Solve the system of inequalities : |x|<7 |x| ≥5
2 answers:
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Answer:
Step-by-step explanation:
Given
1. 5 units down translation
2. Reflection in the x-axis
Required
Determine the resulting function g
1. 5 units down translation
This is defined by the rule:
A down translation is:
Where b is the number of units.
So, we have:
2. Reflection in the x-axis
For a function f(x),
When reflected over the x-axis, it becomes -f(x)
So:
Answer:
The length of the rectangle is 6 feet
Step-by-step explanation:
Given as :
The length of rectangle is 1 feet less than twice the width
So, let The width of rectangle = w feet
The length of rectangle = ( 2 w - 1 ) feet
The area of the rectangle = 21 feet²
Now,
∵ The area of the rectangle = length × width
Or, 21 feet² = ( 2 w - 1 ) feet × w feet
or, 21 = 2 w² - w
or, 2 w² - w - 21 = 0
or, 2 w² + 6 w - 7 w - 21 = 0
or , 2 w ( w + 3 ) - 7 ( w + 3 ) = 0
or, ( w + 3 ) ( 2 w - 7 ) = 0
So, w = - 3 feet , feet
here we consider only positive value of w i.e feet
∴ The length of rectangle = ( 2 w - 1 ) feet
or, The length of rectangle = 2 × - 1
Or, The length of rectangle = 7 - 1 = 6 feet
Hence The length of the rectangle is 6 feet , Answer