Answer:
the system has a unique solution
Step-by-step explanation:
Start with an equation of a line in standard form,

Solve it for y to put it into the slope-intercept form:


The slope is -a/b.
Now look at your system of equations. The slope of the first equation is -a/b = -2/3. The slope of the second equation is -a/b = -6/5.
You have a system of two linear equations with two lines with different slopes, so the lines must intersect at a single point.
Answer: the system has a unique solution
tan2x*cotx - 3 = 0
We know that: tan2x = sin2x/cos2x and cotx = cosx/sinx
==> sin2x/cos2x *cosx/sinx = 3
Now we know that sin2x = 2sinx*cosx
==> 2sinxcosx/cos2x * cosx/sinx = 3
Reduce sinx:
==> 2cos^2 x/ cos2x = 3
Now we know that cos2x = 2cos^2 x-1
==> 2cos^2 x/(2cos^2 x -1) = 3
==> 2cos^2 x = 3(2cos^2 x -1)
==> 2cos^2 x = 6cos^2 x - 3
==> -4cos^2 x= -3
==> 4cos^2 x = 3
==> cos^2 x = 3/4
==> cosx = +-sqrt3/ 2
<span>==> x = pi/6, 5pi/6, 7pi/6, and 11pi/6</span>
Answer:
1.93433
Step-by-step explanation:
Since all triangles have an interior angle sum of 180, the second angle is 45. this also means that x and y are equal. Using the pythagorean theorem, we can produce the equation
. dividing both sides by two we get
. when we take the square root of root 14 we get 1.934335
Answer:
Name a transversal - i
Name all corresponding angles -
6 = 8
1 = 3
2 = 4
5 = 7
Name all alternate exterior angles -
1 = 5
4 = 8