Answer:
--- Length
--- Width
Step-by-step explanation:
Given
Let: 
Required
Find the dimensions of the rectangle
Area (A) is calculated as:
This gives:
Open bracket
Express as a quadratic function
Expand
Factorize:
This gives:
Width can not be negative.
So:
Recall that:
Answer:
x = 9
Step-by-step explanation:
Simplifying
17x + -12 = 114 + 3x
Reorder the terms:
-12 + 17x = 114 + 3x
Solving
-12 + 17x = 114 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
-12 + 17x + -3x = 114 + 3x + -3x
Combine like terms: 17x + -3x = 14x
-12 + 14x = 114 + 3x + -3x
Combine like terms: 3x + -3x = 0
-12 + 14x = 114 + 0
-12 + 14x = 114
Add '12' to each side of the equation.
-12 + 12 + 14x = 114 + 12
Combine like terms: -12 + 12 = 0
0 + 14x = 114 + 12
14x = 114 + 12
Combine like terms: 114 + 12 = 126
14x = 126
Divide each side by '14'.
x = 9
Simplifying
x = 9
Answer:
a) one solution
b) no solution
Step-by-step explanation:
Systems of equations can be described as having one solution, no solution or infinite solutions:
One solution: 'x' and 'y' are equal to only one value
No solution: 'x' and 'y' can not be solved with the given equations
Infinite solutions: values for 'x' and 'y' include all real numbers
In order to evaluate the systems, putting them in the same format is your first step:
a) - y = -5x - 6 or y - 5x = 6
y - 5x = -6
Since both equations have the same expression 'y - 5x', but there are equal to opposite values, this system would have no solution, as this would not be possible to calculate.
b) y + 3x = -1
y = 3x -1 or y - 3x = -1
Solving for 'y' by adding the equations and eliminating 'x', gives us:
2y = -2 or y = -1
Using y = -1 to plug back into an equation and solve for 'x': -1 + 3x = -1 or x = 0. Since 'x' and 'y' can be solved for a value, the system has just one solution.
Answer:
68
Step-by-step explanation:
