Answer: B) False
A counter-example would be the cubic polynomial y = x^3 which doesn't have a max or a min. The graph stretches forever in both directions (up and down) indicating that the range is the set of all real numbers.
Y = 3x - 7 . . . . . (1)
6x - 2y = 12 . . . (2)
Putting (1) into (2) gives
6x - 2(3x - 7) = 12
6x - 6x + 14 = 12
14 = 12
Therefore, there is no solution.
First we have the following equation:
a - b = 0
We clear one of the variables depending on the other:
a = b
Therefore we have to for the following expression:
a + b
We can substitute one of the variables, obtaining:
a + a = 2a
Equivalently:
b + b = 2b
Answer:
a + b = 2a
or
a + b = 2b
Answer:
Largest possible length is <em>21 inches</em>.
Step-by-step explanation:
Given:
Total material available = 60 inches
Length to be 3 more than twice of width.
To find:
Largest possible length = ?
Solution:
As it is rectangular shaped frame.
Let length = 
inches and
Width = 
inches
As per given condition:
..... (1)
Total frame available = 60 inches.
i.e. it will be the perimeter of the rectangle.
Formula for perimeter of rectangle is given as:
Putting the given values and conditions as per equation (1):
Putting in equation (1):
So, the answer is:
Largest possible length is <em>21 inches</em>.
We know that if two lines are Perpendicular then Product of Slopes of both of these Perpendicular lines should be Equal to -1
Given : Equation of 1st Perpendicular line is -x + 3y = 9
This can be written as :
3y = x + 9
y = x/3 + 3
Comparing with standard form : y = mx + c
we can notice that slope of 1st Perpendicular line = 1/3
Slope of 1st Line × Slope of 2nd line = -1
1/3 × Slope of 2nd line = -1
Slope of 2nd line = -3
We know that the form of line passing through point (x₀ , y₀) and having slope m is :
y - y₀ = m(x - x₀)
Here the 2nd Perpendicular line passes through the point (-3 , 2)
x₀ = -3 and y₀ = 2 and we found m = -3
⇒ y - 2 = -3(x + 3)
⇒ -3x - 9 = y - 2
⇒ -3x - y = 7
