For which values of m and n will the binomial m^3n^2 + m^2n^5 have a positive value? A) m = 3 , n = -1

B) m = -2 , n = -2

C) m = -3 , n = -5

D) m = 1 , n = -2

^=means exponent

m = 3 and n = -1

Explanation:

Let's first factor out the GCF

m^3n^2 + m^2n^5

m^2n^2(m + n^3)

The term m^2n^2 is always nonnegative because squaring a negative leads to a positive (eg: (-10)^2 = 100).

So the entire expression is positive when m+n^3 is also positive. In other words when m+n^3 > 0.

If we tried something like m = -2 and n = -2, then,

m + n^3 > 0

-2 + (-2)^3 > 0

-2 + (-8) > 0

-10 > 0

Which is false. So we rule out choice B. You should find that choices C and D lead to similar conclusions. Only choice A works

m + n^3 > 0

3 + (-1)^3 > 0

3 + (-1) > 0

2 > 0

we get a true result here. Note that this happens because the value of m is larger than the absolute value of the result of n^3, which helps keep m+n^3 in positive territory.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."