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Math Problems: Homework Help & Examples

Solve math problems step by step with detailed explanations and examples for equations, distance, speed, and more.

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Math Problems: Homework Help & Examples

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  1. ANSWER 11 Warm-Up #3 1. 780 = 12.5r 2. 9x + 25 = 178 ANSWER 17 ANSWER 62.4 3. 636 = 40g + 28(18 – g) 4.A balloon is released from a height of 5 feet above the ground. Its altitude (in feet) after tminutes is given by the expression 5 + 82t. What is the altitude of the balloon after 6 minutes? 497 ft ANSWER

  2. HomeworkCheck

  3. High-speed Train The Acela train travels between Boston and Washington, a distance of 457miles. The trip takes 6.5 hours. What is the average speed? Rate (miles/hour) = Time (hours) Distance (miles) = r 6.5 457 EXAMPLE 1 Use a formula -I SOLUTION -C You can use the formula for distance traveled as a verbal model.

  4. 70.3 r ANSWER The average speed of the train is about 70.3miles per hour. 70.3miles 457 miles 6.5hours 1hour EXAMPLE 1 Use a formula An equation for this situation is 457 = 6.5r. Solve for r. 457 = 6.5r Write equation. -A -N Divide each side by 6.5. CHECK You can use unit analysis to check your answer.

  5. ANSWER Jet takes about 12.5hours to fly from New York to Tokyo. for Example 1 GUIDED PRACTICE AVIATION: A jet flies at an average speed of 540miles per hour. How long will it take to fly from New York to Tokyo, a distance of 6760miles? 1.

  6. Paramotoring A paramotor is a parachute propelled by a fan-like motor. The table shows the height h of a paramotorist t minutes after beginning a descent. Find the height of the paramotorist after 7 minutes. EXAMPLE 2 Look for a pattern I

  7. EXAMPLE 2 Look for a pattern C A SOLUTION The height decreases by 250feet per minute. You can use this pattern to write a verbal model for the height. An equation for the height ish = 2000 – 250t.

  8. So, the height after 7minutes is h = 2000 – 250(7) = 250 feet. ANSWER EXAMPLE 2 Look for a pattern N

  9. Banners You are hanging four championship banners on a wall in your school’s gym. The banners are 8feet wide. The wall is 62feet long. There should be an equal amount of space between the ends of the wall and the banners, and between each pair of banners. How far apart should the banners be placed? Begin by drawing and labeling a diagram, as shown below. EXAMPLE 3 Draw a diagram -I -C SOLUTION

  10. x + 8 + x + 8 + x + 8 + x + 8 + x 62 = 62 5x + 32 = 5x 30 = x = 6 ANSWER The banners should be placed 6feet apart. EXAMPLE 3 Draw a diagram From the diagram, you can write and solve an equation to find x. -A -N Write equation. Combine like terms. Subtract 32 from each side. Divide each side by 5.

  11. Write a verbal model. Then write an equation. STEP 1 EXAMPLE 4 Standardized Test Practice SOLUTION An equation for the situation is 460 = 30g + 25(16 – g).

  12. Solve for gto find the number of gallons used on the highway. STEP 2 The correct answer is B. ANSWER 30 12 + 25(16 – 12) = 360 + 100 = 460 EXAMPLE 4 Standardized Test Practice 460 = 30g + 25(16 – g) Write equation. 460 = 30g + 400 – 25g Distributive property 460 = 5g + 400 Combine like terms. 60 = 5g Subtract 400 from each side. 12 = g Divide each side by 5. The car used 12 gallons on the highway. CHECK:

  13. PARAMOTORING: The table shows the height h of a paramotorist after tminutes. Find the height of the paramotorist after 8 minutes. 2. So, the height after 8minutes is h = 2400 – 210(8) = 720 ft ANSWER for Examples 2, 3 and 4 GUIDED PRACTICE

  14. ANSWER The space between the banner and walls and between each pair of banners would increase to 9.5feet. for Examples 2, 3 and 4 GUIDED PRACTICE WHAT IF?In Example 3, how would your answer change if there were only three championship banners? 3.

  15. FUEL EFFICIENCY A truck used 28 gallons of gasoline and traveled a total distance of 428 miles. The truck’s fuel efficiency is 16miles per gallon on the highway and 12 miles per gallon in the city. How many gallons of gasoline were used in the city? 4. ANSWER Five gallons of gas were used. for Examples 2, 3 and 4 GUIDED PRACTICE

  16. The solutions are all real numbers less than 2. An open dot is used in the graph to indicate 2 is not a solution. EXAMPLE 1 Graph simple inequalities a. Graph x < 2.

  17. The solutions are all real numbers greater than or equal to –1. A solid dot is used in the graph to indicate –1is a solution. EXAMPLE 1 Graph simple inequalities b. Graph x ≥ –1.

  18. The solutions are all real numbers that are greater than –1 and less than 2. EXAMPLE 2 Graph compound inequalities a. Graph –1 < x < 2.

  19. The solutions are all real numbers that are less than or equal to –2 or greater than 1. EXAMPLE 2 Graph compound inequalities b. Graph x ≤ –2 orx > 1.

  20. Solve– 4 < 6x – 10 ≤ 14. Then graph the solution. ANSWER The solutions are all real numbers greater than 1 and less than or equal to 4. The graph is shown below. EXAMPLE 5 Solve an “and” compound inequality – 4 < 6x – 10 ≤ 14 Write original inequality. – 4 + 10< 6x – 10 + 10≤ 14 + 10 Add 10 to each expression. 6 < 6x ≤ 24 Simplify. 1 < x ≤ 4 Divide each expression by 6.

  21. . Then graph the solution. 11 or 5x – 7 ≥ 23 Solve 3x + 5 ≤ EXAMPLE 6 Solve an “or” compound inequality SOLUTION A solution of this compound inequality is a solution of either of its parts. First Inequality Second Inequality 3x + 5 ≤ 11 5x – 7 ≥ 23 Write first inequality. Write second inequality. 5x ≥ 30 3x ≤ 6 Add 7 to each side. Subtract 5 from each side. x ≥ 6 Divide each side by 5. x ≤ 2 Divide each side by 3.

  22. ANSWER The graph is shown below. The solutions are all real numbers less than or equal to2or greater than or equal to6. EXAMPLE 6 Solve an “or” compound inequality

  23. Biology A monitor lizard has a temperature that ranges from 18°C to 34°C. Write the range of temperatures as a compound inequality. Then write an inequality giving the temperature range in degrees Fahrenheit. EXAMPLE 7 Write and use a compound inequality

  24. 18 ≤ ≤ 34 5 9 5 9 5 Substitute for C. (F – 32) 5 Multiply each expression by , the reciprocal of . 9 (F – 32) 9 EXAMPLE 7 Write and use a compound inequality SOLUTION The range of temperatures Ccan be represented by the inequality 18 ≤ C ≤ 34. Let Frepresent the temperature in degrees Fahrenheit. 18 ≤ C ≤ 34 Write inequality. 32.4 ≤ F – 32 ≤ 61.2 64.4 ≤ F ≤ 93.2 Add 32 to each expression.

  25. CLASSWORK Workbook 1-5 (1-15 odd) Workbook 1-6 (1-23 odd)

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