To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-5x² + 7x²
(-5 + 7)x²
2x²

47% of the water consumption is industrial use and 33% is personal use so (47% - 33%) = 14% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{14}{100} \) x 25,000 gallons = 3,500 gallons.

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.2km + 40.6km + 10.3km
total distance = 51.1km

First, solve for \( \left|b - 6\right| \):

\( \left|b - 6\right| \) - 2 = -8
\( \left|b - 6\right| \) = -8 + 2
\( \left|b - 6\right| \) = -6

The value inside the absolute value brackets can be either positive or negative so (b - 6) must equal - 6 or --6 for \( \left|b - 6\right| \) to equal -6:

So, b = 12 or b = 0.

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.