Which algebraic expression represents the phrase “four times a number”?
2 answers:
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Answer:
The answer is below
Step-by-step explanation:
A) i)
For Anna initially, she has $0 from making 0 envelopes. After making 400 envelopes she has $20. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (400, 20). Using the equation of a line:
The table is:
x: 200 400 600 800 1000
y: 10 20 30 40 50
ii)
For Jason initially, he has $0 from making 0 envelopes. For every 250 envelopes he has $10. Let x represent the number of envelopes and y the earnings. Hence this can be represented by the points (0, 0) and (250, 10). Using the equation of a line:
The table is:
x: 200 400 600 800 1000
y: 8 16 24 32 40
The graph is plotted using geogebra online graphing
b) From the table above we can see that Anna makes more stuffing than Jason.
c) Anna has a savings of $100. Hence this can be represented by the points (0, 100) and (250, 10). Using the equation of a line:
We can see from the graph that there is a y intercept at 100. That is the earnings starts from 100.
The equation of a line is given as y = mx + b, where m is the slope and b is the y intercept (initial value)
For the first graph, the slope is 1/20 and the initial value is 0 while for the second graph the slope is 1/15 and the initial value is 100
D) The line pass through (10, 10) and (100, 40), hence:
<u>Part A
</u><u />To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case,
and 
equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about 3 gallons.
<u>Part B
</u><u /><u />To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.
Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.
Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.
Now, we can simply add our numerators.
We know that he needs
gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.
Using that logic, we can see that the painter needs exactly
gallons of paint.
</u><u />To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case,
<u>Part B
</u><u /><u />To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.
Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.
Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.
Now, we can simply add our numerators.
We know that he needs
Using that logic, we can see that the painter needs exactly