Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
(a)
here m = - 
and c = 6, hence
y = - x + 6 ← equation of line
(b)
here m = 6, hence
y = 6x + c ← is the partial equation
to find c substitute (2, - 6 ) into the partial equation
- 6 = 12 + c ⇒ c = - 6 - 12 = - 18
y = 6x - 18 ← equation of line
(c)
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 3) and (x₂, y₂ ) = (4, 7)
m = 
= 
, hence
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 3 ), then
3 = - + c → c = 3 + = 
y = x + ← equation of line
Answer:
5cm
Step-by-step explanation:
Find the diagram attached.
From ΔBCD, ∠BCD = 90-∠ACD
∠BCD = 90-60
∠BCD = 30°
Also tan60 = CD/BD
tan 60 = CD/5
CD = 5tan60
CD = 5√3 cm
Similarly from ΔACD, tan30 = CD/AD
tan30 = 5√3/AD
AD = 5√3/tan30
AD = 5√3/(1/√3)
AD = 5√3 * √3/1
AD = 5 cm
Hence the length of side AD is 5cm
Answer:
Step-by-step explanation:
sadly there is no good reason..the teachers are also annoying...
Answer:
Problematic x is x = 1
Step-by-step explanation:
Equation:
xy= 2x + y + 1
xy - y = 2x + 1
y(x-1) = 2x + 1
y = (2x+1)/(x-1)
The problematic x is such that when the denominator of the function is 0
x - 1 = 0
x = 1 (the problematic x)
So the domain of f is: x is the subset of R (real number) with the exception of x =/ 1 (x not equal to 1)
To prove this, we can plot the graph and in the graph we can see that as the value of x approaches from negative values to 1, y value will approaches negative infinity, and as the value of x approaches from large positive numbers, y value approaches infinity.
In other words, we'll see an assymptote at x=1
To prove that it is a function, we can do vertical line test by drawing vertical lines accross the graph. We'll see that each line crosses the equation line once hence proving the equation as a function
Answer:
sixteen or 1.6 X 10E2
Step-by-step explanation:
