What’s one way we can check our answer to 2 + 10 + 20?
To check your answer to the addition of 2 + 10 + 20, you can use the method of regrouping the numbers. Start by adding the first two numbers together: 2 + 10 equals 12. Then, take that result and add it to the last number: 12 + 20 equals 32. So, the final answer […]
What is the greatest common factor of 8m, 36m³, and 12?
To find the greatest common factor (GCF) of the numbers 8m, 36m³, and 12, we need to look at the coefficients and the variable parts separately. First, we find the GCF of the numerical coefficients: 8, 36, and 12. The factors of 8 are: 1, 2, 4, 8. The factors of 36 are: 1, 2, […]
What is the solution to this system of linear equations: y = 6x and y = 10?
To find the solution to this system of linear equations, we can set the two equations equal to each other since they both equal y: 6x = 10 Now, we can solve for x by dividing both sides by 6: x = 10 / 6 x = 5/3 Now that we have the value for […]
Explain What is Polynomials Factoring
Factoring polynomials is a method used in algebra to break down a polynomial into simpler components, or factors, that can be multiplied together to obtain the original polynomial. This process is essential for solving polynomial equations, simplifying expressions, and analyzing mathematical behavior. A polynomial is an expression that consists of variables, coefficients, and exponents, such […]
If a polynomial has four terms 3x³ + 5x + 6x² + 10, which factoring method can be considered?
To factor a polynomial with four terms like 3x³ + 5x + 6x² + 10, one effective method to consider is factoring by grouping. In factoring by grouping, we can separate the polynomial into two groups and look for common factors within those groups. Let’s rearrange the polynomial so we can visualize the grouping more […]
If f(x) = x^4 + x^3 + x^2 and g(x) = x^2 where x ≠ 0, what is f(g(x))?
To find f(g(x)), we first need to substitute g(x) into f(x). Given: f(x) = x4 + x3 + x2 g(x) = x2 Now, we substitute g(x) into f(x): f(g(x)) = f(x2) Now, replace every x in f(x) with x2: f(x2) = (x2)4 + (x2)3 + (x2)2 Calculating each term: (x2)4 = x8 (x2)3 = x6 […]
Find the area of the region bounded by the hyperbola 9x² – 4y² = 36 and the line x = 3
To find the area of the region bounded by the hyperbola given by the equation 9x² – 4y² = 36 and the vertical line x = 3, we first need to understand the shape and location of the hyperbola. 1. **Rearranging the hyperbola equation**: We can rewrite the equation of the hyperbola in standard form. […]
If the Discriminant of an Equation is Negative, Which of the Following is True of the Equation?
If the discriminant of a quadratic equation is negative, the correct answer is a) it has 2 complex solutions. The discriminant, typically denoted as D, is given by the formula D = b² – 4ac, where a, b, and c are the coefficients of the equation in the standard form ax² + bx + c […]
What is the least number which when divided by 6, 15, and 18 leaves a remainder of 5 in each case?
To find the least number that leaves a remainder of 5 when divided by 6, 15, and 18, we can follow these steps: First, we need to recognize that if a number gives a remainder of 5 when divided by another number, it can be rewritten in the form: Number = k * divisor + […]
What is the solution of the system of equations 3x + 6y = 2 and 15x + 30y = 10?
To solve the system of equations 3x + 6y = 2 and 15x + 30y = 10, we can start by simplifying the second equation. If we divide every term in the second equation by 5, we get: 3x + 6y = 2 This is exactly the same as the first equation, indicating that the […]