Question

what is 507,000 in scientific notation?
507×10³
0.507×10⁶
50.7×10⁴
5.07×10⁵
which set of numbers can not represent the lengths of the sides of a triangle?
{7,18,11}
{9,12,19}
{7,5,6}
{6,8,11}
which represents an irrational number?
√4
1/4
√3
0
which is the greatest common factor of the expression below?
32a³b² + 36a²c² - 16ab³
8a²b²
6abc

Explanation:

Step1: Scientific Notation

Scientific notation is \(a\times 10^{n}\), where \(1\leqslant a<10\) and \(n\) is an integer. For \(507000\), \(a = 5.07\) and \(n=5\) (since \(507000=5.07\times100000 = 5.07\times 10^{5}\)).

Step2: Triangle Side - Length Rule

The triangle inequality theorem states that for a triangle with side lengths \(x,y,z\), \(x + y>z\), \(x+z > y\), and \(y + z>x\). For \(\{7,18,11\}\), \(7 + 11=18\) (violates \(x + y>z\)). For \(\{9,12,19\}\), \(9+12 = 21>19\), \(9 + 19=28>12\), \(12+19 = 31>9\). For \(\{7,5,6\}\), \(5+6=11>7\), \(5 + 7=12>6\), \(6+7 = 13>5\). For \(\{6,8,11\}\), \(6+8=14>11\), \(6 + 11=17>8\), \(8+11=19>6\).

Step3: Irrational Number Definition

An irrational number cannot be written as a fraction \(\frac{p}{q}\) (\(p,q\in\mathbb{Z},q
eq0\)). \(\sqrt{4}=2\) (rational), \(\frac{1}{4}\) (rational), \(0\) (rational). \(\sqrt{3}\) is irrational as it has a non - repeating, non - terminating decimal expansion.

Answer:

1. \(5.07\times 10^{5}\)
2. \(\{7,18,11\}\)
3. \(\sqrt{3}\)