Without using a calculator, explain why the solution to each equation must be a real number between 1 and 2.
11^x = 12

Explanation:

The intermediate value theorem (IVT) tells you that for continuous function ...

  f(x) = 11^x

if f(1) < 12 and f(2) > 12, then for f(x) = 12, the value of x must be between 1 and 2.

We know f(1) = 11^1 = 11 < 12, and f(2) = 11^2 = 121 > 12, so the conditions are met for the IVT to be applicable.

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In short, the Intermediate Value Theorem says so.

correct answers below:

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.