How many pairs of parallel sides does a rectangle have?
A rectangle has two pairs of parallel sides. This is because in a rectangle, opposite sides are equal in length and are parallel to each other. For instance, if you look at a rectangle, you’ll find that the top side is parallel to the bottom side, and the left side is parallel to the right […]
What is the quotient of 18 and 1000?
The quotient of 18 and 1000 is calculated by dividing 18 by 1000. To perform this division, we set it up as follows: 18 ÷ 1000 = 0.018 When you divide a smaller number by a larger number, the result will be a decimal less than 1. In this case, since 18 is much smaller […]
What is the number part when a number and a variable are multiplied together in a term?
In mathematics, when a number is multiplied by a variable in a term, the number part is known as the coefficient. For example, in the expression 5x, the number 5 is the coefficient of the variable x. The coefficient indicates how many times the variable is being multiplied. So, if we have 3y, it means […]
How many days are in a leap year?
A leap year has 366 days. This extra day is added to February, making it 29 days long instead of the usual 28. A leap year occurs every four years to help synchronize the calendar year with the solar year, which is about 365.24 days long. By adding an extra day every four years, we […]
How to Factorize the Equation x³ + 3x² + 9x + 5?
To factor the polynomial equation x³ + 3x² + 9x + 5, we can first try to find rational roots using the Rational Root Theorem. The possible rational roots can be the factors of the constant term (5) divided by the factors of the leading coefficient (1). The possible rational roots are ±1, ±5. We […]
Which of the following represents the general term for the sequence 2, 4, 6, 8, 10?
The general term for the sequence 2, 4, 6, 8, 10 can be represented as: a(n) = 2n This means that for any positive integer n, if you multiply n by 2, you will get the nth term in the sequence. For instance: For n = 1, a(1) = 2 × 1 = 2 For […]
What is the area of triangle ABC?
The area of triangle ABC can be calculated using the formula: Area = (1/2) × base × height In this formula, the ‘base’ is the length of one side of the triangle, and the ‘height’ is the perpendicular distance from that base to the opposite vertex. To find the area, you simply need to know […]
For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7?
To solve for x in the equation xy = k when we know the values of y and k, we can rearrange the equation to isolate x. We start with the equation: xy = k Substituting the known values (y = 4 and k = 7) into the equation, we get: x(4) = 7 To […]
How to Integrate a Constant Expression 3 dx
To integrate the constant expression 3 with respect to x, we will apply the basic rule of integration for constant functions. The integral of a constant a with respect to x is given by the formula: ∫ a dx = ax + C Here, C represents the constant of integration. In our case, we are […]
Choose the correct simplification of the expression 3×4
The expression 3×4 simplifies to 12. To break it down further, you take the coefficient 3 and multiply it by 4. When you do the multiplication: 3 times 4 equals 12. Thus, the correct simplification of the expression is 12.