First, set the second equation with y as the isolated variable. To do this, subtract 4 from both sides to get

Now that you know the value of y, put that expression in for y in the first equation to get

Then, simplify by adding the x terms together to get

add 4 on both sides to isolate the x terms to get

then divide 6 from both sides to get

Using that x value, plug it into one of the equations as x to find y ( I will use y=3x-4)

x=1 and y=-1 is the answer
Answer:
y = - 4(x + 3)² + 7
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
From the graph (h, k ) = (- 3, 7 ), thus
y = a(x + 3)² + 7
To find a we require a point on the graph other than the vertex
Using (- 2, 3) , substitute into the equation
3 = a(- 2 + 3)² + 7
3 = a + 7 ( subtract 7 from both sides )
a = - 4
Thus
y = - 4(x + 3)² + 7 ← in vertex form
=x^2-8x+16-16
= (x-4) ^2-16
=[(x-4) -4][(x-4) +4]
=(x-8) x
Answer:
x = 36°n + 7° OR x = 90°n + 37.5° for any integer n
Step-by-step explanation:
Since cos(x) = sin(90°-x), we have
sin(7x-20°) = sin(90°-(3x+40°)) = sin( 50° - 3x )
sin( x ) = sin( y ) implies either:
x = 360° n + y
or
x = 360°n + 180° - y
Generally sin(x) = sin(y) ⇒ x = 180°n + (-1)ⁿ y
First case:
7x - 20° = 360°n + 50° - 3x
10x = 360°n + 70°
x = 36°n + 7°
Second case:
7x - 20° = 360°n + 180° - ( 50°-3x )
7x - 20° = 360°n + 180° - 50° + 3x
7x - 20° = 360°n + 130° + 3x
4x - 20° = 360°n + 130°
4x = 360°n + 150°
x = 90°n + 37.5°