Page 732 - Algebra 1

Application: Architecture
An architect is designing a performance center. If the area of the center is 30 square decameters, what is the area of the gallery?
SOLUTION
Example
5
Auditorium
Gallery
g. 6√x =24 (Ex 2)
√ x + 4 = √ 2 x - 1 √ x - 2 = x - 4

i.
(Ex 3)
k.
(Ex 4)
m.
(Ex 5)
(Ex 2)
j.
(Ex 3)
l.
(Ex 4)
3
√ x + 5 - √ 6 x = 0 √ x + 8 = - 3
√ x
√x 6 √x
Simplify.
Combine like terms. Divide both sides by 6. Square both sides. Simplify.
total area = area of auditorium + area of gallery 30 = (√x)2 + √x(6 - √x)
30 = x + 6√ x - x
30 = 6√x 5 = √ x
52 = (√x)2
Math Reasoning
Analyze Is the answer reasonable?
25 = x
The area of the auditorium is 25 square decameters.
To find the area of the gallery, subtract the area of the auditorium from the total area.
30 - 25 = 5
The area of the gallery is 5 square decameters.
Lesson Practice
Solve each equation.
a.
(Ex 1)
c.
(Ex 1)
e.
(Ex 2)
√ x = 6
√ x + 3 = 12 √ x - 8 = 5
b.
(Ex 1)
d.
(Ex 1)
f.
√ 5x = 15 √ 4x - 15 = 7 √x +8=15
(Ex 2)
Breakfast Nook
Practice
Distributed and Integrated
1. Solve x2 = 64. (102)
2. Factor x2 - 9x + 20. (Inv 9)
A breakfast nook has a planter along one side. The entire area of the nook is 42 square yards. What is the area of the planter?
_
h. √x=15
√ x
Planter
√x (7 √x )
Lesson 106 717