What is the value of t in the equation 32t + 5 = 5t + 25?
To find the value of t in the equation 32t + 5 = 5t + 25, we need to rearrange the equation and isolate t. First, we can start by subtracting 5t from both sides: 32t + 5 – 5t = 5t + 25 – 5t This simplifies to: 27t + 5 = 25 Next, […]
A number that has more than two factors is a
A number that has more than two factors is known as a composite number. Composite numbers are integers greater than one that are not prime, meaning they can be divided by numbers other than one and themselves. To illustrate, consider the number 6. Its factors are 1, 2, 3, and 6. Since it has more […]
Which phrase best describes the translation from the graph y = 2x² to the graph of y = 2x² + 5?
The phrase that best describes the translation from the graph of y = 2x² to the graph of y = 2x² + 5 is that it represents a vertical shift upward by 5 units. When you add a constant to a function, it affects the y-values of the graph. In this case, the function y […]
If the quadratic formula is used to solve 2x² + 5x + 4, what are the solutions?
To solve the quadratic equation 2x² + 5x + 4 = 0 using the quadratic formula, we first need to identify the coefficients in the standard form of a quadratic equation, which is ax² + bx + c = 0. In this case, we have: a = 2 b = 5 c = 4 The […]
How can we simplify the expression 3 + 4i – 5 + 2i?
To simplify the expression 3 + 4i – 5 + 2i, we start by combining like terms. First, we can group the real parts together and the imaginary parts together: Real parts: 3 and -5 Imaginary parts: 4i and 2i Now, let’s do the calculations: For the real parts: 3 – 5 = -2 For […]
What is the solution to the system of linear equations 6x + 7y = 59 and 4x + 5y = 41?
To solve the system of linear equations given by 6x + 7y = 59 and 4x + 5y = 41, we can use the method of substitution or elimination. Here, we’ll use the elimination method. First, we’ll align the equations for clarity: 1) 6x + 7y = 59 2) 4x + 5y = 41 We […]
What is the angle between a diagonal of a cube and one of its edges?
To find the angle between a diagonal of a cube and one of its edges, we first need to understand the geometric properties involved. A cube has all its edges of equal length, say a. The body diagonal of a cube connects two opposite corners and can be calculated using the 3D distance formula. The […]
Explain How to Use Multiplication to Check the Answer to a Division Problem
To verify the solution of a division problem, you can use multiplication. This method involves taking the quotient (the result of the division) and multiplying it by the divisor (the number you divided by) to see if you arrive back at the dividend (the original number being divided). For example, let’s say you have the […]
What is the derivative of y = 1/x^2 * x^n at x = 1?
To find the derivative of the function y = rac{1}{x^2} imes x^n at x = 1, we first simplify the function and then differentiate it. First, we can rewrite the function as: y = x^{n-2} Now, we can differentiate this with respect to x. Using the power rule of differentiation: rac{dy}{dx} = (n-2)x^{(n-2)-1} = (n-2)x^{n-3} […]
How many solutions does this linear system have: y = 2x + 5 and 8x – 4y = 20?
To determine how many solutions this linear system has, we need to analyze the two equations provided. The first equation is: y = 2x + 5 This represents a straight line with a slope of 2 and a y-intercept of 5. The second equation is: 8x – 4y = 20 To understand this equation better, […]