Question

• 28. (52) explain evaluate: $b^2 - 4ac$ if $a = 3.6$, $b = 6$, and $c = 2.5$ 29. (43) a. arrange these numbers in order from greatest to least: $-1, \frac{3}{2}, 2.5, 0, -\frac{1}{2}, 2, 0.2$ b. which of the numbers in a are integers? 30. (27) lindsey had the following division to perform: $35 \div 2\frac{1}{2}$ describe how lindsey could form an equivalent division problem that would be easier to perform mentally.

Explanation:

Question 28

Step1: Substitute values into formula

Substitute \(a = 3.6\), \(b = 6\), \(c = 2.5\) into \(b^2 - 4ac\):
\(6^2 - 4\times3.6\times2.5\)

Step2: Calculate each term

Calculate \(6^2 = 36\) and \(4\times3.6\times2.5 = 4\times9 = 36\) (using \(3.6\times2.5 = 9\)).

Step3: Subtract the terms

\(36 - 36 = 0\)

Step1: Convert fractions to decimals

\(\frac{3}{2}=1.5\), \(-\frac{1}{2}=-0.5\)

Step2: Order from greatest to least

Positive numbers: \(2.5 > 2 > 1.5 > 0.2 > 0\); Negative numbers: \(-0.5 > -1\). Combine: \(2.5, 2, \frac{3}{2}, 0.2, 0, -\frac{1}{2}, -1\)

Step1: Recall integer definition

Integers are whole numbers (positive, negative, or zero) without fractions/decimals.

Step2: Identify integers

From the list: \(-1, 0, 2\) (since \(2.5\) is decimal, \(\frac{3}{2}=1.5\) is fraction, \(0.2\) is decimal, \(-\frac{1}{2}=-0.5\) is fraction).

Answer:

\(0\)

Question 29a