Question

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

Answer 1

Answer:

D. between -14 and 35

Step-by-step explanation:

Given:

$-5<a<2\\ \\-7<b<1$

Find: possible values for the product $a\cdot b$

Find all products of endpoints:

$(-5)\cdot (-7)=35\\ \\(-5)\cdot 1=-5\\ \\(-7)\cdot 2=-14\\ \\1\cdot 2=2$

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

$-14<a\cdot b<35$

Answer 2

The possible values for the product $a\cdot b$ are between -14 and 35. (Choice: D)

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

$c = a\cdot b$, for all $a,b\in \mathbb{R}$ (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:

$(-x)\cdot (-y) = x\cdot y$ (2)

$(-x)\cdot y = x\cdot (-y) = -x\cdot y$ (3)

Now we proceed to determine the limits:

Lower bound

$(-7)\cdot (2) = -14$

Upper bound

$(-5)\cdot (-7) = 35$

The possible values for the product $a\cdot b$ are between -14 and 35.

We kindly invite to see this question on algebra: https://brainly.com/question/22114719