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10th Edition

Jerome E. Kaufmann + 1 other

Publisher: Cengage Learning

ISBN: 9781285195728

Chapter 10.4, Problem 28PS

Textbook Problem

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Solve each of the following problems by setting up and solving a system of three linear equations in three variables.

**(Objective 2)**

The perimeter of a triangle is 45 centimeters. The longest side is 4 centimeters less than twice the shortest side. The sum of the lengths of the shortest and longest sides is 7 centimeters less than three times the length of the remaining side. Find the lengths of all three sides of the triangle.

To determine

**To find:**

Three sides of triangle.

**Procedure:**

Step-1: Assume unknown quantities in terms of *x*, *y*, *z*, etc.….

Step-2: Write the equations in terms of variables using given information.

Step-3: Solve the equations for variables.

Step-4: Find the values which is asked for.

**Calculation:**

Let the shortest side be *x* cm, the longest side be *z* cm and third side by *y* cm. Perimeter is sum of all three sides of triangle. Here perimeter is 45 centimeters. We get

The longest side is 4 centimeters less than twice the shortest side. We get

The sum of the lengths of the shortest and longest sides is 7 centimeters less than three times the length of the third side.

Multiply equation (1) by 3 and add equation (3).

Intermediate Algebra

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For problems 6-15, perform the indicated...Ch. 10.CM - For problems 6-15, perform the indicated...Ch. 10.CM - For problems 6-15, perform the indicated...Ch. 10.CM - For problems 6-15, perform the indicated...Ch. 10.CM - For problems 16-19, simplify each of the complex...Ch. 10.CM - For problems 16-19, simplify each of the complex...Ch. 10.CM - For problems 16-19, simplify each of the complex...Ch. 10.CM - For problems 16-19, simplify each of the complex...Ch. 10.CM - For problems 20-25, factor each of the algebraic...Ch. 10.CM - For problems 20-25, factor each of the algebraic...Ch. 10.CM - For problems 20-25, factor each of the algebraic...Ch. 10.CM - For problems 20-25, factor each of the algebraic...Ch. 10.CM - For problems 20-25, factor each of the algebraic...Ch. 10.CM - For problems 20-25, factor each of the algebraic...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 26-33, evaluate each of the numerical...Ch. 10.CM - For problems 34-36, find the indicated products...Ch. 10.CM - For problems 34-36, find the indicated products...Ch. 10.CM - For problems 34-36, find the indicated products...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems 37-44, express each radical...Ch. 10.CM - For problems, 45-47, use the distributive property...Ch. 10.CM - For problems, 45-47, use the distributive property...Ch. 10.CM - For problems, 45-47, use the distributive property...Ch. 10.CM - For problems 48 and 49, rationalize the...Ch. 10.CM - For problems 48 and 49, rationalize the...Ch. 10.CM - For problems 50-52, use scientific notation to...Ch. 10.CM - For problems 50-52, use scientific notation to...Ch. 10.CM - For problems 50-52, use scientific notation to...Ch. 10.CM - For problems 53-56, find each of the indicated...Ch. 10.CM - For problems 53-56, find each of the indicated...Ch. 10.CM - For problems 53-56, find each of the indicated...Ch. 10.CM - For problems 53-56, find each of the indicated...Ch. 10.CM - Find the slope of the line determined by the...Ch. 10.CM - Find the slope of the line determined by the...Ch. 10.CM - Find the length of the line segment whose...Ch. 10.CM - Write the equation of the line that contains the...Ch. 10.CM - Write the equation of the line that is...Ch. 10.CM - Find the center and the length of a radius of the...Ch. 10.CM - For the parabola y=x2+10x+21, find the coordinates...Ch. 10.CM - For the ellipse x2+4y2=16, find the length of the...Ch. 10.CM - For problems 65-70, graph each of the equations....Ch. 10.CM - For problems 65-70, graph each of the equations....Ch. 10.CM - For problems 65-70, graph each of the equations....Ch. 10.CM - For problems 65-70, graph each of the equations....Ch. 10.CM - For problems 65-70, graph each of the equations....Ch. 10.CM - For problems 65-70, graph each of the equations....Ch. 10.CM - For problems 71-76, graph each of the functions....Ch. 10.CM - For problems 71-76, graph each of the functions....Ch. 10.CM - For problems 71-76, graph each of the functions....Ch. 10.CM - For problems 71-76, graph each of the functions....Ch. 10.CM - For problems 71-76, graph each of the functions....Ch. 10.CM - For problems 71-76, graph each of the functions....Ch. 10.CM - If f(x)=x3 and g(x)=2x2x1, find (gf)(x) and...Ch. 10.CM - Find the inverse (f1) of f(x)=3x7.Ch. 10.CM - Find the inverse of f(x)=12x+23.Ch. 10.CM - Find the constant of variation if y varies...Ch. 10.CM - If y is inversely proportional to the square of x,...Ch. 10.CM - The volume of a gas at a constant temperature...Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 83-103, solve each of the equations....Ch. 10.CM - For problems 104-113, solve each of the...Ch. 10.CM - For problems 104-113, solve each of the...Ch. 10.CM - For problems 104-113, solve each of the...Ch. 10.CM - For problems 104-113, solve each of the...Ch. 10.CM - For problems 104-113, solve each of the...Ch. 10.CM - For problems 104-113, solve each of the...Ch. 10.CM - For problems 104-113, solve each of the...Ch. 10.CM - For problems 114-118, solve each of the systems of...Ch. 10.CM - For problems 114-118, solve each of the systems of...Ch. 10.CM - For problems 114-118, solve each of the systems of...Ch. 10.CM - For problems 114-118, solve each of the systems of...Ch. 10.CM - For problems 114-118, solve each of the systems of...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...Ch. 10.CM - For problems 119-130, set up an equation, an...

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