Justify each step in solving the equation 4x=7(x-3) by writing a reason for each statement.
2 answers:
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The right answer is c. –2.24, 2, 2.24
This question needs to be solved in two ways. First, using a graphing calculator. Next, using a system of equations.
1. Using a graphing calculator.
We have the following polynomial equation:
By ordering this equation we have:
So, we can say that this equation comes from a function given by:
Thus, by plotting this function, we have that the graph of this function is indicated in Figure 1. By zooming, we can see, in Figure 2, that the roots of the polynomial equation are the x-intercepts of which are:
Finally, rounding noninteger roots to the nearest hundredth we have:
2. Using a system of equations.
The ordered equation is:
By arranging to factor out we have:
Then, by factoring:
Term is a common factor, thus:
Let's look at an example:
2.24 x 21.6
Do normal multiplication and get
48384 This is not correct, until we put the decimals in. To know how to do this, count the number of decimal spaces from the factors. In 2.24, there are 2, because .24. In 21.6 there are 1 because of .6. This mean three places, so 48384 becomes
48.384
~theLocoCoco
This can be easily solved, especially with a calculator.
With the calculator, you can find that is about 6.4807.
Multiply that by 2, you get about 13 inches.
If you can't use a calculator, then you can just estimate. Since we know that is 6 and
is 7,
is in between them, so you can just say somewhere around 6.5.
Multiply 2 * 6.5 and you get 13 inches.