To find the distance between two points on a plane, use the Pythagorean idea: distance is the square root of the sum of the squares of the horizontal and vertical differences. Here the horizontal difference is 5 and the vertical difference is 12. So the distance is sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13. This is a classic 5-12-13 right triangle, which is why the numbers line up so neatly. The other options would come from not including both horizontal and vertical changes or from different differences, but the actual straight-line distance between the points is 13 units.

Adding and subtracting integers uses the same idea you already know from whole numbers, just with signs that show direction. When you add two integers, look at their signs. If both are the same sign, add their absolute values and keep that sign. If they have different signs, subtract the smaller absolute value from the larger and keep the sign of the number with the larger magnitude. This fits because adding a negative is like moving in the opposite direction, and subtracting a negative is like moving in the positive direction. For example, 5 plus a negative 3 equals 2, and negative 4 plus 7 equals 3. Subtraction can be seen as adding the opposite: 6 minus 2 is the same as 6 plus negative 2, which is 4, and 6 minus negative 2 becomes 6 plus 2, which is 8. This approach directly extends what you know about whole-number operations and doesn’t involve fractions or prime-factor ideas, which aren’t part of adding or subtracting integers.

Converting a fraction to a decimal means expressing how many hundredths it represents. Since 1/20 equals 0.05, multiplying by 7 gives 7/20 = 7 × 0.05 = 0.35. Another way is to scale to denominator 100: 7/20 = 35/100 = 0.35.

Combining like terms is what we’re practicing here. When simplifying, you add or subtract coefficients of terms that have the same variable and exponent. In 5y - 2y + 12, the terms with y are like terms, so you combine 5y and -2y to get 3y. The 12 is a constant and doesn’t have a y, so it stays as +12. Therefore, the expression simplifies to 3y + 12. If you see something like 7y + 12, that would come from treating the subtraction as addition, which isn’t correct here; or 5y + 12 would miss subtracting the 2y, which changes the result.