To graph the inequality 2x + y < 4, follow these steps: Step 1: Rewrite the Inequality First, rewrite the inequality in slope-intercept form (y = mx + b). Start by isolating y: y < -2x + 4 This tells us that the slope (m) is -2 and the y-intercept (b) is 4. Step 2: ... Read more
To find the values of b that satisfy the equation 43b² + 2 = 64, we first need to isolate the b² term. We can do this by following these steps: Subtract 2 from both sides: This gives us: 43b² = 64 – 2 Which simplifies to: 43b² = 62 Next, divide both sides by … Read more
The area of a circle can be calculated using the formula: Area = π × r2 Where π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle. In this case, the radius (r) of circle C is 32 units. Plugging this value into the formula, we get: Area … Read more
To solve the equation log3(2) + 6x = log3(2x) + 12, we begin by rearranging the terms to isolate the logarithmic and linear components. First, we can express the equation as: log3(2x) = log3(2) + 6x – 12 Next, we will use the property of logarithms that states loga(b) = c can be rewritten as … Read more
To solve the problem, let’s start by defining the unknown number as x. According to the given condition, we can write the equation as follows: 2x + (1/2)x = 10 Now, we will combine the terms on the left side of the equation. First, notice that (1/2)x is equivalent to 0.5x. Thus, our equation transforms … Read more
To find the completely factored form of the quadratic expression 16x² + 8x + 32, we will first check if there are any common factors that can be factored out from all the terms. All the coefficients (16, 8, and 32) have a common factor of 8. We can factor out 8 from the expression: … Read more
To solve the system of equations y = 2x + 8 and y = x + 4, we can use the substitution method since both equations are already set to y. 1. **Set the two equations equal to each other:** Since both expressions equal y, we can set them equal to each other: 2x + … Read more
How to Calculate the Area and Diagonals of a Rhombus To find the area of a rhombus, you can use the following formulas: Area based on side length and altitude: Area = Side × Altitude Area based on diagonals: Area = (Diagonal 1 × Diagonal 2) / 2 Calculating the Area Given that the side … Read more
To solve the equation 0 = 2sin²(x)cos²(x), we can start by simplifying the equation. Notice that 2sin²(x)cos²(x) can be rewritten using the double angle identity for sine. The identity states: sin(2x) = 2sin(x)cos(x) Therefore, we can express 2sin²(x)cos²(x) as: 2sin²(x)cos²(x) = (sin(2x))² / 2 Now, the equation becomes: 0 = (sin(2x))² / 2 Multiplying both … Read more
To simplify the expression x² + 15x + 56x + 7, we can follow these steps: Combine like terms: In this expression, we have two like terms related to ‘x.’ These are 15x and 56x. Adding these together gives us: 15x + 56x = 71x Now we can rewrite the expression: x² + 71x + … Read more