What's the name of the property given below? If a×b=0 then a=0 b=0 or both a=0 and b=0

Mathematics

1 answer:

max2010maxim [7]4 years ago

4 0

Answer:

This is the zero product rule.

Step-by-step explanation:

a: b = 0, then a = 0, b = 0, or both a = 0 and b = 0.

This is the zero product rule.

It shows that for the product to be zero, at least one factor must be zero

If a*b= 0: It shows that one of the factor is zero or may be both the factors are zero that is why their resultant product is 0.

So therefore, the product to be zero at least one of the factors must be zero.

If a x b = 0 then a = 0 and/or b = 0

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Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

ss7ja [257]

The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.