The ideal length of a particular metal rod is 30.5 cm. the measured length may vary from the ideal length by at most 0.015cm. what is the range of acceptable lengths of the rod?

The range of the acceptable lengths of the rod is [29.485  30.515]

Step-by-step explanation:

Given,

The ideal length of the metal rod = 30.5 cm,

Also, it can be vary by 0.015 cm,

So, the maximum length that is acceptable = 30.5 + 0.015 = 30.515 cm,

Also, the minimum length that is acceptable = 30.5 - 0.015 = 29.485 cm,

⇒ 29.485 cm ≤ Acceptable length ≤ 30.515 cm

Hence, the range of acceptable lengths would be,

[29.485  30.515]

the monthly balance will be $75,000

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!