Answer:
Step-by-step explanation:
1). Given equation is,
2x² - 3x = 6
2x² - 3x - 6 = 0
To find the solutions of the equation we will use quadratic formula,
x = 
Substitute the values of a, b and c in the formula,
a = 2, b = -3 and c = -6
x = 
x = 
x = 
x = 
Therefore, there are two real solutions.
2). Given equation is,
x² + 1 = 2x
x² - 2x + 1 = 0
(x - 1)² = 0
x = 1
Therefore, there is one real solution of the equation.
3). 2x² + 3x + 2 = 0
By applying quadratic formula,
x =
x = 
x = 
x = 
x = 
Therefore, there are two complex (non real) solutions.
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Answer:
y = 2x - 5
Step-by-step explanation:
The slope for a parallel line is the same as the slope in the given equation. Therefore the slope of the new line will be 2 m= 2
use that slope and (2, -1) to find b
-1 = 2(2) + b
-1 = 4 + b
-5 = b
Plug m and b into y = mx + b
y = 2x - 5
Answer:
area of the rectangle = 5(m⁶ - 2m⁵ - m⁴) or 5m⁴(m² - 2m - 1)
Step-by-step explanation:
The rectangle has a height of 5m⁴ and the width is m² - 2m - 1.The area of the rectangle is the product of the width and the height.
width = m² - 2m - 1
height = 5m⁴
area of rectangle = 5m⁴ × (m² - 2m - 1)
area of rectangle = 5m⁴(m² - 2m - 1)
area of the rectangle = 5m⁶ - 10m⁵ - 5m⁴
area of the rectangle = 5(m⁶ - 2m⁵ - m⁴)
The area of the entire rectangle can be expressed as 5(m⁶ - 2m⁵ - m⁴) or 5m⁴(m² - 2m - 1)
