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Given the function [tex]f(x) = x^2 - 5x + 4[/tex], find [tex]f\left(-\frac{2}{3}\right)[/tex].

A. [tex]\frac{70}{9}[/tex]
B. [tex]\frac{60}{9}[/tex]
C. [tex]\frac{70}{3}[/tex]
D. [tex]\frac{60}{3}[/tex]

Answer :

To find [tex]f\left(-\frac{2}{3}\right)[/tex] for the function [tex]f(x) = x^2 - 5x + 4[/tex], we need to substitute [tex]x = -\frac{2}{3}[/tex] into the function and simplify.

Step 1: Substitute [tex]x = -\frac{2}{3}[/tex] into the function.

[tex]f\left(-\frac{2}{3}\right) = \left(-\frac{2}{3}\right)^2 - 5\left(-\frac{2}{3}\right) + 4[/tex]

Step 2: Calculate [tex]\left(-\frac{2}{3}\right)^2[/tex].

[tex]\left(-\frac{2}{3}\right)^2 = \frac{4}{9}[/tex]

Step 3: Calculate [tex]-5\left(-\frac{2}{3}\right)[/tex].

[tex]-5\left(-\frac{2}{3}\right) = \frac{10}{3}[/tex]

Step 4: Add all the terms together.

[tex]\frac{4}{9} + \frac{10}{3} + 4[/tex]

To combine these terms, we need a common denominator (which is 9 in this case).

Step 5: Convert [tex]\frac{10}{3}[/tex] and [tex]4[/tex] to fractions with a denominator of 9.

[tex]\frac{10}{3} = \frac{30}{9}[/tex]

[tex]4 = \frac{36}{9}[/tex]

Step 6: Add all the fractions together.

[tex]\frac{4}{9} + \frac{30}{9} + \frac{36}{9} = \frac{70}{9}[/tex]

Therefore, [tex]f\left(-\frac{2}{3}\right) = \frac{70}{9}[/tex].

The correct multiple-choice answer is A. 70/9.

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