Determine the value of: (82 (92 − 32)) / (42 62). Work out the value of the square of 2 4/5.

Question

ScanSolve AI Tutor · Accepted Answer

here are the solutions for questions 8 and 9:

8. Determine the value of: $\frac{8^2 (9^2 - 3^2)}{4^2 \times 6^2}$

Calculate the squares of the numbers.
$8^2 = 64$ $9^2 = 81$ $3^2 = 9$ $4^2 = 16$ $6^2 = 36$
Substitute these values into the expression.
$\frac{64 (81 - 9)}{16 \times 36}$
Perform the subtraction in the parenthesis.
$81 - 9 = 72$
Substitute the result back into the expression.
$\frac{64 \times 72}{16 \times 36}$
Simplify the expression.
We can simplify by cancelling common factors:
$\frac{64 \times 72}{16 \times 36} = \frac{(16 \times 4) \times (36 \times 2)}{16 \times 36}$
Cancel 16 from the numerator and denominator, and 36 from the numerator and denominator:
$= 4 \times 2$ $= 8$
The correct option is B. $\boxed{8}$

9. Work out the value of the square of $2 \frac{4}{5}$ .
Convert the mixed number to an improper fraction.
$2 \frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5}$
Square the improper fraction.
$\left(\frac{14}{5}\right)^2 = \frac{14^2}{5^2}$
Calculate the squares of the numerator and the denominator.
$14^2 = 196$ $5^2 = 25$
Write the result as a mixed number.
$\frac{196}{25}$
Divide 196 by 25:
$196 \div 25 = 7$ with a remainder of $196 - (7 \times 25) = 196 - 175 = 21$ .
So, the mixed number is $7 \frac{21}{25}$ .
The correct option is A. $\boxed{7 \frac{21}{25}}$

Determine the value of: (82 (92 - 32)) / (42 62). Work out the value of the square of 2 4/5.