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Complete Task II: calculations with squares, square roots, simplifying expressions, and solving equations.
Mathematics
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13 stepshere are the solutions for Task II:
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The table is already completed in the image provided.
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Find: *a)
Calculate the squares.
$$ 3^2 = 9 $$ $$ 5^2 = 25 $$Add the results.
$$ 9 + 25 = 34 $$ $$ \boxed{\text{34}} $$ *b) $\sqrt{49}$Find the square root of 49.
$$ \sqrt{49} = 7 $$ $$ \boxed{\text{7}} $$3. Simplify the following expressions. *a)
Remove the parentheses.
$$ 2x + 3 + x - 5 $$Combine like terms.
$$ (2x + x) + (3 - 5) = 3x - 2 $$ $$ \boxed{\text{3x - 2}} $$ *b) $(3x^2 - 2x + 1) - (x^2 + x - 4)$Remove the parentheses, distributing the negative sign to the second expression.
$$ 3x^2 - 2x + 1 - x^2 - x + 4 $$Combine like terms.
$$ (3x^2 - x^2) + (-2x - x) + (1 + 4) = 2x^2 - 3x + 5 $$ $$ \boxed{\text{2x^2 - 3x + 5}} $$ *c) $2(x + 4) - 3(x - 2)$Distribute the numbers into the parentheses.
$$ 2x + 8 - 3x + 6 $$Combine like terms.
$$ (2x - 3x) + (8 + 6) = -x + 14 $$ $$ \boxed{\text{-x + 14}} $$4. Solve the following equations. *a)
Subtract 5 from both sides of the equation.
$$ 2x + 5 - 5 = 17 - 5 $$ $$ 2x = 12 $$Divide both sides by 2.
$$ \frac{2x}{2} = \frac{12}{2} $$ $$ x = 6 $$ $$ \boxed{\text{x = 6}} $$ *b) $3(x - 2) = 15$Divide both sides by 3.
$$ \frac{3(x - 2)}{3} = \frac{15}{3} $$ $$ x - 2 = 5 $$Add 2 to both sides of the equation.
$$ x - 2 + 2 = 5 + 2 $$ $$ x = 7 $$ $$ \boxed{\text{x = 7}} $$
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