Pregunta
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1.2 Simplify \( 362,67(29,74-12,456)+\sqrt{457,8} \) (correct to THREE decimal places) 1.3 Calculate \( \frac{1}{3} \times 27-\sqrt{64} \) \( 1.4 \quad \begin{array}{l}\text { Joey paid } R 202,50 \text { for petrol. Determine how many litres of petrol he bought if it is } \\ \text { sold at } R 8,10 \text { per litre. }\end{array} \) 1.5 Calculate \( \frac{\sigma-12}{18-3} \) 1.6 Convert 2459,00 Dollar to Rand. Use the exchange rate \( \$ 1=R 7,92 \). Determine the length of ONE side of a square if its area is \( 81 \mathrm{~cm}^{2} \).

Ask by Sullivan Schwartz. in South Africa
Feb 22,2025

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1.2 6289.790 1.3 1 1.4 25 litres 1.5 (σ – 12) / 15 1.6 a) R 19,475.28  b) 9 cm

Solución

Below are the step‐by‐step solutions for each part. ────────────────────────────── 1.2 Simplify   362,67 (29,74 – 12,456) + √457,8   (to three decimal places) Step 1. Rewrite the numbers using a decimal point:   362.67 × (29.74 – 12.456) + √457.8 Step 2. Evaluate the parentheses:   29.74 – 12.456 = 17.284 Step 3. Multiply:   362.67 × 17.284   A good way is to break it up:    • First, 362.67 × 17 ≈ 6165.39    • Next, 362.67 × 0.284 ≈ 102.998   Adding these gives:    6165.39 + 102.998 ≈ 6268.388 Step 4. Evaluate the square root:   √457.8 ≈ 21.402   (since 21.4² ≈ 457.96, close enough) Step 5. Add the two results:   6268.388 + 21.402 ≈ 6289.790 Rounded to three decimal places, the answer is:   6289.790 ────────────────────────────── 1.3 Calculate   (1/3) × 27 – √64 Step 1. Compute (1/3) × 27:   27/3 = 9 Step 2. Compute √64:   √64 = 8 Step 3. Subtract:   9 – 8 = 1 Answer: 1 ────────────────────────────── 1.4 Joey paid R 202,50 for petrol which is sold at R 8,10 per litre. Determine how many litres he bought. Step 1. Divide the total amount paid by the price per litre:   202.50 ÷ 8.10 = 25 Answer: 25 litres ────────────────────────────── 1.5 Calculate   (σ – 12) / (18 – 3) Step 1. Evaluate the denominator:   18 – 3 = 15 Step 2. Write the result in simplified form:   (σ – 12) / 15 Since σ is not given a numerical value, the simplified answer is:   (σ – 12) / 15 ────────────────────────────── 1.6 There are two tasks here: a) Convert 2459,00 Dollars to Rand using the exchange rate $1 = R 7,92. Step 1. Multiply the dollar amount by the exchange rate:   2459.00 × 7.92 One way to calculate:   2459 × 7.92 = 2459 × (8 – 0.08) = (2459 × 8) – (2459 × 0.08)    2459 × 8 = 19672    2459 × 0.08 = 196.72   So, 19672 – 196.72 = 19475.28 Answer: R 19,475.28 b) Determine the length of one side of a square if its area is 81 cm². Step 1. Use the fact that the area A of a square is given by:   A = side² Step 2. Solve for the side:   side = √81 = 9 Answer: 9 cm ────────────────────────────── Summary of Answers: 1.2 6289.790 1.3 1 1.4 25 litres 1.5 (σ – 12) / 15 1.6 a) R 19,475.28  b) 9 cm

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To simplify \( 362,67(29,74-12,456)+\sqrt{457,8} \), you first calculate the expression inside the parentheses: \( 29,74 - 12,456 = 17,284 \). Next, multiply by \( 362,67 \) to get \( 362,67 \times 17,284 \approx 6265,34 \). Then, calculate \( \sqrt{457,8} \approx 21,42 \). Finally, add them together: \( 6265,34 + 21,42 \approx 6286,76 \), so rounded to three decimal places, the result is \( 6286,760 \). For the calculation \( \frac{1}{3} \times 27 - \sqrt{64} \), you first find \( \frac{1}{3} \times 27 = 9 \). Then calculate \( \sqrt{64} = 8 \). So, \( 9 - 8 = 1 \). To find out how many liters of petrol Joey bought, divide his total payment by the price per litre. So, \( \frac{202,50}{8,10} \approx 24,938 \), which means Joey bought approximately 25 liters of petrol when rounded. For \( \frac{\sigma-12}{18-3} \), simplify the denominator first: \( 18 - 3 = 15 \). So the expression simplifies to \( \frac{\sigma - 12}{15} \). To convert 2459,00 Dollar to Rand, multiply by the exchange rate: \( 2459,00 \times 7,92 = 19429,68 \) Rand. Finally, to determine the length of ONE side of a square with an area of \( 81 \mathrm{~cm}^{2} \), use the formula for area \( A = s^2 \). Here, \( s = \sqrt{81} = 9 \mathrm{~cm} \).

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