AC is tangent to circle O at A. If ∠MBy = 34 degrees, what is ∠YAC?
To find the angle ∠YAC, we need to use some properties of circles and tangents. When a tangent line touches a circle at a point, it creates a right angle with the radius drawn to the point of tangency. In this case, since AC is tangent to circle O at point A, we know that […]
How do you write the quadratic equation fx = x² + 3x + 2 in vertex form?
To rewrite the quadratic equation fx = x² + 3x + 2 into vertex form, we will complete the square. The vertex form of a quadratic equation is given by: f(x) = a(x – h)² + k where (h, k) is the vertex of the parabola. Let’s start with the given equation: f(x) = x² […]
What is the next number in the series 2, 5, 11, 20, 32, 47?
To find the next number in the series 2, 5, 11, 20, 32, 47, let’s first look at the differences between consecutive terms: 5 – 2 = 3 11 – 5 = 6 20 – 11 = 9 32 – 20 = 12 47 – 32 = 15 So, the differences are: 3, 6, 9, […]
Find the Lengths of the Missing Sides in the Triangle
To find the lengths of the missing sides in a triangle, we can use the properties of triangles and, if needed, apply the Pythagorean theorem for right triangles, or the law of sines or cosines for other types of triangles. Firstly, if we have a right triangle, and we know one leg and the hypotenuse, […]
A Rational Number Equivalent to 5/7
To find a rational number equivalent to 5/7, we can multiply both the numerator and the denominator by the same non-zero integer. For example, if we multiply both by 2, we get: 5 x 2 / 7 x 2 = 10 / 14 Thus, 10/14 is an equivalent rational number to 5/7. We can choose […]
What is a Perfect Square?
A number is considered a perfect square if it can be expressed as the square of an integer. In simpler terms, if you take a whole number and multiply it by itself, the result is a perfect square. For example, the number 16 is a perfect square because it can be obtained by squaring the […]
If you flip a coin 3 times what is the probability of getting at least 2 heads?
To determine the probability of getting at least 2 heads in 3 flips of a fair coin, we first need to understand the possible outcomes. When flipping a coin, each flip can result in either heads (H) or tails (T). Therefore, when flipping the coin 3 times, the possible outcomes are: HHH HHT HTH HTT […]
What is the distance between (13, 9) and (11, 2) on a coordinate grid?
To find the distance between the points (13, 9) and (11, 2) on a coordinate grid, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by: d = √((x2 – x1)² + (y2 – y1)²) where (x1, y1) and (x2, y2) are the coordinates of the […]
What is the greatest common factor of the terms in the polynomial 4x^4, 32x^3, 60x^2?
The greatest common factor (GCF) of the terms in the polynomial 4×4, 32×3, and 60×2 is 4×2. To find the GCF, we start by determining the coefficients and the variable portions of each term. The coefficients are 4, 32, and 60. The GCF of these numbers is 4, since: 4 can be divided by 4 […]
How to Solve the Inequality 2x + 3 < 2x + 3x + 5?
To solve the inequality 2x + 3 < 2x + 3x + 5, we start by simplifying it. Step 1: Combine like terms on the right side: 2x + 3 < 2x + 3x + 5 This simplifies to: 2x + 3 < 5x + 5 Step 2: Subtract 2x from both sides: 3 < […]