Solve Propertiesstraightline G(x)=1/20x(x-100) Tiger Algebra Solver

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : g*(x)-(1/20*x*(x-100))=0

Step 1 :

1 Simplify —— 20

Equation at the end of step 1 :

1 gx - ((—— • x) • (x - 100)) = 0 20

Step 2 :

Equation at the end of step 2 :

x • (x - 100) gx - ————————————— = 0 20

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a fraction from a whole Rewrite the whole as a fraction using 20 as the denominator :

gx gx • 20 gx = —— = ——————— 1 20

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

gx • 20 - (x • (x-100)) 20gx - x2 + 100x ——————————————————————— = ———————————————— 20 20

Step 4 :

Pulling out like terms :

4.1 Pull out like factors : 20gx - x2 + 100x = x • (20g - x + 100)

Equation at the end of step 4 :

x • (20g - x + 100) ——————————————————— = 0 20

Step 5 :

When a fraction equals zero :

5.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.Here's how:

x•(20g-x+100) ————————————— • 20 = 0 • 20 20

Now, on the left hand side, the 20 cancels out the denominator, while, on the right hand side, zero times anything is still zero.The equation now takes the shape : x • (20g-x+100) = 0

Theory - Roots of a product :

5.2 A product of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

5.3 Solve : x = 0 Solution is x = 0

Equation of a Straight Line

5.4 Solve 20g-x+100 = 0 Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK). "y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.In this formula :y tells us how far up the line goesx tells us how far alongm is the Slope or Gradient i.e. how steep the line isb is the Y-intercept i.e. where the line crosses the Y axisThe X and Y intercepts and the Slope are called the line properties. We shall now graph the line 20g-x+100 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of g is -5/1 so this line "cuts" the g axis at g=-5.00000

g-intercept = -100/20 = -5

Calculate the X-Intercept :

When g = 0 the value of x is 100/1 Our line therefore "cuts" the x axis at x=100.00000

x-intercept = 100/1 = 100.00000

Calculate the Slope :

Slope is defined as the change in g divided by the change in x. We note that for x=0, the value of g is -5.000 and for x=2.000, the value of g is -4.900. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -4.900 - (-5.000) = 0.100 in g. (The change in g is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 0.100/2.000 = 0.050

Geometric figure: Straight Line

1. Slope = 0.100/2.000 = 0.050
2. x-intercept = 100/1 = 100.00000
3. g-intercept = -100/20 = -5
4. x = 0