Answer:
Width of the rectangle = 17 inches
Length of the rectangle = 31 inches
Step-by-step explanation:
Let w be the width of the rectangle.
Given:
Width of the rectangle = w
Length of the rectangle = 2w - 3
Area of the rectangle 
Solution:
We know that the area of the rectangle.
Now, we first find the root of the above equation.
Use quadratic formula with 
.
Put a, b and c value in above equation.
For positive sign
w = 17 inches
So, width of the rectangle is 17 inches.
Length of the rectangle.
Length = 31 inches
So, length of the rectangle is 31 inches.
Therefore, width and length of the rectangle is 17 inches and 31 inches.
In order to find CPU (Cost per unit) we must take the cost, and divide it by the number of units.
So,
Since we are talking about money, it is implied to round to the nearest cent, so the final answer is
$3.44
Answer:
x = 3 and 7
There are two true solutions.
Step-by-step explanation:
To solve 
, use inverse operations by squaring both sides of the equal sign.
The quadratic expression can be factored into binomials and set equal to 0 by the zero product property to find x.
(x - 3) ( x - 7) = 0
x-3 = 0 so x=3
x-7 = 0 so x=7
Now check each solution into the original equation to be sure it solve the solution and is not extraneous.
and
![3-7 = \sqrt{-4(3)+28}\\[tex]-4 = \sqrt{16}\\-4 =-4](https://tex.z-dn.net/?f=3-7%20%3D%20%5Csqrt%7B-4%283%29%2B28%7D%5C%5C%5Btex%5D-4%20%3D%20%5Csqrt%7B16%7D%5C%5C-4%20%3D-4)
[/tex]
Answer:
<em>a) x = -2+√3 and -2-√3</em>
<em>b) x = -1 + 2√3/3 and -1 - 2√3/3</em>
<em>c) x = 3.185 and 0.315</em>
Step-by-step explanation:
To solve the following quadratic equation, we will use the general formula
x = -b±√b²-4ac/2a
a) x²+4x+1 = 0
a = 1, b = 4 and c = 1
Substitute into the formula
x = -4±√4²-4(1)(1)/2(1)
x = -4±√16-4/2
x = -4±√12/2
x = -4±2√3/2
x = (-4+2√3)/2 and (-4-2√3)/2
<em>x = -2+√3 and -2-√3</em>
b) 3x²+6x-1 = 0
a = 3, b = 6 and c = -1
Substitute into the formula
x = -6±√6²-4(3)(-1)/2(3)
x = -6±√36+12/6
x = -6±√48/6
x = -6±4√3/6
x = (-6+4√3)/6 and (-6-4√3)/6
<em>x = -1 + 2√3/3 and -1 - 2√3/3</em>
<em></em>
c) 2x² - 7x + 2 = 0
a = 2, b = -7 and c = 2
x = -(-7)±√(-7)²-4(2)(2)/2(2)
x = 7±√49-16/4
x =7±√33/4
x = 7±5.74/4
x = 7+5.74/4 and 7-5.74/4
x = 12.74/4 and 1.26/4
<em>x = 3.185 and 0.315</em>
<em></em>
10) Enlarging by a factor of 7 corresponds to an increase by a factor of
for the area, or 49. The new rectangle has area 980 square-inches.
To verify, let's say the dimensions of the original rectangle are
. We increase each dimension by a factor of 7 to get
. This new area is 980 square-inches.
11) We use the same concept. Increasing by a factor of 0.6 corresponds to increasing the area by
(n.b., an increase by a factor less than 1 is shrinking). Original area is
. New area is
.
12) We multiply 15 by 11/30 to get 5.5 ft. We multiply 8.25 by the same factor to get 3.025 ft. The area is
.
