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
If we draw a perpendicular line from one of the vertices of the triangle we get 2 right angled triangles each with altitude 9 ins and vertex angle = 30 degrees. So:-
cos 30 = 9 /h where h = one of the sides of the equilateral triangle
h = 9 / cos 30 = 10.392 inches
Therefore the perimeter of the triangle = 3 * 10.392 = 31.1769 ins
Answer is 31.18 inches to the nearest hundredth.
Step-by-step explanation:
9x - 2x = 8 + 5
7x = 13
x =13÷7
x = 1.8571
approximately = 1.86
I think this is it
Answer:
7/17 and 1/9 0r 9/1
Step-by-step explanation:
Answer:
A, g(x) = 7x + 5
Step-by-step explanation:
applying these translations to the parent function f(x) = x, we would get the following equation:
g(x) = 7x + 5
a vertical compression is written before the parent function (in this case f(x)=x), and a shift up is written next to the function. both of these are without parentheses
the answer would be A, g(x) = 7x + 5
