Answer:
C
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (9, 3) ← 2 points on the line
m = 
= 
= 
, thus
y = x
Or
y = 
→ C
CF = CD + DF (since D is simply a point on the line, and C to that point added onto F to that point is CF), so 4y-9+2y-7=14. Adding it up, we get 6y-16=14 and adding by 16 we get 30=6y. Dividing both sides by 6, we get y=5. Plugging that into DF, we get 10-7=DF=3
To answer this, first make an equation representing the data:
15+ 0.20X= Bill
now plug in data you know:
15 + 0.20(30)= bill
and finally solve it:
Bill= $21.00
First, we are going to find the vertex of our quadratic. Remember that to find the vertex
of a quadratic equation of the form
, we use the vertex formula
, and then, we evaluate our equation at
to find
.
We now from our quadratic that
and
, so lets use our formula:
Now we can evaluate our quadratic at 8 to find
:
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is
The x-coordinate of the minimum is 8
