How do you solve the equation x + 4x + 4 = 9?
To solve the equation x + 4x + 4 = 9, we first combine like terms on the left side. The terms x and 4x can be added together: x + 4x becomes 5x. So the equation now looks like this: 5x + 4 = 9 Next, we want to isolate x. To do this, […]
One Quintal is Equal to How Many Kgs?
One quintal is equal to 100 kilograms (kgs). The term ‘quintal’ is used primarily in countries that follow the metric system, and it represents a mass measurement. The conversion is relatively straightforward: since a quintal is defined as 100 kilograms, whenever you need to convert quintals to kilograms, you simply multiply the number of quintals […]
What is the value of h h 15 h 9 h 10 h 135?
The expression ‘h h 15 h 9 h 10 h 135’ appears to be a sequence of variables and numbers rather than a standard mathematical expression. To interpret it, we need to clarify the notation. If we assume ‘h’ represents a variable and the numbers are constants, we might consider this as a concatenation of […]
In order to apply the law of cosines to find the length of the side of a triangle, it is enough to know which of the following?
To apply the law of cosines effectively, you need to know either: Two sides and the included angle (often referred to as the SSA case). All three sides of the triangle (the SSS case). Let’s break this down: The law of cosines states that for any triangle with sides a, b, and c, and the […]
The table represents a linear function. What is the slope of the function?
The slope of a linear function represents the rate of change of the function. To find the slope from a table of values, you can use the formula: Slope (m) = (y2 – y1) / (x2 – x1) Choose two points from the table, where each point is represented as (x1, y1) and (x2, y2). […]
What number must be added in the expression x² + 8x to make a perfect square trinomial?
To determine what number must be added to the expression x² + 8x to make it a perfect square trinomial, we can utilize the method of completing the square. A perfect square trinomial takes the form (x + a)² = x² + 2ax + a². In our case, we can compare the given expression with […]
When 2 lines cross, 2 pairs of vertical angles are formed. What is the sum of all 4 angles: 180° 270° 360° or 540°?
When two lines intersect, they create four angles. These angles can be divided into two pairs of vertical angles. Vertical angles are opposite each other and are always equal in measure. Let’s denote the four angles created by the intersection of the two lines as angle A, angle B, angle C, and angle D. Since […]
What is the value of the smaller number if the difference between two numbers is 25 and the smaller number is 1/6th of the larger number?
Let’s denote the larger number as x and the smaller number as y. According to the problem, we have two pieces of information: The difference between the two numbers: x – y = 25 The smaller number is 1/6th of the larger number: y = rac{1}{6}x We can substitute the second equation into the first […]
Find all solutions to the equation in the interval 0 < x < 2π: cos x sin 2x = 0
To find all solutions to the equation cos x sin 2x = 0 in the interval 0 < x < 2π, we can set each part of the product to zero and solve for x. 1. The first part of the equation is cos x = 0. The cosine function is zero at: x = […]
What is the Distributive Property?
The distributive property is a fundamental principle in mathematics that explains how to multiply a number by a sum or difference of numbers. It states that you can distribute the multiplication over addition or subtraction. For example, if you have an expression like a(b + c), you can apply the distributive property to rewrite it […]