348.8745 rounded to the nearest hundredth is?
35.86 rounded to the nearest hundredth is?
$42.19 rounded to the nearest dollar is?
158.097 rounded to the nearest tenth is?
try to provide explanations, i want to try to learn how to do these by myself.

348.8745 --> 348.87

35.86 --> 35.86

$42.19 --> $42

158.097 --> 158.1

Step-by-step explanation:

If the number after the number we are rounding to is less than or equal to 4, we round down.

Ex : 123.454 to the nearest hundredths is 123.45 because the 4 in the thousandths place is equal to 4.

If the number after the number we are rounding to is greater than or equal to 5, we round up.

Ex : 123.456 to the nearest hundredths is 123.46 because the 6 in the thousandths place is greater than 6.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240