This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the problems: 1. Simplifying 3^3 + 3^3 + 3^3 Step 1: Recognize that the expression is the sum of three identical terms. 3^3 + 3^3 + 3^3 = 3 × 3^3 Step 2: Apply the exponent rule a^m × a^n = a^m+n. Here, 3 = 3^1. 3^1 × 3^3 = 3^1+3 = 3^4 The correct option is B. The final answer is 3^4. 2. f: x 1-2x, x R. The values of ff(2) gives Step 1: Find f(2) by substituting x=2 into the function f(x). f(2) = 1 - 2(2) = 1 - 4 = -3 Step 2: Find ff(2) by substituting the result from Step 1 (which is f(2)=-3) into the function f(x). ff(2) = f(-3) = 1 - 2(-3) = 1 + 6 = 7 The correct option is D. The final answer is 7. 3. When a regular polygon has 45^ as an exterior angle. Then the number of sides of the polygon is: Step 1: Recall the formula for the exterior angle of a regular polygon. Exterior Angle = (360^)/(n) where n is the number of sides. Step 2: Substitute the given exterior angle and solve for n. 45^ = (360^)/(n) n = (360^)/(45^) n = 8 The correct option is D. The final answer is 8. 4. The diagonals of a kite measure 50cm by 80cm. The area of the kite in cm^2 is Step 1: Recall the formula for the area of a kite. A = (1)/(2) d_1 d_2 where d_1 and d_2 are the lengths of the diagonals. Step 2: Substitute the given diagonal lengths d_1 = 50 cm and d_2 = 80 cm. A = (1)/(2) (50 cm)(80 cm) A = (1)/(2) (4000 cm^2) A = 2000 cm^2 The correct option is C. The final answer is 2000 cm^2. 5. In the figure 1, the shaded region is called The shaded region in the figure is bounded by two radii and the arc between them. This geometric shape is known as a sector of a circle. The correct option is C. The final answer is a sector. 6. A store keeper sold 2 pens and 3 books for 4,150FCFA. Given that a book costs 250FCFA, then the cost of a pen in FCFA is Step 1: Let p be the cost of a pen and b be the cost of a book. Set up an equation based on the given information. 2p + 3b = 4150 Step 2: Substitute the given cost of a book, b = 250 FCFA. 2p + 3(250) = 4150 2p + 750 = 4150 Step 3: Solve for p. 2p = 4150 - 750 2p = 3400 p = (3400)/(2) p = 1700 There seems to be a discrepancy between the calculated answer (1700 FCFA) and the provided options (A: 50, B: 100, C: 150, D: 200). Let me re-check the calculation. 2p + 3(250) = 4150 2p + 750 = 4150 2p = 3400 p = 1700 It's possible there's a typo in the question or the options. If the total cost was 1150 FCFA instead of 4150 FCFA, then: 2p + 3(250) = 1150 2p + 750 = 1150 2p = 1150 - 750 2p = 400 p = 200 This matches option D. Given that this is a multiple-choice question, it is highly probable that the total cost was intended to be 1150 FCFA. Assuming the total cost was 1150 FCFA to match an option: 2p + 3(250) = 1150 2p + 750 = 1150 2p = 1150 - 750 2p = 400 p = 200 The correct option, assuming the total cost was 1150 FCFA, is D. The final answer is 200 FCFA. 7. The number of cubic boxes of side 2cm that can fit exactly in a big box which is 6cm long, 5cm wide and 4cm high is equal to Step 1: Calculate the number of small boxes that fit along each dimension of the big box. Length: 6 cm2 cm = 3 boxes Width: 5 cm2 cm = 2.5 boxes. Since boxes must fit exactly, we can only fit 2 boxes along the width. Height: 4 cm2 cm = 2 boxes Step 2: Multiply the number of boxes that fit along each dimension to find the total number of boxes. Total boxes = 3 × 2 × 2 = 12 The correct option is not listed among A (15), B (18), C (30), D (45). Let's re-evaluate if the question implies volume division without considering integer fits. Volume of small cubic box: V_small = (2 cm)^3 = 8 cm^3 Volume of big box: V_big = 6 cm × 5 cm × 4 cm = 120 cm^3 Number of boxes (by volume): V_bigV_small = 120 cm^38 cm^3 = 15 If the question implies fitting by volume, then 15 boxes would fit. However, "fit exactly" usually implies integer dimensions. Given the options, it's likely that the question intends for a simple volume division. If the big box dimensions were, for example, 6cm x 6cm x 4cm, then 3 × 3 × 2 = 18 boxes would fit. If it was 6cm x 4cm x 4cm, then 3 × 2 × 2 = 12 boxes. Given the options, and the common interpretation in such problems, the volume division is often implied. Let's assume the question implies volume division. Number of boxes = Volume of big boxVolume of small box V_big = 6 cm × 5 cm × 4 cm = 120 cm^3 V_small = (2 cm)^3 = 8 cm^3 Number of boxes = 120 cm^38 cm^3 = 15 The correct option is A. The final answer is 15. 8. The perimeter of a rectangle is 64cm. If the width is 8cm, then the length is Step 1: Recall the formula for the perimeter of a rectangle. P = 2(l+w) where P is the perimeter, l is the length, and w is the width. Step 2: Substitute the given values P = 64 cm and w = 8 cm. 64 = 2(l+8) Step 3: Solve for l. (64)/(2) = l+8 32 = l+8 l = 32 - 8 l = 24 cm The correct option is B. The final answer is 24 cm. 9. The line segment passing through (-3) and (-5, -7) has equation Step 1: The first point is given as (-3). Assuming this means (-3, y_1) and the second point is (-5, -7). We need to find the equation of the line. Let's test the given options by substituting the point (-5, -7). A) y = 2x + 3 Substitute x=-5: y = 2(-5) + 3 = -10 + 3 = -7. This matches the point (-5, -7). B) y = -5x - 7 Substitute x=-5: y = -5(-5) - 7 = 25 - 7 = 18. This does not match. C) $