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Section 7.4 Applications of Quadratic Equations

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**Objective 1: Use quadratic equations to solve word problems.**

Strategy for Solving Word Problems Step 1. Read the problem carefully to determine what you are being asked to find. Step 2. Select a ____________ to represent each unknown quantity. Specify precisely what each variable represents and note any restrictions on each variable. Step 3. If necessary, make a ____________ and translate the problem into a word equation or a system of word equations. Then translate each word equation into an ____________ equation. Step 4. Solve the equation or system of equations, and answer the question completely in the form of a sentence. Step 5. Check the __________________ of your answer.

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**1. Find two consecutive odd integers whose product is 195.**

(a) Identify the variable: Let n = the smaller odd integer Let _________________ = the larger odd integer (b) Write the word equation: The ___________ of the two odd integers is _________ .

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**1. Find two consecutive odd integers whose product is 195.**

(c) Translate the word equation into an algebraic equation: (d) Solve this equation:

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**1. Find two consecutive odd integers whose product is 195.**

(e) Write a sentence that answers the question: (f) Is this answer reasonable?

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**2. The sum of the squares of two consecutive even integers**

is Find these integers.

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**3. One number is two less than six times another number.**

Find these numbers if their product is 48.

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**Area of a Rectangle The length of a rectangle is 3 cm more**

than 2 times the width. Find the dimensions of this rectangle if the area is 65 cm2. (a) Identify the variable: Let w = the width of the rectangle in _________ Let _____________ = the _____________ of the rectangle in _________ . (b) Write the word equation: The ___________ is ____________ .

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**Area of a Rectangle The length of a rectangle is 3 cm**

more than 2 times the width. Find the dimensions of this rectangle if the area is 65 cm2. (c) Translate the word equation into an algebraic equation: (d) Solve this equation:

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**Area of a Rectangle The length of a rectangle is 3 cm**

more than 2 times the width. Find the dimensions of this rectangle if the area is 65 cm2. (e) Write a sentence that answers the question: (f) Is this answer reasonable?

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**Finding Dimensions If each side of a square is increased**

by 10 inches, the total area of both the new square and the original square will be 210 square inches. What is the length of each side of the original square? Round to the nearest tenth of an inch.

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**Height of a Baseball The height in feet of a baseball is**

given by where t represents the time in seconds the ball is in flight. (a) Determine the number of seconds before the baseball hits the ground at a height level of 0 ft.

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**Height of a Baseball The height in feet of a baseball is**

given by where t represents the time in seconds the ball is in flight. (b) Determine the time interval for which the height of the ball is above 20 ft.

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**7. Calculating an Interest Rate If the formula computing the**

amount A of an investment of principal P invested at interest rate r for 1 year and compounded semiannually is , what interest rate is necessary for $12,000 to grow to $12,484.80?

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**Objective 2: Use the Pythagorean Theorem.**

If triangle ABC is a right triangle, then: Algebraically Verbally The sum of the areas of the squares formed on the legs of a right triangle is equal to the area of the square formed on the hypotenuse. (The converse of this theorem is also true. If , then triangle ABC is a right triangle.)

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Use the Pythagorean Theorem to find the length of the side that is not given. Round to the nearest hundredth. 8. 26 24 b

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Use the Pythagorean Theorem to find the length of the side that is not given. Round to the nearest hundredth. 9. c 15 36

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Use the Pythagorean Theorem to find the length of the side that is not given. Round to the nearest hundredth. 10. 7 4 b

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Use the Pythagorean Theorem to find the length of the side that is not given. Round to the nearest hundredth. 11. c 3 6

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**12. A 42-inch wide screen television is advertised as having a**

8:5 aspect ratio. (The aspect ratio is the ratio of the width to the height of the screen.) Determine the actual dimensions and the viewable area of this television.

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**13. Two airplanes depart simultaneously from an airport. One**

flies due south; the other flies due east at a rate 20 miles per hour faster than that of the first airplane. After 4 hours radar indicates that the airplanes are 800 miles apart. What is the ground speed of each airplane? Round the speed to the nearest whole number.

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