Let's solve each part step-by-step for the function \( f(x) = 3x^2 + 3x - 4 \): --- ### (a) \( f(0) \) Substitute \( x = 0 \) into the function: \[ f(0) = 3(0)^2 + 3(0) - 4 \] \[ f(0) = 0 + 0 - 4 \] \[ f(0) = -4 \] --- ### (b) \( f(5) \) Substitute \( x = 5 \) into the function: \[ f(5) = 3(5)^2 + 3(5) - 4 \] \[ f(5) = 3(25) + 15 - 4 \] \[ f(5) = 75 + 15 - 4 \] \[ f(5) = 90 - 4 \] \[ f(5) = 86 \] --- ### (c) \( f(-5) \) Substitute \( x = -5 \) into the function: \[ f(-5) = 3(-5)^2 + 3(-5) - 4 \] \[ f(-5) = 3(25) - 15 - 4 \] \[ f(-5) = 75 - 15 - 4 \] \[ f(-5) = 60 - 4 \] \[ f(-5) = 56 \] --- ### (d) \( f(-x) \) Substitute \( x \) with \( -x \): \[ f(-x) = 3(-x)^2 + 3(-x) - 4 \] \[ f(-x) = 3x^2 - 3x - 4 \] --- ### (e) \( -f(x) \) Take the negative of the function: \[ -f(x) = -(3x^2 + 3x - 4) \] \[ -f(x) = -3x^2 - 3x + 4 \] --- ### (f) \( f(x+1) \) Substitute \( x \) with \( x+1 \): \[ f(x+1) = 3(x+1)^2 + 3(x+1) - 4 \] \[ f(x+1) = 3(x^2 + 2x + 1) + 3x + 3 - 4 \] \[ f(x+1) = 3x^2 + 6x + 3 + 3x + 3 - 4 \] \[ f(x+1) = 3x^2 + 9x + 2 \] --- ### (g) \( f(5x) \) Substitute \( x \) with \( 5x \): \[ f(5x) = 3(5x)^2 + 3(5x) - 4 \] \[ f(5x) = 3(25x^2) + 15x - 4 \] \[ f(5x) = 75x^2 + 15x - 4 \] --- ### (h) \( f(x+h) \) Substitute \( x \) with \( x+h \): \[ f(x+h) = 3(x+h)^2 + 3(x+h) - 4 \] \[ f(x+h) = 3(x^2 + 2xh + h^2) + 3x + 3h - 4 \] \[ f(x+h) = 3x^2 + 6xh + 3h^2 + 3x + 3h - 4 \] --- **Summary of answers:** - (a) \( f(0) = -4 \) - (b) \( f(5) = 86 \) - (c) \( f(-5) = 56 \) - (d) \( f(-x) = 3x^2 - 3x - 4 \) - (e) \( -f(x) = -3x^2 - 3x + 4 \) - (f) \( f(x+1) = 3x^2 + 9x + 2 \) - (g) \( f(5x) = 75x^2 + 15x - 4 \) - (h) \( f(x+h) = 3x^2 + 6xh + 3h^2 + 3x + 3h - 4 \)

Let's analyze each option to determine which transportation improvement can lead to urban economic revitalization. **Step 1: Understanding the goal** Urban economic revitalization involves stimulating economic activity, improving mobility, attracting investments, and enhancing the quality of urban life. **Step 2: Evaluating options** - **Option A: Investing in public transit systems** Investing in public transit can improve accessibility, reduce traffic congestion, lower transportation costs, and attract residents and businesses. This often leads to increased economic activity and urban renewal. - **Option B: Increasing tolls on highways** Higher tolls may discourage travel, reduce congestion temporarily, but can also burden commuters and limit accessibility, potentially hindering economic growth. - **Option C: Closing down existing road networks** This could restrict movement, increase congestion elsewhere, and impede commerce, which is unlikely to promote revitalization. - **Option D: Decreasing funding for transportation** Less funding can deteriorate transportation infrastructure, negatively impacting mobility and economic prospects. **Step 3: Conclusion** The most effective improvement for urban economic revitalization among these options is **Investing in public transit systems** because it directly enhances urban mobility, attracts development, and can stimulate economic growth. **Final answer:** **A Investing in public transit systems**

The correct completion of the sentence is: "A **section** shows the interior construction of a building as if it was cut apart, while A **detail** is an enlarged view of a specific construction element." **Explanation:** - **Section:** A drawing that depicts a cut-through view of a building or structure, revealing internal features as if sliced open. - **Detail:** An enlarged, more specific view of a particular part of the construction, showing finer details for clarity. **Final answer:** **section** and **detail**

**Title Section** **Project #: 1** **Unit Conversions** **Your Full Name:** [Your Name] **Course Name:** [Course Name] **Date:** [Submission Date] --- **Room Measurements and Sketches** (10 pts) **Describe the room:** The room is a rectangular classroom used for lectures and activities. **Measurements:** - Length: 20 feet 6 inches - Width: 15 feet 3 inches - Height: 10 feet 0 inches **Sketch of the room layout:** (You can hand-draw or insert a scanned photo here.) - Rectangular shape with length and width labeled. - Door located on one of the shorter walls, approximately centered. - Major obstacle: a large window on the opposite wall. --- **Unit Conversions** (15 pts) **Convert measurements to metric:** - **Length in meters:** - Length in inches: \( 20\, \text{ft} \times 12 + 6\, \text{in} = 240 + 6 = 246\, \text{in} \) - Convert to cm: \( 246\, \text{in} \times 2.54\, \text{cm/in} = 624.84\, \text{cm} \) - Convert to meters: \( 624.84\, \text{cm} \div 100 = 6.2484\, \text{m} \) - **Width in meters:** - Width in inches: \( 15\, \text{ft} \times 12 + 3\, \text{in} = 180 + 3 = 183\, \text{in} \) - Convert to cm: \( 183\, \text{in} \times 2.54\, \text{cm/in} = 465.82\, \text{cm} \) - Convert to meters: \( 465.82\, \text{cm} \div 100 = 4.6582\, \text{m} \) - **Height in meters:** - Height in feet: 10 ft - Convert to meters: \( 10\, \text{ft} \times 0.3048\, \text{m/ft} = 3.048\, \text{m} \) **Calculate area and perimeter:** - **Area (floor):** - \( 6.2484\, \text{m} \times 4.6582\, \text{m} = \boxed{29.12\, \text{m}^2} \) - **Perimeter (for baseboards):** - \( 2 \times (6.2484 + 4.6582) = 2 \times 10.9066 = \boxed{21.81\, \text{m}} \) --- **Material Costs** ### Carpet Option (10 pts) - **Area to cover with carpet:** same as floor area: 29.12 m² - **Number of liters of paint needed:** - Paint covers 3/8 m² per liter = 0.375 m²/liter - Liters needed: \( \frac{29.12\, \text{m}^2}{0.375} \approx 77.65\, \text{liters} \) - **Cost of paint:** - Price per liter: $11.25 - Total paint cost: \( 77.65 \times 11.25 \approx \$874.31 \) - **Cost of carpet:** - Price per m²: $2.00 - Total carpet cost: \( 29.12 \times 2.00 = \$58.24 \) - **Number of baseboard pieces:** - Assume each piece is 2.5 meters long - Number of pieces: \( \frac{21.81\, \text{m}}{2.5\, \text{m}} \approx 8.72 \) → 9 pieces - Total baseboard cost: \( 9 \times 4 = \$36 \) - **Total cost for carpet option:** - Sum all: \[ \boxed{\$874.31 + \$58.24 + \$36 = \$968.55} \] --- ### Hardwood Flooring Option (5 pts) - **Cost per m²:** $5.50 - **Total hardwood cost:** \[ 29.12\, \text{m}^2 \times 5.50 = \$160.16 \] - **Percent increase from carpet to hardwood:** \[ \frac{160.16 - 58.24}{58.24} \times 100 = \frac{101.92}{58.24} \times 100 \approx 175.05\% \] **Note:** Ensure to compare the total project costs: - Total with carpet (including paint and baseboards): \$968.55 - Total with hardwood (including paint and baseboards): \[ \$874.31 + \$160.16 + \$36 = \$1070.47 \] **Percent increase in total project cost:** \[ \frac{1070.47 - 968.55}{968.55} \times 100 \approx 10.43\% \] --- **Summary and Final Answers** - The total cost for the carpet option is approximately **\$968.55**. - The total cost for upgrading to engineered hardwood is approximately **\$1070.47**. - The hardwood flooring is about **\$101.92** more expensive than the carpet option. - The percent increase in total project cost when upgrading to hardwood flooring is approximately **10.43%**. **Final statements:** The project costs about \$968.55 for carpet and baseboards, including paint. Upgrading to engineered hardwood increases the total cost to roughly \$1070.47, which is about 10.43% more expensive than the carpet option.