Question

Оцените значение выражений, если известно, что: 4 <х <6 и - 0,3 <у <0,1. Верно неравенство 16,3 <4х - y <23,9;

Answer 1

4/х/6/0.1 
16,3^4
Х_23,9 
Равенство верное

Answer 2

I will try to answer your question in detail. To evaluate the value of the expressions, we need to use the given inequalities and the properties of inequalities.

First, let's simplify the inequality 16.3 < 4x - y < 23.9 by adding y to both sides and dividing by 4. We get 4.075 + y/4 < x < 5.975 + y/4.

Now, we can use the fact that -0.3 < y < 0.1 to find the possible range of x. If we substitute y = -0.3, we get 4.05 < x < 5.95. If we substitute y = 0.1, we get 4.1 < x < 6.

Since we also know that 4 < x < 6, we can combine these inequalities and get the final range of x: 4.1 < x < 5.95.

Next, let's evaluate the expressions using this range of x and the given range of y.

- 4x - y: This expression is smallest when x is smallest and y is largest, and largest when x is largest and y is smallest. So, we can substitute x = 4.1 and y = 0.1 to get the minimum value: 4 * 4.1 - 0.1 = 16.3. Similarly, we can substitute x = 5.95 and y = -0.3 to get the maximum value: 4 * 5.95 - (-0.3) = 23.9.

- x + y: This expression is smallest when x and y are both smallest, and largest when x and y are both largest. So, we can substitute x = 4.1 and y = -0.3 to get the minimum value: 4.1 + (-0.3) = 3.8. Similarly, we can substitute x = 5.95 and y = 0.1 to get the maximum value: 5.95 + 0.1 = 6.05.

- xy: This expression is smallest when x is smallest and y is negative, and largest when x is largest and y is positive. So, we can substitute x = 4.1 and y = -0.3 to get the minimum value: 4.1 * (-0.3) = -1.23. Similarly, we can substitute x = 5.95 and y = 0.1 to get the maximum value: 5.95 * 0.1 = 0.595.

Therefore, we can conclude that:

- The inequality 16.3 < 4x - y < 23.9 is true for any values of x and y in the given ranges. - The value of x + y is between 3.8 and 6.05. - The value of xy is between -1.23 and 0.595.

I hope this helps you understand how to evaluate expressions using inequalities.

If you want to learn more about inequalities, you can check out some of these resources:

- [A video tutorial on solving linear inequalities] - [A lesson on solving systems of linear inequalities] - [An interactive quiz on inequalities]