How do I graph the line with slope m = 7 passing through the point (2, 9)?
To graph a line with a given slope and a point, we can use the slope-intercept form of the equation of a line, which is given by: y = mx + b In this case, the slope (m) is 7 and the line passes through the point (2, 9). We will first determine the y-intercept […]
What is the value of s in the equation 3r + 10 = 5s when r = 10?
To find the value of s in the equation 3r + 10 = 5s given that r = 10, we will substitute the value of r into the equation and solve for s. Starting with the equation: 3r + 10 = 5s Substituting r with 10: 3(10) + 10 = 5s This simplifies to: 30 […]
What is the solution of the system of equations y = 2x + 8 and y = x + 4?
To solve the system of equations, we start with the two equations: Equation 1: y = 2x + 8 Equation 2: y = x + 4 Since both equations are equal to y, we can set them equal to each other: 2x + 8 = x + 4 Now, we can solve for x. First, […]
What is the value of the expression 12 4 3 2 9?
To evaluate the expression 12 4 3 2 9, we need to determine the operations implied between these numbers. Assuming the standard mathematical operations of addition and multiplication, we can try to figure out a reasonable calculation. However, as presented, the expression does not include explicit operations like + or ×, which makes it ambiguous. […]
A vessel has 4 liters and 500 ml of curd; in how many glasses each of 25 ml capacity can it be filled?
To determine how many glasses of curd can be filled from the vessel, we first need to convert the total amount of curd into milliliters. We know that 1 liter equals 1000 milliliters. The vessel contains: 4 liters of curd = 4 × 1000 ml = 4000 ml 500 ml of curd. Now, we can […]
If the integral of sin(2x) cos(2x) dx from 1 to 2 is equal to 1/2 sin(2x) at limits a and b, then find a and b.
To solve the integral of sin(2x) cos(2x), we can use the identity: sin(2x) = 2 sin(x) cos(x). This means: sin(2x) cos(2x) = (1/2) sin(4x). Thus, we can rewrite the integral: ∫ sin(2x) cos(2x) dx = (1/2) ∫ sin(4x) dx. The integral of sin(4x) is: = -1/4 cos(4x) + C. Now, substituting this back into the […]
What is the completely factored form of the expression 16x² + 8x + 32?
To find the completely factored form of the expression 16x² + 8x + 32, we first start by looking for common factors and then simplifying the expression. 1. **Identify Common Factors**: The coefficients of the terms are 16, 8, and 32. The greatest common factor (GCF) of these numbers is 8. 2. **Factor out the […]
How to Write an Improper Fraction as a Mixed Number
To convert an improper fraction into a mixed number, follow these simple steps: Identify the numerator and denominator: The numerator is the top number of the fraction, and the denominator is the bottom number. Divide the numerator by the denominator: Perform the division to find out how many whole numbers fit into the fraction. The […]
How to Write the Quadratic Equation in Standard Form and Choose the Value of b for 2x, 1x, and 5 = 0?
To write a quadratic equation in standard form, we generally follow the format: ax² + bx + c = 0, where a, b, and c are constants. For the given expression 2x, 1x, 5 = 0, we can interpret this as 2x² + 1x + 5 = 0. In this equation: a = 2 b […]
If cos x sin20 x and 0 x 90 the value of x is
To determine the value of x satisfying the equation cos(x) = sin(20x) within the range 0 < x < 90, we can start by using the identity relating cosine and sine. Recall that sin(θ) = cos(90° – θ). Thus, we can rewrite the equation as: cos(x) = cos(90° – 20x) This leads us to two […]