Which figure has the same order of rotational symmetry as a rectangle?
A rectangle has an order of rotational symmetry of 2. This means that if you rotate a rectangle by 180 degrees, it looks the same. The figure that has the same order of rotational symmetry as a rectangle is a rhombus. Both shapes can be rotated halfway around (180 degrees) and still appear unchanged. However, […]
If the length of one side of a square is 120m, what is the perimeter of the square?
To find the perimeter of a square, you can use the formula: Perimeter = 4 × length of one side In this case, the length of one side of the square is 120 meters. Plugging that value into the formula gives us: Perimeter = 4 × 120m = 480m Therefore, the perimeter of the square […]
A population is growing at a rate of 2, 4, 8, 16, 32. What type of growth does this describe?
The growth described by the rates of 2, 4, 8, 16, and 32 is an example of exponential growth. In this scenario, the population is doubling at each interval: from 2 to 4 is a doubling, from 4 to 8 is another doubling, and so forth. This type of growth occurs when the increase in […]
What are the coordinates of the vertex of the graph of the function y = 3x² + 12x + 3?
To find the vertex of the quadratic function given by the equation y = 3x² + 12x + 3, we can use the vertex formula. The vertex form of a quadratic function is given by: y = a(x – h)² + k Where (h, k) are the coordinates of the vertex. Alternatively, we can find […]
If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81 degrees?
To find the length of the arc subtended by an angle in a circle, we can use the formula: Arc Length = (θ / 360) × 2πr Where: θ = angle in degrees r = radius of the circle π (pi) ≈ 3.14159 In this case, the radius (r) is 10 feet, and the angle […]
Using the Proportional Method, Solve for x in This Ratio: 2 : x = 4 : 2
To solve for x using the proportional method, we start by setting up the equation based on the given ratio: 2 : x = 4 : 2. In mathematical terms, this can be expressed as: 2/x = 4/2 Next, we can cross-multiply to eliminate the fractions. This means that we multiply the extremes and the […]
What is the speed of the stream in a motorboat going upstream and downstream?
To solve this problem, we need to break it down step by step. We know that the speed of the motorboat in still water is 24 km/hr. Let’s denote the speed of the stream as ‘x’ km/hr. Therefore, the effective speed of the motorboat going upstream (against the current) is (24 – x) km/hr, and […]
How do you find p when q varies directly as p?
To solve this problem, we first need to understand what it means for p to vary directly as q. When we say that p varies directly as q, we can express this relationship mathematically as: p = kq where k is the constant of proportionality. From the information given, we know that when q = […]
Without Graphing, is the System Independent, Dependent, or Inconsistent? y = 2x + 8 and 2x – y = 8
To determine whether the system of equations is independent, dependent, or inconsistent, we can analyze the equations algebraically. The first equation is: 1. y = 2x + 8 The second equation can be rewritten as: 2. y = 2x – 8 If we take a closer look, both equations have the same slope. The first […]
How do you find an equation of the line that passes through the point (7, 2) and has the indicated slope 3?
To find the equation of a line given a point and a slope, we can use the point-slope form of a linear equation. The point-slope form is given by: y – y1 = m(x – x1) Where: (x1, y1) is a point on the line. In your case, this is (7, 2). m is the […]