Question

solve for y.
3.4 + 5.1(y + 8) = 85
show factor tree to receive credit
simplify.
√75

Explanation:

Solve for \( y \) in \( 3.4 + 5.1(y + 8) = 85 \)

Step 1: Distribute \( 5.1 \)

Multiply \( 5.1 \) with each term inside the parentheses.
\( 3.4 + 5.1y + 5.1 \times 8 = 85 \)
\( 3.4 + 5.1y + 40.8 = 85 \)

Step 2: Combine like terms

Add \( 3.4 \) and \( 40.8 \).
\( 5.1y + 44.2 = 85 \)

Step 3: Subtract \( 44.2 \) from both sides

Isolate the term with \( y \).
\( 5.1y = 85 - 44.2 \)
\( 5.1y = 40.8 \)

Step 4: Divide by \( 5.1 \)

Solve for \( y \).
\( y = \frac{40.8}{5.1} \)
\( y = 8 \)

Simplify \( \sqrt{75} \) (with factor tree)

Step 1: Factor \( 75 \)

Factor \( 75 \) into prime factors.
\( 75 = 25 \times 3 \) (since \( 25 \times 3 = 75 \))

Step 2: Simplify square roots

\( \sqrt{75} = \sqrt{25 \times 3} \)
Using the property \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \) (\( a,b \geq 0 \)):
\( \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} \)

Step 3: Evaluate \( \sqrt{25} \)

\( \sqrt{25} = 5 \), so:
\( \sqrt{75} = 5\sqrt{3} \)

Answer:

s:

• For \( 3.4 + 5.1(y + 8) = 85 \): \( y = \boldsymbol{8} \)
• For \( \sqrt{75} \): \( \boldsymbol{5\sqrt{3}} \)