Which of the following is a factor of xy + 3y + 7x + 21?
To determine the factors of the expression xy + 3y + 7x + 21, we can group the terms in pairs: (xy + 3y) + (7x + 21) Now, we can factor out the common terms from each pair: y(x + 3) + 7(x + 3) Next, we can notice that both groups contain a […]
How to Solve the Differential Equation cosec y dx + sec 2x dy = 0 Using Separation of Variables
To solve the differential equation cosec y dx + sec 2x dy = 0 using separation of variables, we first rearrange the equation. Starting with: cosec y dx + sec 2x dy = 0 We can isolate the terms involving y and x. Rearranging gives: cosec y dx = -sec 2x dy Now, we separate […]
An item which is regularly $460 is on sale for one fourth off. What is the sale price?
To determine the sale price of an item that is regularly priced at $460 and is currently offered at one fourth off, we first need to calculate the discount. The discount can be calculated as follows: Discount = Regular Price × Discount Rate Here, the discount rate is one fourth, which is equivalent to 0.25. […]
State the explicit form of the pattern 4 9 14 19
The explicit form of the pattern 4, 9, 14, 19 can be derived by examining the differences between consecutive terms. The sequence starts at 4 and each subsequent number increases by 5. To express this mathematically, we first note down the terms: 1st term: 4 2nd term: 9 3rd term: 14 4th term: 19 The […]
What is the missing number in the following sequence 1, 16, 100, 169?
The missing number in the sequence is 36. This sequence consists of numbers that are perfect squares. Let’s analyze them: 1 is the square of 1 (1 x 1) 16 is the square of 4 (4 x 4) 100 is the square of 10 (10 x 10) 169 is the square of 13 (13 x […]
What is the slope intercept form equation of the line that passes through (5, 7) and (8, 22)?
To find the slope-intercept form of the equation of the line that passes through the points (5, 7) and (8, 22), we first need to calculate the slope of the line. The slope (m) can be found using the formula: m = (y₂ – y₁) / (x₂ – x₁) Here, we can set (x₁, y₁) […]
What is the equation of the horizontal line that passes through the point (2, 4)?
The equation of a horizontal line can be written in the form y = c, where c is a constant representing the y-value for all points on the line. In this case, the point given is (2, 4). This means that for every point on this line, the y-coordinate remains constant at 4, regardless of […]
How much interest is earned on 2700 in one year if it is invested at 3%?
To calculate the interest earned on an investment of $2700 at an interest rate of 3% over one year, you can use the simple interest formula: Interest = Principal × Rate × Time In this case: Principal (P) = $2700 Rate (R) = 3% (or 0.03 as a decimal) Time (T) = 1 year Now, […]
What is the polynomial function of lowest degree with lead coefficient 1 and roots i, 2, and 2?
To find the polynomial function of the lowest degree with a leading coefficient of 1 and the given roots, we start by writing down the roots. We have the roots i (which is a complex root) and 2 (which is a real root, with a multiplicity of 2). For complex roots, we know that if […]
Which value of y forms the solution of the system defined by y = 11x + 1 and 11x + 12y = 12?
To find the value of y in the given system of equations, we need to solve the equations step by step. The first equation is: 1. y = 11x + 1 Now, we can substitute the expression for y into the second equation: 2. 11x + 12y = 12 Substituting y from equation 1 into […]