Find the slope of the line whose equation is 5y = x + 3
To find the slope of the line given by the equation 5y = x + 3, we first need to rewrite it in the slope-intercept form, which is y = mx + b. Here, m represents the slope. Starting with the given equation: 5y = x + 3 Next, we divide both sides of the […]
Find 3 Irrational Numbers Between √2 and √3
To find three irrational numbers between the square roots of 2 and 3, we first need to establish the numerical values of these square roots. √2 is approximately 1.414 and √3 is approximately 1.732. Now, we can look for irrational numbers in this interval. One simple method is to take averages or combinations of these […]
How to Solve the Equation 8 + 2x + 8x = 14
To solve the equation 8 + 2x + 8x = 14, we first combine like terms on the left-hand side. 1. Combine the terms with x: 2x + 8x = 10x. Now the equation looks like this: 8 + 10x = 14. 2. Next, we need to isolate the x term. Start by subtracting 8 […]
What is a positive angle less than 2π that is coterminal with the angle 11π over 3?
To find a positive angle less than 2π that is coterminal with 11π/3, we first need to understand what coterminal angles are. Coterminal angles are angles that differ by a multiple of 2π. This means that if we add or subtract 2π (or its multiples) from a given angle, we will result in an angle […]
Which of the following is a trinomial: c² + c + 6, c² + 16, 8c + c³ + 4c² + 12c + 7?
To determine which of the given expressions is a trinomial, we first need to understand what a trinomial is. A trinomial is a polynomial that has exactly three terms. Let’s examine each option: c² + c + 6: This expression has three terms: c², c, and 6. Therefore, it is a trinomial. c² + 16: […]
Which of the following shows the factors of 9x² – 3x – 2?
To factor the quadratic expression 9x² – 3x – 2, we first look for two numbers that multiply to the product of the leading coefficient (9) and the constant term (-2), which is -18, and also add up to the middle coefficient (-3). The numbers that satisfy these conditions are -6 and 3, since (-6) […]
What is a factor of 144 and 49x²?
To understand the factors of both 144 and 49x², we’ll first look at each part separately. Starting with 144, we can find its factors by looking for numbers that divide evenly into it. The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. Each […]
How many terms are in the expression shown 2n + 5 + 3p + 4n?
To determine how many terms are in the expression 2n + 5 + 3p + 4n, we first need to identify what a term is in an algebraic expression. A term is typically a single mathematical expression that can be a number, a variable, or a combination of both, multiplied together. In this case, we […]
In a trapezium ABCD where AB || CD, if angle ADC is twice angle ABC, AD = a cm, and CD = b cm, then what is the length of AB?
To find the length of AB in the trapezium ABCD, we can use the properties of trapeziums and the relationships between their angles. Given that AB is parallel to CD and that angle ADC is twice angle ABC, we can denote angle ABC as θ. Therefore, angle ADC would be 2θ. By using the properties […]
What is the measure of angle ABD on trapezoid ABCD?
To find the measure of angle ABD in trapezoid ABCD, we first need to understand the properties of trapezoids. A trapezoid has one pair of parallel sides. In this case, let’s assume that side AB is parallel to side CD. In trapezoid ABCD, angles ABD and ABC are consecutive angles on the same side of […]