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# Algebra

See the attached file.

Solve by completing the square
________________________________________________________________________
The width of a rectangle is 1ft less than the length. The area is find the length and width.

The width is __________ft

The Length is _________ft

A farmer decides to enclose a rectangular garden, using the side of a bard as one side of the rectangle. What is the maximum area that the farmer can enclose with 100ft of fence. What should the dimensions of the garden be to give this area?

The maximum area that the farmer can enclose with 100ft of Fence is ______sq ft

The dimensions of the garden to give this area is 50 ft by ______ft

Find the x-intercepts and y -intercepts for

The x intercept(s) is (are) __________
The y intercept(s) is (are) __________

(type an ordered pair. Type an integer or a decimal. Round to the nearest tenth. Use commas to separate answers as needed. Type N if there is no intercept.

Write a quadriatic equation in the variable x having the given numbers as solutions. Type the equation in standard form, .

Solution: 3, only solution

The equation is ____________=0

Determine the nature of the solutions of the equation.

a. 2 real soluions
b. 1 real solutions
c. 2 imaginary solutions

Find the x intercepts of:
What are the x intercepts___________________
(type an ordered pair. Simplify your answer. Type an exact answer, using radicals as needed. Express complex numbers in terms of i. use a comma to separate answers as needed)

A. Solve
B. Find the x-intercepts of

a) what are the solutions?
X=________________
(type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. use a comma to separate answers as needed)

b) What are the x intercepts?
_______________________
(type an ordered pair, type an exact answer using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. use a comma to separate answers as needed. Type N if there is no x intercepts)

A student opens a mathematics book to two facing pages. The product of the page numbers is 110. Find the page numbers.

The first page is_____
The second page is _________.

#### Solution Preview

Solve by completing the square

________________________________________________________________________
The width of a rectangle is 1ft less than the length. The area is find the length and width.

Assume length is: x
Then width is: x - 1

6 = x * (x - 1)
x2 - x = 6

x2 - x + ¼ = 6 + ¼
(x - ½) 2 = 25/4
x - ½ = 5/2
x = 3

The width is ____2______ft

The Length is __3_______ft

A farmer decides to enclose a rectangular garden, using the side of a bard as one side of the rectangle. What is the maximum area that the farmer can enclose with 100ft of fence. What should the dimensions of the garden be to give this area?

2 x + 2 y = 100
y = 50 - x

S = x * (50 - x)
S = - x2 + 50x

S' = -2x + 50
S' = 0
x = 25
y = ...

#### Solution Summary

The solution assists by competing the square.

\$2.19