaining piece of paper is <code class='latex inline'>\frac{4}{5}</code> of the area of the original piece of paper. If the width of the rectangle removed from the paper is 4 inches, what is the length of the rectangle?</p><img src="/qimages/24468" /> <p>A plane flies at <code class='latex inline'> x </code> kilometres per hour in still air. The wind speed is <code class='latex inline'> y </code> kilometres per hour. Write algebraic expressions for the speed of the plane when it is flying</p><p>b) with the wind</p> <p>In science lab, Devin and his classmates are asked to determine how many grams of hydrogen and how many grams of oxygen are in 477 grams of water. Devin used what he learned in class to determine that for every 8 grams of oxygen in water, there is 1 gram of hydrogen.</p><p>How many grams of oxygen are in 477 grams of water?</p> <p>Research conducted by a daily U.S. newspaper has shown that about one seventh of people in the world are left-handed.</p><p>If there are 65 left-handed people in a group, about how many people are in that group?</p> <p>In baseball, if all other factors are the same, the speed of a four-seam fastball is faster than a two-seam fastball. The distance from the pitcher’s mound to home plate is 60.5 feet.</p><p>How long does it take a four-seam fastball to go from the pitcher’s mound to home plate? Round to the nearest hundredth.</p> <p>At a computer store, packages of DVDs sell for$15 each. One customer buys $120 worth of DVDs.</p><p>Solve the equation.</p> <p>Adila sells T-shirts at a rock concert. She earns$8.00/h, plus $0.50 for each T-shirt she sells.</p><p>a) How much will Adila earn in a 4-h shift if she sells 35 T-shirts?</p><p>b) How many T-shirts must Adila sell to earn$80 in a 6-h shift?</p>
<p>The number of students at Franklin High School increased from 840 to 910 over a 5-year period. Which proportion represents the percent of change?</p><p>A. <code class='latex inline'>\frac{70}{910}=\frac{r}{100}</code></p><p>B. <code class='latex inline'>\frac{70}{840}=\frac{r}{100}</code></p><p>C. <code class='latex inline'>\frac{r}{910}=\frac{70}{100}</code></p><p>D. <code class='latex inline'>\frac{r}{840}=\frac{70}{100}</code></p>
<p>The price of a computer dropped $34.95 each month for 7 months. If the starting price was$1450, what was the price after 7 months?</p>
<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>Ebony burns 4.5 Calories per minute pushing a lawn mower.</p><p>Write a multiplication equation representing the number of Calories <code class='latex inline'>C</code> burned if Ebony pushes the lawn mower for <code class='latex inline'>m</code> minutes.</p>
<p>Write an equation for each problem. Then solve the equation.</p><p>Negative three eighths times a number equals 12. What is the number?</p>
<p>Traci invested <code class='latex inline'> \$x </code> at <code class='latex inline'> 7 \% </code> and <code class='latex inline'> \$ y </code> at <code class='latex inline'> 6 \% </code> . Write algebraic expressions for</p><p>a) the total amount of money Traci invested</p>
<p>Derrick and Samantha are selling tickets for their school music. Floor seats cost $7.50 and balcony seats cost$5.00. Samantha sells 60 floor seats and 70 balcony seats, Derrick sells 50 floor seats and 90 balcony seats. </p><p>Write an expression to show how much money Samantha and Derrick have collected for tickets. </p>
<p>The sum of the first <code class='latex inline'>n</code> even natural numbers can be found using the formula <code class='latex inline'>S=n(n+1)</code></p> <ul> <li> The sum of the first <code class='latex inline'>n</code> even natural numbers is 306. What is the value of <code class='latex inline'>n</code>?</li> </ul>
<p>A math contest has 30 multiple-choice questions. A correct answer gains 4 points. while a wrong answer loses 1 point. Rolly answered every question and scored 55 points. How many questions did he answer correctly?</p>
<p>Ebony burns 4.5 Calories per minute pushing a lawn mower.</p><p>How long will it take Ebony to burn 150 Calories mowing the lawn?</p>
<p>The discharge of a river is defined as the width of the river times the average depth of the river times the speed of the river. At one location in St. Louis, the Mississippi River is 533 meters wide, its speed is 0.6 meter per second, and its discharge is 3198 cubic meters per second. How deep is the Mississippi River at this location?</p>
<p>An architect&#39;s starting salary is $73 000. The company has guaranteed a raise of$2275 every 6 months with satisfactory performance.</p><p>What will the architects salary be after 8 years?</p>
<p>During a highly rated one-hour television program, the entertainment portion lasted 15 minutes longer than 4 times the advertising portion.</p><p>If <code class='latex inline'>a</code> represents the time spent on advertising, write an expression for the entertainment portion.</p>
<p>Sarah delivers flyers in the summer to make some extra money. She charges $10.00 per hour. Ads-R-Us Delivery Service charges$120 for the season. </p><p>a) Write an equation for the amount Sarah charges to deliver the flyers for the season.</p><p>b) Write an equation for the amount Ads-R-Us Delivery Service charges. </p><p>c) What is the intersection point of the two linear equations?</p><p>d) In the context question, what does the point of intersection represent?</p>
<p>Twice the greater of two consecutive odd integers is 13 less than three times the lesser number. Find the integers.</p>
<p>Sven sells hamburgers at a ballpark. He earns $7.50/h, plus$0.40 for each hamburger he sells.</p><p>a) How much will Sven earn in a 3-h shift if he sells 24 hamburgers?</p><p>b) How many hamburgers must Sven sell to earn $100 in a 6.5-h shift?</p> <p>The hourly rate of a waiter is <code class='latex inline'>\displaystyle \$ 4 </code> plus tips. On a particular day, the waiter worked 8 hours and received more than <code class='latex inline'>\displaystyle \$150 </code> in pay. Which could be the amount of tips the waiter received?</p><p><code class='latex inline'>\displaystyle \begin{array}{llll}\text { (A) } \$ 18.75 & \text { (B) } \$32 & \text { (C) } \$ 118 & \text { D } \$120.75\end{array} </code></p> <p>Tickets to a college swim meet cost <code class='latex inline'> \$ 10 </code> for general admission and <code class='latex inline'> \$5 </code> for students. There were <code class='latex inline'> x </code> general admission tickets and <code class='latex inline'> y </code> student tickets sold. Write algebraic expressions for</p><p>b) the revenue, in dollars, from the general admission tickets</p> <p>Research conducted by a daily U.S. newspaper has shown that about one seventh of people in the world are left-handed.</p><p>Write a multiplication equation relating the number of left-handed people 􏳲 and the total number of people p.</p> <p>In science lab, Devin and his classmates are asked to determine how many grams of hydrogen and how many grams of oxygen are in 477 grams of water. Devin used what he learned in class to determine that for every 8 grams of oxygen in water, there is 1 gram of hydrogen.</p><p>If x represents the number of grams of hydrogen, write an expression to represent the number of grams of oxygen.</p> <p>If <code class='latex inline'>a</code> and <code class='latex inline'>b</code> represent the lengths of the bases of a trapezoid and <code class='latex inline'>h</code> represents its height, then the formula for the area <code class='latex inline'>A</code> of the trapezoid is <code class='latex inline'>A=\frac{1}{2}h(a+b)</code>. Wrote the formula in words. </p><img src="/qimages/24379" /> <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>Doreen has $10 to buy apples and pears.</p><img src="/qimages/9604" /><p>Use each representation below to determine the possible amounts of each type of fruit she can buy.</p><p>a) table</p><p>b) graph</p><p>c) equation</p> <p>Use the information on energy at the left. The amount of energy <code class='latex inline'>E</code> in BTUs needed to raise the temperature of water is represented by the equation <code class='latex inline'>E=w(t_f - t_O)</code>. In this equation, <code class='latex inline'>w</code> represents the weight of the water in pounds, <code class='latex inline'>t_f</code> represents the final temperature in degrees Fahrenheit, and <code class='latex inline'>t_O</code> represents the original temperature in degrees Fahrenheit. A 50-gallon water heater is 60% efficient. If 10 cubic feet of natural gas are used to raise the temperature of water with the original temperature of 50°F, what is the final temperature of the water? (One gallon of water weighs about 8 pounds.)</p> <p>In a soccer league, teams receive 3 points for a win, 2 points for a loss, and 1 point for a tie.</p><p>a) Write an algebraic expression to represent a team’s total points.</p><p>b) What variables did you choose? Identify what each variable represents.</p><p>c) The Falcons’ record for the season was 5 wins, 2 losses, and 3 ties. Use your expression to find the Falcons’ total points.</p><p>d) The 10-game season ended with the Falcons tied for second place with the same number of points as the Eagles. The Eagles had a different record than the Falcons. How is this possible?</p> <p>On a multiple-choice test, you earn 2 points for each correct answer and lose 1 point for each incorrect answer.</p><p>a) Write an expression for a student&#39;s total score.</p><p>b) If you answered 15 questions correctly and 3 incorrectly, what is the score?</p> <p> In a hockey tournament, teams are awarded 3 points for a win, 2 points for an overtime win, and 1 point for an overtime loss.</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 4 wins, 1 overtime win, and 2 overtime losses.</p> <p>In baseball, if all other factors are the same, the speed of a four-seam fastball is faster than a two-seam fastball. The distance from the pitcher’s mound to home plate is 60.5 feet.</p><img src="/qimages/24389" /><p>How long does it take a two-seam fastball to go from the pitcher’s mound to home plate? Round to the nearest hundredth. (Hint: <code class='latex inline'>rt=d</code>)</p> <p>Mrs. Patton is planning to place a fence around her vegetable garden. The fencing costs$1.75 per yard. She buys <code class='latex inline'>f</code> yards of fencing and pays $3.50 in tax. If the total cost of the fencing is$73.50, write an equation to represent the situation.</p>
<p>A fitness centre charges an initiation fee of <code class='latex inline'> \$x </code> , plus a monthly charge of <code class='latex inline'> \$ y . </code> Write algebraic expressions to show how much it costs to be a member for</p><p>a) 7 months</p>
<p>Cindy is at a baseball game with her younger brother, Mike. She has $18 to spend on hamburgers and pop. Hamburgers cost$3 each and pop cost $2 each.</p><p>a) If Cindy buys only hamburgers, how many can she buy?</p><p>b) If she buys only pop, how many can she buy?</p><p>c) The equation <code class='latex inline'>2x + 3y = 18</code> can used to model this problem. Graph this line. What other combinations can Cindy buy?</p> <p>John has$23.65 to spend on a book and magazines. The book costs $5.95. The magazines cost$2.95 each.</p><p>a) Write an equation that models the number of magazines that John can afford.</p><p>b) Solve the equation.</p>
<p>Edgar Rice Burroughs is the author of the Tarzan of the Apes stories. He published his first Tarzan story in 1912. Some years later, the town in southern California where he lived was named Tarzana.</p><p>Let <code class='latex inline'>y</code> represent the number of years after 1912 that the town was named Tarzana. Write an expression for the year the town was named.</p>
<p>Traci invested <code class='latex inline'> \$x </code> at <code class='latex inline'> 7 \% </code> and <code class='latex inline'> \$ y </code> at <code class='latex inline'> 6 \% </code> . Write algebraic expressions for</p><p>b) the interest Traci earned at <code class='latex inline'> 7 \% </code> in one year</p>
<p>When exercising, a person’s pulse rate should not exceed a certain limit, which depends on his or her age. This maximum rate is represented by the expression <code class='latex inline'>0.8(220-a)</code>, where <code class='latex inline'>a</code> is age in years. Find the age of a person whose maximum pulse is 152.</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>The perimeter of a rectangle is 18 m. </p><p>a) State how you will assign variables. </p><p>b) Write an equation to represent this situation. Then, write an equivalent linear equation. </p>
<img src="/qimages/38007" />
<p>At a computer store, packages of DVDs sell for $15 each. One customer buys$120 worth of DVDs.</p><p>Write an equation to model the number of packages of DVDs the customer bought.</p>
<img src="/qimages/12393" /><p>Sightseeing While on vacation, you rent</p><p>a bicycle. You pay <code class='latex inline'>\displaystyle \$9 </code> for each hour you use it. It costs <code class='latex inline'>\displaystyle \$ 5 </code> to rent a helmet while you use the bicycle.</p><p>Bike Rental Number of Hours &amp; Rental Cost \1 &amp; <code class='latex inline'>\displaystyle (\$9 \times 1)+\$ 5 </code> \2 &amp; <code class='latex inline'>\displaystyle (\$9 \times 2)+\$ 5 </code> \3 &amp; <code class='latex inline'>\displaystyle (\$9 \times 3)+\$ 5 </code> \<code class='latex inline'>\displaystyle n </code> &amp; <code class='latex inline'>\displaystyle \square </code></p><p>Sightseeing While on vacation, you rent</p><p>a bicycle. You pay <code class='latex inline'>\displaystyle \$9 </code> for each hour you use it. It costs <code class='latex inline'>\displaystyle \$ 5 </code> to rent a helmet while you use the bicycle.</p><p>Bike Rental Number of Hours &amp; Rental Cost \1 &amp; <code class='latex inline'>\displaystyle (\$9 \times 1)+\$ 5 </code> \2 &amp; <code class='latex inline'>\displaystyle (\$9 \times 2)+\$ 5 </code> \3 &amp; <code class='latex inline'>\displaystyle (\$9 \times 3)+\$ 5 </code> \<code class='latex inline'>\displaystyle n </code> &amp; <code class='latex inline'>\displaystyle \square </code></p>
<p>The Pacific Ocean covers about 46% of Earth. If <code class='latex inline'>P</code> represents the area of the Pacific Ocean and<code class='latex inline'>E</code> represents the area of Earth, write an equation for this situation.</p><img src="/qimages/24374" />
<p>One half of a number increased by 16 is four less than two thirds of the number. Find the number.</p>
<p>The volume <code class='latex inline'>V</code> of a cone equals one-third times the product of 􏰉<code class='latex inline'>\pi</code>, the square of the radius <code class='latex inline'>r</code> of the base, and the height <code class='latex inline'>h</code>.</p><p>Write the formula for the volume of a cone.</p>
<p>In science lab, Devin and his classmates are asked to determine how many grams of hydrogen and how many grams of oxygen are in 477 grams of water. Devin used what he learned in class to determine that for every 8 grams of oxygen in water, there is 1 gram of hydrogen.</p><p>How many grams of hydrogen are in 477 grams of water?</p>
<p>In a quiz show, contestants receive 10 points for each correct answer but lose 5 points for each incorrect answer.</p><p>a) Write an expression for a contestant’s total score.</p><p>b) Theo answered 12 questions correctly and 5 questions incorrectly. Find his total score.</p>
<p>Research conducted by a daily U.S. newspaper has shown that about one seventh of people in the world are left-handed.</p><p>About how many left-handed people are there in a group of 350 people?</p>
<p>Darius is training to prepare for wrestling season. He weighs 155 pounds now. He wants to gain weight so that he starts the season weighing 160 pounds.</p><p>How many pounds does Darius need to gain to reach his goal?</p>
<img src="/qimages/12412" /><p>A state park charges an entrance fee plus <code class='latex inline'>\displaystyle \$18 </code> for each night of Camping camping. The table shows this relationship. Which algebraic expression describes the total cost of camping for <code class='latex inline'>\displaystyle n </code> nights?</p><p>A <code class='latex inline'>\displaystyle 20 n+18 </code></p><p>(C) <code class='latex inline'>\displaystyle 18 n+20 n </code>Nights &amp; Total Cost \1 &amp; <code class='latex inline'>\displaystyle (\$ 18 \times 1)+\$20 </code> \2 &amp; <code class='latex inline'>\displaystyle (\$ 18 \times 2)+\$20 </code> \3 &amp; <code class='latex inline'>\displaystyle (\$ 18 \times 3)+\$20 </code> \<code class='latex inline'>\displaystyle n </code> &amp; <code class='latex inline'>\displaystyle \mid </code> (B) <code class='latex inline'>\displaystyle 18 n+20 </code></p><p>D <code class='latex inline'>\displaystyle 18 n-20 </code></p> <p>In 1993, a group of people in Utica, New York, made a very large round jelly doughnut which broke the world record for doughnut size. It weighed 1.5 tons and had a circumference of 50 feet. What was the diameter of the doughnut? (Hint: <code class='latex inline'>C=\pi d</code>)</p> <p>Tickets to a college swim meet cost <code class='latex inline'> \$ 10 </code> for general admission and <code class='latex inline'> \$5 </code> for students. There were <code class='latex inline'> x </code> general admission tickets and <code class='latex inline'> y </code> student tickets sold. Write algebraic expressions for</p><p>d) the total revenue from all the tickets</p> <p>The volume <code class='latex inline'>V</code> of a sphere is four-thirds times 􏰉<code class='latex inline'>\pi</code> times the radius <code class='latex inline'>r</code> of the sphere cubed.</p><p>Find the volume of a sphere if <code class='latex inline'>r</code> is 4 inches.</p> <img src="/qimages/12394" /><p>Sales At a shoe store, a salesperson earns a weekly salary of <code class='latex inline'>\displaystyle \$ 150 </code>. A salesperson is also paid <code class='latex inline'>\displaystyle \$2.00 </code> for each pair of shoes he or she sells during the week.</p><p>Shoe Sales Pairs of Shoes Sold &amp; Total Earned \5 &amp; <code class='latex inline'>\displaystyle \$ 150+(\$2 \times 5) </code> \10 &amp; <code class='latex inline'>\displaystyle \$ 150+(\$2 \times 10) </code> \15 &amp; <code class='latex inline'>\displaystyle \$ 150+(\$2 \times 15) </code> \<code class='latex inline'>\displaystyle n </code> &amp; <code class='latex inline'>\displaystyle \square </code></p> <p>Analyze the following problem.</p><p>Misae has$1900 in the bank. She wishes to increase her account to a total of $3500 by depositing$30 per week from her paycheck. Will she reach her savings goal in one year?</p><p>a. How much money did Misae have in her account at the beginning?</p><p>b. How much money will Misae add to her account in 10 weeks? in 20 weeks?</p><p>c. Write an expression representing the amount added to the account after w weeks have passed.</p><p>d. What is the answer to the question? Explain.</p>
<p>During a highly rated one-hour television program, the entertainment portion lasted 15 minutes longer than 4 times the advertising portion.</p><p>Use your equation and the guess-and-check strategy to determine the number of minutes spent on advertising. Choose different values of <code class='latex inline'>a</code> and evaluate to find the solution.</p>
<p>Dawson knows that the formula for the perimeter of a rectangle is <code class='latex inline'>\displaystyle P=2 l+2 w </code>. He has <code class='latex inline'>\displaystyle 180 \mathrm{~m} </code> of fencing to enclose a rectangular play area with a maximum width of <code class='latex inline'>\displaystyle 32 \mathrm{~m} </code>. What is the minimum length of the play area? Explain.</p>
<p>During a highly rated one-hour television program, the entertainment portion lasted 15 minutes longer than 4 times the advertising portion.</p><p>Write an equation to represent the situation.</p>
<p>Write an equation for each problem. Then solve the equation.</p><p>One and one third times a number is 􏰁-4.82. What is the number?</p>
<p>The total number of males and females and Andy&#39;s math class is 14. </p><p>a) State how you will assign variables. </p><p>b) Write the equation to represent this situation. Then, write and equivalent linear equation. </p>
<p>The volume <code class='latex inline'>V</code> of a cone equals one-third times the product of 􏰉<code class='latex inline'>\pi</code>, the square of the radius <code class='latex inline'>r</code> of the base, and the height <code class='latex inline'>h</code>.</p><p>Find the volume of a cone if <code class='latex inline'>r</code> is 10 centimeters and <code class='latex inline'>h</code> is 30 centimeters.</p>
<p>Numbers Let <code class='latex inline'> x </code> represent the larger of two numbers, and <code class='latex inline'> y </code> , the smaller. Write algebraic expressions for</p><p>b) the smaller subtracted from the larger</p>
<p>Derrick and Samantha are selling tickets for their school music. Floor seats cost $7.50 and balcony seats cost$5.00. Samantha sells 60 floor seats and 70 balcony seats, Derrick sells 50 floor seats and 90 balcony seats. </p><p>Evaluate the expression to determine how much they collected. </p>
<p>A hockey 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. </p><p>Which expression can be used to describe the total points?</p> <ul> <li><strong>A.</strong> <code class='latex inline'>2w + 1</code></li> <li><strong>B.</strong> <code class='latex inline'>w + t</code></li> <li><strong>C.</strong> <code class='latex inline'>2w + 1t</code></li> <li><strong>D.</strong> <code class='latex inline'>2w + t</code></li> </ul>
<p>The sum of one half of a number and 6 equals one third of the number. What is the number?</p>
<p>Three times the greatest of three consecutive even integers exceeds twice the least by 38. What are the integers?</p>
<p>Which equation represents the following sentence? &quot;One fourth of a number plus five equals the number minus seven.&quot;</p><p>A. <code class='latex inline'>\frac{1}{4}n+7=n-5</code></p><p>B. <code class='latex inline'>\frac{1}{4}n+5=n-7</code></p><p>C. <code class='latex inline'>4n+7=n-5</code></p><p>D. <code class='latex inline'>4n+5=n-7</code></p>
<p>Are the following expressions sometimes, always, or never equal? Explain your reasoning.</p><p>x% of y</p><p>y% of x</p>
<p>Write an expression that represents the perimeter of the rectangle. </p><img src="/qimages/23667" />
<p>Write an equation for each problem. Then solve the equation.</p><p>One fifth of a number is 12. Find the number.</p>
<p>Determine the constant of variation for the direct variation.</p><p>The distance travelled on a trip varies directly with the amount of gas used. A car travelled 375 km and used 25 litres of gas.</p>
<p>Write a problem based on the given information.</p><p><code class='latex inline'>c=</code> cost of a suit</p><p><code class='latex inline'>c-25=150</code></p>
<p>Edgar Rice Burroughs is the author of the Tarzan of the Apes stories. He published his first Tarzan story in 1912. Some years later, the town in southern California where he lived was named Tarzana.</p><p>Use what you know about numbers to determine the number of years between the first Tarzan story and the naming of the town.</p>
<p>In baseball, if all other factors are the same, the speed of a four-seam fastball is faster than a two-seam fastball. The distance from the pitcher’s mound to home plate is 60.5 feet.</p><p>How much longer does it take for a two-seam fastball to reach home plate than a four-seam fastball?</p>
<p>Darius is training to prepare for wrestling season. He weighs 155 pounds now. He wants to gain weight so that he starts the season weighing 160 pounds</p><p>If <code class='latex inline'>g</code> represents the number of pounds he wants to gain, write an equation to represent the situation.</p>
<p>The list price of a television is $249.00. If it is on sale for 30% off the list price, what is the sale price of the television?</p><p>A.$74.70</p><p>B. $149.40</p><p>C.$174.30</p><p>D. $219.00</p> <p>Write an equation for each problem. Then solve the equation.</p><p>Seven times a number equals 􏰁-84. What is the number?</p> <p>Write an equation for each problem. Then solve the equation.</p><p>Five times a number is 120. What is the number?</p> <p>The total number of graphing calculators and scientific calculators in Carly&#39;s classroom is 14. </p><p>a) State how you will assign variables. </p><p>b) Write an equation to represent this situation. Then, write an equivalent linear equation. </p> <p>Tickets to a college swim meet cost <code class='latex inline'> \$ 10 </code> for general admission and <code class='latex inline'> \$5 </code> for students. There were <code class='latex inline'> x </code> general admission tickets and <code class='latex inline'> y </code> student tickets sold. Write algebraic expressions for</p><p>a) the total number of tickets sold</p> <p>Numbers Let <code class='latex inline'> x </code> represent the larger of two numbers, and <code class='latex inline'> y </code> , the smaller. Write algebraic expressions for</p><p>a) the sum of the two numbers</p> <p>Which sentence can be represented by <code class='latex inline'>7(x+y)=35</code>?</p><p>A. Seven times x plus y equals 35.</p><p>B. One seventh of the sum of x and y equals 35.</p><p>C. Seven plus x and y equals 35.</p><p>D. Seven times the sum of x and y equals 35.</p> <p>Banquet hall charges according to the equation <code class='latex inline'>40n-C+250=0</code>.</p> <ul> <li>Illustrate the relation graphically</li> </ul> <p>A computer store has certain software on sale at 3 for$20.00, with a limit of 3 at the sale price. Additional software is available at the regular price of \$9.95 each.</p><p>Write an expression you could use to find the cost of 5 software packages. </p>
<p>Numbers Let <code class='latex inline'> x </code> represent the larger of two numbers, and <code class='latex inline'> y </code> , the smaller. Write algebraic expressions for</p><p>c) the larger subtracted from five times the smaller</p>
<p>Write an equation for each problem. Then solve the equation.</p><p>Negative nine times a number is -117. Find the number.</p>
<p>Numbers Let <code class='latex inline'> x </code> represent the larger of two numbers, and <code class='latex inline'> y </code> , the smaller. Write algebraic expressions for</p><p>d) the sum of six times the larger and two times the smaller</p>
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