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Vika [28.1K]
3 years ago
10

Which strategy best explains how to solve this problem? Rebecca bought a meal and two snacks for lunch each day. The meal cost $

5.50 and the snacks cost $0.75 each. What is the total amount of money Rebecca spent after 12 days? A. Make a table. Write the numbers 1 to 12 in the top row of the table (the number of days). In the first box on the second row, write $7. This is how much Rebecca spends in 1 day. In each of the next boxes in the second row, write the amount Rebecca spends by adding $7 to the previous amount. The answer in box 12 is the total amount Rebecca spent after 12 days. B. Work backward. Start with the price of the two snacks ($1.50). Add the cost of the meal and then divide by 12. C. Guess and test. Guess that Rebecca spent $95. Multiply $0.75 by 2. Then add that answer to $5.50. Divide this number by 95. If the answer is not 12, then revise your guess, and test your answer again.
Mathematics
1 answer:
Fittoniya [83]3 years ago
6 0
Given:
Cost of lunch per day = 1 meal and 2 snacks

C = 5.5 + 2(0.75) = 5.5 + 1.5 = 7

7 * 12 days = 84

Based on the choices, the best strategy would be:

<span> A. Make a table. Write the numbers 1 to 12 in the top row of the table (the number of days). In the first box on the second row, write $7. This is how much Rebecca spends in 1 day. In each of the next boxes in the second row, write the amount Rebecca spends by adding $7 to the previous amount. The answer in box 12 is the total amount Rebecca spent after 12 days.</span>

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1) This question may be easily answered if you are aware of the shape of the graph of sq. root x, and the effect of translations to graphs.

1. x - 7 means that the original graph is translated 7 units in the positive direction of the x-axis (ie. to the right), thus the minimum value for x is also shifted from 0 to 7

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3. We know that the graph will continue to infinity, both in the x- and y-direction

Thus, the domain would be [7, ∞) and the range [9, ∞)

2) Another way to think about it is to ask yourself when it would make sense for the graph to exist. For this, we must consider that you cannot take the square root of a negative number.

Thus, if we have the square root of (x - 7), for what value of x would (x - 7) be negative? If x = 7:

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If we have already found the domain, then we can simply substitute the values for this into the equation to obtain the range (note that this will work for a square root function, however some functions will have turning points and in this case you must calculate the range based on the turning points as well as the minimum and maximum x-values):

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if we have x = ∞, then the y value will also be infinitely great, therefor the maximum y-value is also ∞. Thus, the range is [9, ∞).

These questions are much easier to solve however if you are already aware of the basic graph and the effect of dilations, translations and reflections so that you may visualise it better.

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