How many real number solutions are there to the equation 3x² + 4 = 0?
To find the number of real number solutions to the equation 3x² + 4 = 0, we can start by rearranging the equation: 3x² = -4 Next, we divide both sides by 3: x² = -\frac{4}{3} Now, we can see that we have x² equal to a negative number. In real numbers, the square of […]
How many ways can eight people be seated in a row if two of them must sit next to each other?
To solve the problem of seating eight people in a row where two specific people must sit next to each other, we can treat the two people who want to sit together as a single entity or block. Let’s denote the two people who want to sit together as A and B. By treating them […]
What is the value of n in the equation 2n 4 6 9 4 2n 1?
To find the value of n in the equation 2n 4 6 9 4 2n 1, we need to clarify the structure of the equation. The equation seems to lack clear operational symbols such as ‘+’, ‘-‘, ‘*’, or ‘/’. Assuming that the context is algebraic and we can interpret the equation as a series […]
What is the axis of symmetry for the function f(x) = 2x² + 8x + 8?
The axis of symmetry for the quadratic function f(x) = 2x² + 8x + 8 can be found using the formula: x = -b / (2a) In the equation f(x) = 2x² + 8x + 8, the coefficients are: a = 2 b = 8 Now, substituting the values of a and b into the […]
The terminal side of an angle in standard position passes through P(3, 4). What is the value of tan θ?
To find the value of tan θ, we start with the coordinates of point P, which are (3, 4). In trigonometry, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can consider the point P as part of […]
How do you write an equation in the point slope form of the line that passes through the given points 1 8 4 6?
To write the equation of a line in point-slope form, we first need to determine the slope of the line that passes through the two points. The points given are (1, 8) and (4, 6). The formula to find the slope (m) between two points (x1, y1) and (x2, y2) is: m = (y2 – […]
Which of the following is the basic unit of volume in the metric system?
The basic unit of volume in the metric system is the liter (L). The liter is defined as the volume of a cube that measures 10 centimeters on each side, which equates to 1,000 cubic centimeters (cm³). It is widely used to measure liquids and is a fundamental unit in scientific and everyday contexts. In […]
What is the volume of an oblique prism with a rectangular base?
To find the volume of the oblique prism, we start with understanding its dimensions. The base is a rectangle with a width of 10 units and a length of 13 units. The formula for the area of the rectangular base is: Area = Width × Length Plugging in the values, we get: Area = 10 […]
What is the height of a triangle that has an area of 60 yd² and a base with a length of 12 yd?
To find the height of a triangle when you know its area and base length, you can use the formula for the area of a triangle, which is: Area = 0.5 × base × height In this case, the area is 60 yd² and the base is 12 yd. Plugging these values into the formula […]
How do you subtract the expression 2x^3 + 9x + 8 – 4x^2 – 15x – 7?
To subtract the expression 2×3 + 9x + 8 and 4×2 + 15x + 7, we need to combine like terms. First, let’s rearrange the terms in descending order of their degree: 2×3 – 4×2 + (9x – 15x) + (8 – 7) Now, we can combine the like terms: There is only one cubic […]