If the value of "a" lies between −5 and 2 and the value of "b" lies between −7 and 1, what are the possible values for the product a· b?

(a) between 2 and 35 (b) between −35 and 5 (c) between −14 and 2
(d) between −14 and 35 (e) between −12 and 3

The possible values for the product are between -14 and 35. (Choice: D)

In this question we must determine the bounds associated with the following operation:

, for all (1)

In this case, we must determine the lowest negative number (lower bound) and the highest positive number (higher bound), based on the following two properties from algebra:

(2)

(3)

Now we proceed to determine the limits:

Lower bound

Upper bound

The possible values for the product are between -14 and 35.

We kindly invite to see this question on algebra: link

D. between -14 and 35

Step-by-step explanation:

Given:

Find: possible values for the product

Find all products of endpoints:

Here, the greatest product is 35 and the smallest product is -14, thus

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.