Matt wants to purchase a watch for $64.50. If there was a 25% discount and the tax rate was 7%, what was the total price that it
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A cube has all sides of equal length.
So let the side be x
that will be length = width = height = x
Now, when we cut the loaf into 5 equal slices, the length and height of the slices are the same as the original loaf. But the width will become less with each slicing. Here the width corresponds to the thickness of the slices.
For each slice the dimensions are -
Length = x
height = x
width = 0.6
Volume of the original loaf is x³.
Volume of 5 slices is 5(x * x * 0.6).
Volume that is left after the cutting the slices is 235 inch³.
So, equation of the volume is=
x³ - 5(0.6x²) = 235
Solve for x using this equation.
x³ - 3x² = 235
x³ - 3x² - 235 = 0
Using a graph calculator to find the roots, we get
x = 7.35
Hence the dimensions of the original loaf is 7.35 inches for each side.
Please find attached the graph.
Step-by-step explanation:
There are certain methods for solving a system of equations. Some of which are:
- Substitution Method
- Elimination Method
- Graphing Method
<em>Substitution Method</em>
Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.
For example, for the following system of equations
x - 2y = 11....[A]
x = 5 - y....[B]
substituting the value of x = 5 - y from equation [B] into equation [A], so that
(5 - y) - 2y = 11
5 - y - 2y = 11
3y = -6
y = -2
<em>Elimination Method</em>
Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.
For example, for the following system of equations
2x + 7y = -5....[C]
5x - 7y = 12....[D]
Adding Equation [C] and Equation [D].
7x + 0 = 7
x = 1
<em>Graphing Method</em>
Sometimes graphing method may be used to solve the system of the equation and visualize the solution.
For example,
y = -2....[E]
y = 3x + 1....[F]
The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).
Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.
<em>Keywords: system of equations, elimination method, substitution method, graphing method</em>
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