What are the solutions of the equation x^4 + 5x^2 – 36 = 0? Use factoring to solve.
To solve the equation x4 + 5×2 – 36 = 0 using factoring, we first make a substitution to simplify the equation. Let’s set y = x2. This transforms our equation into: y2 + 5y – 36 = 0 Now, we need to factor this quadratic equation. We are looking for two numbers that multiply […]
What is the solution set of 7x² + 3x = 0?
To find the solution set of the equation 7x² + 3x = 0, we can start by factoring the equation. First, we can factor out the common term, which is x: x(7x + 3) = 0 Now, we set each factor equal to zero: x = 0 7x + 3 = 0 Solving the second […]
What is the probability that Judy answers all questions correctly by guessing on a multiple-choice test with 10 questions?
To determine the probability that Judy answers all questions correctly by guessing, we first need to examine the structure of the test. Each question has 4 possible answers, with only 1 being correct. The probability of Judy guessing the correct answer for a single question is: P(correct) = 1/4 Since the questions are independent, we […]
What is a possible value for the missing term of the geometric sequence 1250, 50?
To find the missing term in the geometric sequence, we need to understand the properties of such sequences. In a geometric sequence, each term is found by multiplying the previous term by a constant, called the common ratio. Given the terms 1250 and 50, we can find the common ratio. If we denote the missing […]
How do you solve for y in the equation 2x + 3y = 6?
To solve for y in the equation 2x + 3y = 6, follow these steps: Start with the original equation: 2x + 3y = 6 Isolate the term with y by subtracting 2x from both sides: 3y = 6 – 2x Now, divide each side by 3 to solve for y: y = (6 – […]
What is a quadrilateral with two sets of parallel sides?
A quadrilateral with two sets of parallel sides is known as a parallelogram. In geometry, a parallelogram is a four-sided figure where opposite sides are both equal in length and parallel. This property of parallelism leads to some interesting characteristics: the opposite angles are equal, the adjacent angles are supplementary (adding up to 180 degrees), […]
If a stadium seats 1600 people and sells 2/4 of its seats, how many tickets does it sell?
To find out how many tickets the stadium sells, we first need to determine what 2/4 of the total seating capacity is. The total number of seats in the stadium is 1600. To calculate 2/4 of 1600, we can simplify 2/4 to 1/2. This means the stadium sells half of its total seats. Now, let’s […]
How do you solve x² + 12x + 11 by completing the square?
To solve the quadratic equation x² + 12x + 11 = 0 by completing the square, we start by rearranging the equation: x² + 12x + 11 = 0 can be rewritten as x² + 12x = -11. Next, we need to complete the square on the left side. To do this, we take the […]
Which of the following is the best definition of a linear pair of angles?
A linear pair of angles is defined as two adjacent angles that are formed when two lines intersect. The key characteristics of a linear pair are that the angles must be next to each other (adjacent) and their non-common sides form a straight line, which means the angles are supplementary. To explain further, when two […]
What is the solution to the linear equation 6k + 105 + 3k + 12 + k + 05 + k + 2 + k + 73 + k + 9?
To solve the linear equation, we first need to combine like terms. The equation can be rewritten by grouping all the k terms and the constant terms together: 6k + 3k + k + k + k + k + 105 + 12 + 5 + 2 + 73 + 9 = 0 Now, let’s […]