Consider the contrapositive of the statement you want to prove.
The contrapositive of the logical statement
<em>p</em> ⇒ <em>q</em>
is
¬<em>q</em> ⇒ ¬<em>p</em>
In this case, the contrapositive claims that
"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."
The first equation is captured by a system of linear equations,
or in matrix form,
If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be
and this is what we wanted to prove. QED
Answer:
A = 108 units²
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = 
h (b₁ + b₂ )
where h is the height between the 2 bases and b₁, b₂ are the parallel bases
Here h = 24 , b₁ = 8 , b₂ = 1 , then
A = × 24 × (8 + 1) = 12 × 9 = 108 units²
Answer:
f=8
Step-by-step explanation:
fx0.5=4
f=4x2
f=8
The point-slope form:
We have the point (1, 6) and the slope m = 7/3. Substitute:
<em>use distributive property</em>
<em>add 6 to both sides</em>
<em>multiply both sides by 3</em>
<em>subtract 7x from both sides</em>
<em>change the signs</em>
Answer:
point-slope form:
slope-intercept form:
standard form:
Answer:
A. As the value of x increases, the value of f(x) moves toward a constant
Step-by-step explanation:
An exponential function with a base less than 1 will decay to zero. Here, the exponential has -2 added to it, so the decay is toward the value -2.
An exponential function is defined for all real numbers. This one has a y-intercept of -1.
