a. Answer f ( h ) = 23 + h Explanation Given information : Third side of the triangle is given as h . Hence the function for perimeter is, f ( h ) = 13 + 10 + h f ( h ) = 23 + h b. To determine To determine the independent and dependent variables. Answer h is independent whereas f is dependent. Explanation Here the perimeter of the triangle depends on the third side of the triangle that is h . Hence we can say that f that represents the perimeter is dependent whereas h is an independent variable. c. To determine To determine the range and domain of the function. Answer The domain is (3, 23) The range of the function is (26, 46) Explanation Given information : We know that the sum of two sides of a triangle is always greater than the third side. Hence we get, h < 10 + 13 or h < 23 13 < h + 10 or 3 < h Hence the domain is (3, 23) Now put the value of h in the perimeter function we get, f ( 3 ) = 23 + 3 = 26 f ( 23 ) = 23 + 23 = 46 Therefore the range of the function is (26, 46)

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

1st Edition

ISBN: 9781608408382

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 3.1, Problem 39E

To determine

To write a function that represents perimeter of the triangle.

Expert Solution

Answer to Problem 39E

f(h)=23+h

Explanation of Solution

Given information :

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015, Chapter 3.1, Problem 39E , additional homework tip 1

Third side of the triangle is given as h .

Hence the function for perimeter is,

f(h)=13+10+hf(h)=23+h

To determine

To determine the independent and dependent variables.

Expert Solution

Answer to Problem 39E

h is independent whereas f is dependent.

Explanation of Solution

Here the perimeter of the triangle depends on the third side of the triangle that is h .

Hence we can say that f that represents the perimeter is dependent whereas h is an independent variable.

To determine

To determine the range and domain of the function.

Expert Solution

Answer to Problem 39E

The domain is (3, 23)

The range of the function is (26, 46)

Explanation of Solution

Given information :

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015, Chapter 3.1, Problem 39E , additional homework tip 2

We know that the sum of two sides of a triangle is always greater than the third side.

Hence we get,

h<10+13 or h<2313<h+10 or 3<h

Hence the domain is (3, 23)

Now put the value of h in the perimeter function we get,

f(3)=23+3=26f(23)=23+23=46

Therefore the range of the function is (26, 46)

Chapter 3.1, Problem 38E

Chapter 3.1, Problem 40E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - 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