Evaluate the function f(x) = 2x² + 3x + 5 for the input value 3
To evaluate the function f(x) = 2x² + 3x + 5 for the input value of 3, we need to substitute 3 into the function in place of x. First, we replace x with 3: f(3) = 2(3)² + 3(3) + 5 Now, let’s calculate each term: (3)² = 9, so 2(3)² = 2 * […]
What is the sum of the first 15 terms of the sequence an = 10n + 21?
To find the sum of the first 15 terms of the sequence defined by an = 10n + 21, we first need to identify the first 15 terms of the sequence. We can calculate the first 15 terms by substituting values of n from 1 to 15: a1 = 10(1) + 21 = 31 a2 […]
How to Simplify the Expression 3 + 22 – 6 + 28 – 42?
To simplify the expression 3 + 22 – 6 + 28 – 42, we begin by performing the operations step by step, following the order of operations. 1. First, we add 3 + 22, which equals 25. 2. Next, we subtract 6 from 25: 25 – 6 = 19. 3. Then we add 28 to […]
Find the probability that of 25 randomly selected students at least two share the same birthday
To find the probability that at least two out of 25 randomly selected students share the same birthday, we can use the complementary probability approach. First, we calculate the probability that no two students share a birthday and then subtract that from 1. Assuming there are 365 days in a year (ignoring leap years), the […]
A circle has a radius of 3 inches. How do you find the length of an arc intercepted by a central angle whose measure is 25 radians?
To find the length of an arc intercepted by a central angle in radians, you can use the formula: Arc Length = Radius × Central Angle In this case, the radius (r) of the circle is 3 inches and the central angle (θ) is 25 radians. Plugging these values into the formula gives: Arc Length […]
Find the radius of a circle in which an inscribed square has a side of 8 inches
To find the radius of a circle that circumscribes a square, we first need to understand the relationship between the square and the circle. An inscribed square touches the circle at its corners. Given that the side length of the square is 8 inches, we can find the radius of the circumscribing circle using the […]
If 8z 9 8z 9 az2 b, what is the value of a?
To solve the expression 8z 9 8z 9 az2 b, we need to analyze the components presented. However, it seems like there may be some misunderstanding or typo in the expression itself. It looks like it was meant to convey a mathematical relationship but is currently ambiguous. If we treat ‘z’ as a variable and […]
Find the number of sides of a regular polygon if one interior angle is 60 degrees
To determine the number of sides of a regular polygon when one interior angle is given as 60 degrees, we can use the formula for finding the measure of an interior angle of a regular polygon: Interior Angle = (n – 2) * 180° / n Where n is the number of sides of the […]
What is the solution set of the given systems 5x + 2y = 7 and y = x + 1?
To find the solution set of the given system of equations, we need to solve them simultaneously. The first equation is: 5x + 2y = 7 The second equation is: y = x + 1 We can substitute the expression for y
Find the remainder when x³ – 2 is divided by x – 1. What is the remainder?
To find the remainder when dividing a polynomial by a linear factor, we can use the Remainder Theorem. The theorem states that the remainder of the division of a polynomial f(x) by x – c is f(c). In this case, we need to divide the polynomial f(x) = x³ – 2 by x – 1. […]