If we write y=f(x)=(x-h)²+k, then y-k=(x-h)². This is vertex form where the vertex is (h,k)=(3,3) so h and k are both 3. We can see this if we put x=3 in the shifted function. This is a minimum point for the function because for every other x f(x) is greater then 3. The minimum point is the vertex.
Answer:
(x, y) = (2, -1.5)
Step-by-step explanation:
x + 2y = -1
5x - 4y = 16
<=>
(2)x + (2)2y = (2)(-1)
5x - 4y = 16
<=>
2x + 4y = -2
5x - 4y = 16
<=>
7x = 14
<=>
x = 2
(*)x + 2y = -1
=> 2 + 2y = -1
=> 2y = -3
=> y = -1.5
=> (x, y) = (2, -1.5)
For a parallelogram, the parallel sides must be the same length. This means you can set their lengths equal to each other. Get like terms on the same side to calculate x.
3x-5=2x+3
3x-5+5=2x+3+5
3x=2x+8
3x-2x=2x-2x+8
x=8
x=8
3.75 as a decimal, 3 &3/4 as a fraction
The information from the first equation gives you the information needed for the second. To solve the first equation you must rearrange the equation to isolate X. In order to do that you can first move the 3 to the other side of the equation by subtracting it from both sides (5x + 3 - 3 = 4 - 3) and then simplify that to (5x = 4 - 3) and further to (5x = 1). Then to move the 5 you must divide both sides by 5 so you get (5x/5 = 1/5) which can be simplified to (x = 1/5)
From this you can use the X value and input it into the second equation
Y = -3(1/5) and then solve for Y.
Hope this helps!
