Please answer this question fast
1 answer:
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Answer:
See below.
Step-by-step explanation:
1)
So we have the equation:
To change into the slope-intercept form, we need to isolate the y-variable. Thus, subtract 2x from both sides:
The left side cancels:
Now, divide both sides by 3. The left side cancels:
The slope-intercept form is:
Where m is the slope and b is the y-intercept.
Thus, the slope is -2/3 and the y-intercept is 490.
2)
So, since we already know the y-intercept is 490, plot a point at (0,490).
The slope is too small to use. Thus, multiply the fraction by 100. It is now (-200/300). This means that we move <em>down</em> 200 for every 300 (recall that the slope means rise over run. Thus, we move down 200 for every 300 to the right). Thus, another possible point would be (0+300,490-200) or (300,290). Plot that. Then, connect them.
3)
To write in in function notation, simply substitute the y-variable for the function notation. Our independent variable here is x so we'll use that.
This means that for every x sandwiches made, there is f(x) wraps made for the total sum to be $1,470.
For example, if 105 sandwiches were made, then f(105)=-2/3(105)+490=420 wraps were made for the total profit to be $1,470.
4)
Please refer to the attached graph.
5)
First, since the total profit has now increased, the graph above and to the right of the old graph. This is because Sal needs to sell more sandwiches and wraps. Likewise, because of this, the x- and y-intercepts will also be different. Nevertheless, if converted into the slope-intercept equation, the slope will remain the same.
Answer:
1. leave the radical symbol and don't try to convert it to a decimal form
2. The approximated value differs from the exact solution and doesn't give a true equation.
3. Depending on the case, if she needs a mathematical answer, the exact value should be used, but for more practical applications, the rounded decimal form would be more usable.
Step-by-step explanation:
The step by step solution to the equation:
1.- Exact solution means that if in the final step when solving for x the value of is not a perfect cube, one needs to leave it indicated as a radical expression (with the radical symbol).
in our case, the cubic root of 189 is not a perfect cube. The factor form of 189 is: , so there is a perfect cube factor (
), but the other factor (7) is a prime number. Therefore 3 can get out of the root, while 7 stays inside.
2.- The equation was solved above, in exact form. Now to solve it giving a decimal approximation, we use a calculator to find the cubic root of 7, which is an irrational number with infinite number of decimals, the first of which we type here:
Therefore, the decimal approximation to the solving for x would be:
Where we rounded to two decimals as requested.
When we replace the exact answer in the original expression, we get a perfect equality:
While if we use the approximate answer, we get:
which is NOT a true equality.
3.- I would stick with the idea of showing the exact answer as answer to the mathematical equation. but for a practical case (for example she needs to by some material as a result of her equation solving, it would be more practical to take the numerical approximation to the store, instead of a cubic root of a number.