Simplified the expression 5x-3(4-x)
2 answers:
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Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters
Answer:
Part 1) "a" value is
Part 2) The vertex is the point
Part 3) The equation of the axis of symmetry is
Part 4) The vertex is a minimum
Part 5) The quadratic equation in standard form is
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
where
(h,k) is the vertex of the parabola
if a > 0 then the parabola open upward (vertex is a minimum)
if a < 0 then the parabola open downward (vertex is a maximum)
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
In this problem we have
-----> this is the equation in vertex form of a vertical parabola
The value of
so
a>0 then the parabola open upward (vertex is a minimum)
The vertex is the point
so
The equation of the axis of symmetry is
The equation of a vertical parabola in standard form is equal to
Convert vertex form in standard form
see the attached figure to better understand the problem
