Since we already have 3^7 you should know that 3 times 3 is 9. Here is how I would simplify it.
3^7 times 3^4 times 3^3
You should add all the exponents and get
3^14
27 is basically 3 times 3 times 3 which is why I chose to put 27 that way
Direct Variation equation: y=kx, k=y/x
42/14=3
k=3
y=3x
y=3(90)
y=270
Answer:
y = 
x - 3
Step-by-step explanation:
5x - 2y = 6 ( subtract 5x from both sides )
- 2y = - 5x + 6 ( divide through by - 2 )
y = x - 3 ← in slope- intercept form
<span>(3.5, 3) is the circumcenter of triangle ABC.
The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors.
Line segment AB:
Slope
(4-2)/(1-1) = 2/0 = infinity.
This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3).
So the equation for this perpendicular bisector is y = 3.
Line segment BC
(2-2)/(6-1) = 0/5 = 0
This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2)
So the equation for this perpendicular bisector is x=3.5
So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC.
Now let's do a cross check to make sure that's correct.
Line segment AC
Slope = (4-2)/(1-6) = 2/-5 = -2/5
The perpendicular will have slope 5/2 = 2.5. So the equation is of the form
y = 2.5*x + b
And will pass through the point
((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3)
Plug in those coordinates and calculate b.
y = 2.5x + b
3 = 2.5*3.5 + b
3 = 8.75 + b
-5.75 = b
So the equation for the 3rd bisector is
y = 2.5x - 5.75
Now let's check if the intersection with this line against the other 2 works.
Determining intersection between bisector of AC and AB
y = 2.5x - 5.75
y = 3
3 = 2.5x - 5.75
8.75 = 2.5x
3.5 = x
And we get the correct value. Now to check AC and BC
y = 2.5x - 5.75
x = 3.5
y = 2.5*3.5 - 5.75
y = 8.75 - 5.75
y = 3
And we still get the correct intersection.</span>
Answer:
x = 105 degrees.
Step-by-step explanation:
The small polygon is a regular hexagon so each internal angle = 120 degrees while the large polygon is a regular octagon with internal angle =
135 degrees.
So angle x = 360 - ( 120 + 135)
= 360 - 255
= 105 degrees.
Note we use the fomula T = 180( n - 2) to find total internal angles in an n sided polygon. So for hexagon T = 180(6-2) = 180*4 = 720 so each internal angle in a regular hexagon = 720/6 = 120 degrees.
