In the diagram below, OPis circumscribed about quadrilateral ABCD. What is the value of x?
1 answer:
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So, the container was 2/5 full
someone came over and dumped a bucket of water in it with 8 gallons
and the container went UP to 2/3 full
so, 8 gallons, and the container goes up by some fraction,
whatever that is
bear in mind that, 2/3 is over 1/2, and 2/5 is less than 1/2
so, 2/3 is really more than 2/5
so... whatever 8 gallons is in fraction of the container,
is the difference of 2/3 and 2/5
so.. let's say the container when full holds "x" amount of gallons
2/5 of x is... well, 2x/5
and 2/3 of x is well, 2x/3
so... we could say that
solve for "x", since "x" is how many gallons, the container holds when full
someone came over and dumped a bucket of water in it with 8 gallons
and the container went UP to 2/3 full
so, 8 gallons, and the container goes up by some fraction,
whatever that is
bear in mind that, 2/3 is over 1/2, and 2/5 is less than 1/2
so, 2/3 is really more than 2/5
so... whatever 8 gallons is in fraction of the container,
is the difference of 2/3 and 2/5
so.. let's say the container when full holds "x" amount of gallons
2/5 of x is... well, 2x/5
and 2/3 of x is well, 2x/3
so... we could say that
solve for "x", since "x" is how many gallons, the container holds when full
We can look at the graph
Vertex:
we know that vertex is the point where parabola changes it's shape
we can see that
vertex is at (0.5,-0.75)
Axis of symmetry:
we know that axis of symmetry of parabola is always x-value of vertex
we can see that
x-value of vertex is 0.5
so, axis of symmetry is
Formula for the function:
we know that this is graph of parabolas
so, we can use vertex formula of parabola
where
(h,k) is vertex
Here , we got
vertex as (0.5 , -0.75)
h=0.5 and k=-0.75
now, we can plug these values
now, we need to find 'a'
we can select any one point of parabola
and then we can find 'a'
We can see that one of point is (0,-1)
so, we can plug x=0 and y=-1
now, we can plug it back
and we get
now, we can expand it
so, option-D..........Answer