The required value of x is 4.
Given equation of the parabola y= -5x^2 -10x -13.
We need to apply formla for x-coordinate of the vertex.
x=-b/2a.
For the given equation we have a=-5 and b=-10.
Plugging values of a and b in formula of x-coordinate of the vertex.
x= -(-10)/2(-5)
x= 10/(-10) = -1.
So, we got x-coordinate of the vertex = -1.
Now, we need to plug x=-1 in given equation to find the y-coordinate of the vertex.
Plugging x=-1 in y= -5x^2 -10x -13, equation we get
y=-5(-1)^2-10(-1)-13.
y= -5(1) +10 -13.
y=-5 +10-13.
y=-18+10.
y=-8.
So, we got y-coordinate of the vertex -8.
Therefore, vertex of the parabola is (-1,-8).
The length of eastern continental trail is 5400 miles and length of erie canal trail is 360 miles.
Step-by-step explanation:
Given,
Combined length of both trails = 5760 miles
Let,
x be the length of eatern continental trail.
y be the length of Erie canal trail.
According to given statement;
x+y=5760 Eqn 1
x = 15y Eqn 2
Putting value of x from Eqn 2 in Eqn 1

Dividing both sides by 16

Putting y=360 in Eqn 2

The length of eastern continental trail is 5400 miles and length of erie canal trail is 360 miles.
Keywords: linear equation, substitution method
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Change 4 feet to inches
4 feet is 48 inches
48-10=38