To factor this quadratic function, there are many ways that you can do this, the most common approach used to graph anything would be to make a table of values. Basically, make a chart with x coordinates on one side and y coordinates on the other side. Pick any values for your x coordinates and then find the correct y coordinate that results when you place that specific x coordinate into the function. After getting many points, plot those points on the grid and it should give you a parabola.
Another way to graph the function is to find the x intercepts, you can do this by setting the function to zero, and factoring the trinomial, using the appropriate method, then find the x intercepts
y = 2x^2 - 8x + 6
0 = (2x^2 - 6x - 2x + 6)
0 = 2x(x - 3) - 2(x - 3)
0 = (2x - 2)(x - 3).
First, you multiply all terms by 2.8 to get rid of the denominator:
m-13.72 = -19.908
then, you isolate the m on one side of the equation and all other terms on the other side:
m = -19.908+13.72
m = -6.188
Q 16. The energy is 308.7 J.
Q 17. The energy is 896000 J.
Step-by-step explanation:
Q 16. Given,
Mass (m) of the carriage and baby = 1.5 kg
Height (h) = 21 m
To find the energy.
We will find the potential energy as it rests at the top.
Formula
Potential energy = mgh where g be the gravitational force of the earth = 9.8m/s²
So,
Energy = 1.5×9.8×21 J
= 308.7 J.
Hence,
The energy is 308.7 J.
Q 17. Given,
Mass (m) = 1120 kg
Speed (v) = 40 m/s
To find out the energy.
We will find out the kinetic energy as the car is in motion.
Formula
Kinetic energy = 
mv²
So,
Energy = ×1120×40² J
= 896000 J
Hence,
The energy is 896000 J.
An arithmetic sequence is one where each term is a constant difference, called the common difference, from the preceding term. The arithmetic sequence can always be expressed as:
a(n)=a+d(n-1), a=first term, d=common difference, n=term number.
We are given two terms and term numbers, so we can solve for the common difference...
101=5+d(25-1)
101=5+25d-d
101=5+24d
96=24d
d=4
So the common difference is 4.
