1/4 - 1/3 = 3/12 - 4/12 = - 1/12
In radical form, the shortest distance from ( -4 , 4 ) and the line y = -2x + 6 is
2√5 units.
Attached below is the calculation to arrive at the answer as well as a graph.
Answer:
(c) will be perpendicular to the line y = 3x+2
Step-by-step explanation:
We have given the the equation of line as y = 3x+2
We know the equation of line as y = mx+c , here m is slope and c is intercept
On comparing with standard equation of line m = 3
We know that slope of perpendicular line is
So the slope of the line which is perpendicular to y = 3x+2 will be
Now (a) Line is given as its slope is so it will be not perpendicular
(b) Line is given as its slope is so it will be not perpendicular
(c) Line is given as its slope is so it will be perpendicular to the line y = 3x+2
(d) Line is given as its slope is 3 so it will not perpendicular to the line y = 3x+2
Answer:
7
Step-by-step explanation:
Quadratic Equation: 3x² - 24x + 72
The form we are to convert the equation to:
3x² - 24x + 72
a(x + b)² + 72
3(x² - 8x + 24)
Step 1
Make the Quadratic equation (x² - 8x) in the bracket factorisable using completing the square method
3( x² - 8x +(- 8/2)²) + 24
3( x² - 8x + 16 = -24 + 16
3( x² - 8x + 16 + 8 = 0)
3( x² - 8x + 16) + 8
3( x² - 4x + 4x + 16) + 8
3( x(x - 4) -4(x - 4) + 8
3((x - 4)(x - 4) )+ 8
3( (x - 4)² + 8
Using this form
a(x + b)² + c
a = 3
b = -4
c = 8
We were asked to add up constants a, b, c
Therefore,
3 +(-4) + 8
= 7
A
The domain is -∞ < x < ∞
B
The range is -∞ < x ≤ 3
C
The graph is increasing from -∞ < y < 3
D
The graph is decreasing from 3 > y > -∞
E
The local maximum is at ( - 2, 3 )
F
There are no local minimums