A shoe store is having a sale. All running shoes are 30% off and all basketball shoes are 20% off. Supposed you buy 2 pairs of running shoes that originally cost $50 each and 1 pair of basketball shoes that originally cost $75. What percent of the total have you saved? Round to the nearest whole percent.

26%

Step-by-step explanation:

running shoes: 30% off

basketball shoes: 20% off

2 pairs of running shoes + 1 pair of basketball shoes cost

2 * $50 + $75 = $175

The total original price before the discount was $175

Now we find the discounted prices and the total discounted price.

running shoes: 30% off means you pay 70% of the original price

70% of $100 = 0.7 * $100 = $70

basketball shoes: 20% off means you pay 80% of the original price

80% of $75 = 0.8 * 75 = $60

The total discounted price is $70 + $60 = $130

Now we find the actual discount.

Original total undiscounted price: $175

Total discounted price: $130

Actual total amount of discount: $175 - $130 = $45

Now we find the percent that 45 is of 175.

45/175 * 100% = 25.714...%

26%

this question relies purely on our observation of the graph and a knowledge of the behaviour of a graph of a hyperbola.

now, what we should realise is that there are two asymptotes - one at x = 0 and one at y = 0. what this means is that the graph will gradually approach, but never touch, these two lines. so, as x becomes more positive (ie. 'a very large positive number'), it will get closer to the line y = 0 (ie. the x-axis) - which means that the value of f(x) will gradually become smaller and closer to 0 - but will never reach it.

we can also observe this from the right half of the graph, where the graph gradually lowers closer and closer to the x-axis as x increases. what is important to note however is that it will never actually touch the x-axis (ie. f(x) will not equal 0) since there is an asymptote there. given this, we can see that option d, f(x) is a very small positive number, would be correct.