Q. 4.100 Loreen has a calligraphy busines... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 4: Q. 4.100 (page 511)

Loreen has a calligraphy business. The equation $C = 1.8 n + 35$ models the relation between her weekly cost, $C$ , in dollars and the number of wedding invitations, $n$ , that she writes.
鈸� Find Loreen鈥檚 cost for a week when she writes no invitations.
鈸� Find the cost for a week when she writes $75$ invitations.
鈸� Interpret the slope and C-intercept of the equation.
鈸� Graph the equation.

Short Answer

Expert verified

鈸� Loreen鈥檚 cost for a week when she writes no invitations : $$ 35$

鈸� Loreen鈥檚 cost for a week when she writes $75$ invitations is : $$ 170$

鈸� The slope, $1.8$ , means that when the number of invitations increases by $1$ , weekly cost increases by $$ 1.8$ . The C-intercept means that the weekly cost is $$ 35$ when number of invitations written is $0$ .

鈸� Graph of the equation

Step by step solution

Part (a) Step 1. Given Information

The equation $C = 1.8 n + 35$ models the relation between Loreen's weekly cost, $C$ , in dollars and the number of wedding invitations, $n$ , that she writes.

Part (a) Step 2. Loreen's cost for a week when no invitations were written

Put $n = 0$ in the given equation $C = 1.8 n + 35$

鈬� C = 1.8 (0) + 35 鈬� C = 0 + 35 鈬� C = 35

Part (b) Step 1. Loreen's cost for a week when 75 invitations were written

Put $n = 75$ in the given equation $C = 1.8 n + 35$

鈬� C = 1.8 (75) + 35 鈬� C = 135 + 35 鈬� C = 170

Part (c) Step 1. Interpreting the slope and C-intercept of the equation

The equation $C = 1.8 n + 35$ is in slope-intercept form $y = m x + b$

By comparison, we get, slope, $m = 1.8$ , which means that when the number of invitations increases by $1$ , weekly cost increases by $$ 1.8$ . The C-intercept means that the weekly cost is $$ 35$ when the number of invitations written is $0$ .

Part (d) Step 1. Graphing the equation

Graphing the equation $C = 1.8 n + 35$ .

Take two points calculated above: $(0, 35)$ and $(75, 170)$ . Join them to get the required graph of the line.

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91影视

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Loreen's cost for a week when no invitations were written

Part (b) Step 1. Loreen's cost for a week when 75 invitations were written

Part (c) Step 1. Interpreting the slope and C-intercept of the equation

Part (d) Step 1. Graphing the equation

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