Is 0.81 the same as 0.081
2 answers:
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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
Answer:
We are have the function f(x).
Part 1: It is given that the function f(x) is transformed to f(x)+2.
This gives us that the function is translated 2 units upwards.
As, the y-intercept of f(x) is f(0). So, the y-intercept of f(x)+2 is f(0)+2, which is also translated 2 units up.
Translation does not change the behavior of the function.
So, if f(x) is increasing (or deceasing), then f(x)+2 will be increasing(or decreasing) respectively.
Moreover, f(x)+2 will be even or odd if f(x) is even or odd respectively.
Part 2: It is given that the function f(x) is transformed to
This gives us that the function is shrinked vertically by a factor of followed by a reflection across x-axis.
Also, the y-intercept of is .
The graph of f(x) after changing to will flip over the x-axis.
So, the function will increase or decrease when f(x) decrease or increase respectively.
Moreover, will be even if f(x) is even or odd respectively.