gwendolyn7
contestada


For each pair of expressions below, without substituting in specific values, determine which of the expressions in the given pairs is larger. Explain your reasoning in a sentence or two. If you need to, test with values, but your explanation should explain what's going on without simply describing the values
you plugged in.

For each pair of expressions below without substituting in specific values determine which of the expressions in the given pairs is larger Explain your reasoni class=

Respuesta :

sqdancefan

Answer:

  1. 5+t²
  2. 15/x²
  3. it depends (see below)
  4. it depends (see below)

Step-by-step explanation:

1. t² is a positive number. Adding a positive number to 5 will always produce a larger result than subtracting the same positive number from 3. The larger expression is 5+t².

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2. The expressions are only defined for x ≠ 0, so for x² a positive number. For any x, the expressions are both positive. 15/(7x²) is 1/7 of 15/x², so will always be smaller. The larger expression is 15/x².

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3. As in 2, these expressions are only defined for x ≠ 0. One expression is the opposite of the other. A number is greater than its opposite when it is positive, so 1/x > 1/-x for x > 0; and 1/-x > 1/x for x < 0.

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4. The expression (k -6)² has the same range of values as k², but its graph is shifted 6 units to the right. The left branch of (k -6)² will be greater than k² for any k < 3. Similarly, the right branch of k² will be greater than (k -6)² for any k > 3.

Ver imagen sqdancefan
whitneytr12

1) 5 + t² will always be larger than 3 - t².

2) 15/x² is larger than 15/7x²

3) 1/x will be larger than 1/(-x), only if the values of x take positive numbers.

4) k² will be larger than the second (k-6)². if k takes only positive numbers.

1)

If we see the first term, 5 is adding the function t² and in the second term,  t² is negative so we can conclude that 5 + t² will always be larger than 3 - t².

2)

Here, we can analyze the independent values. The first term has 15 and the second 15/7 = 2.14. Now, as we have x² in the bottom, the function decrease as x increase. Therefore, the first term 15/x² is larger than the second 15/7x²

3)

We can see that the second term is negative, so 1/x will be larger than 1/(-x), only if the values of x take positive numbers.

4)

Here we have the same case, if k takes only positive numbers, the first term k² will be larger than the second (k-6)² because we have 6 substracting.

You can learn more about quadratic function here:

https://brainly.com/question/10606041

https://brainly.com/question/12672838  

I hope it helps you!  

 

Ver imagen whitneytr12