Since you need the vertex, and knowing the vertex will tell you the axis of symmetry, it is convenient to put the equation in vertex form.
.. -x^2 -4x +1
.. = -(x^2 +4x) +1
.. = -(x^2 +4x +(4/2)^2) +1 -(-(4/2)^2) . . . . complete the square
.. = -(x +2)^2 +5
The vertex is (-2, 5).
The axis of symmetry is x = -2.
This is the concept of quadratic equations. We are required to find the missing factor in the partially factored quadratic equation given;
n(n-3)+2(n-3)=()(n-3)
here we proceed as follows;
n(n-3)+2(n-3)
when we factor this we get:
(n-3)(n+2)
this can be written as:
(n+2)(n-3)
The answer is (n+2)
Answer:
Hypotenuse² = Base² + Altitude²
35² = 15² + x²
1225 = 225 + x²
x² = 1225 - 225
x² = 1000
<u>X = 10√10</u>
Since the train travels at a rate of 70 miles/hour, the train will take 5 hours to have traveled a total of 350 miles. The missing information in the question you've proposed is the value of "H" or the number of hours (as the unit hours is indicated in the question). This can be determined with the formula <em>Distance = rate X time. </em>350 = 70 X H, in this case. To isolate the variable H, 70 (the rate) divides 350 (the total distance) into 5. 350 ÷ 70 = H. 5 = H, the amount of time spent traveling for 350 miles at a rate of 70 miles/hour.
