Michael's dad is 30 years of age. He is 2 years more than four times Michaels age m. Write and solve a two-step equation to dete
2 answers:
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The sum of the inner angles of any triangle is always 180°, i.e. you have
In the particular case of an equilater triangle, all three angles are the same, so
and the expression becomes
which implies
So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.
Of course, this is equivalent to a clockwise rotation of 120 degrees.
Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)
Answer:
The solution to the system is the pair (9, 6)
Step-by-step explanation:
Hi!
First, let´s write the system of equations:
-y² + 6y + x -9 = 0
6y = x +27
The solutions of the system are the pairs (x, y) that satisfy both equations.
Let´s take the second equation and solve it for x:
6y = x +27
Subtract 27 from both sides of the equation
6y - 27 = x
Now, we can replace x in the first equation and solve it for y:
-y² + 6y + x -9 = 0
-y² + 6y + 6y - 27 -9 = 0
-y² + 12y - 36 = 0
Notice that -y² + 12y - 36 = -(y - 6)², then:
-(y - 6)² = 0
y - 6 = 0
y = 6
(alternatively you can solve the quadratic equation using the quadratic formula).
Now let´s find the value of x:
x = 6y -27
x = 6·6 -27
x = 9
The solution to the system is the pair (9, 6)
Please see the attached figure. The point where the curves intersect is the solution to the system.
