What is the solution set to the inequality 5x + 2x – 4 < 0?
To solve the inequality 5x + 2x – 4 < 0, we first combine like terms. This simplifies to 7x – 4 < 0. Next, we can isolate x by adding 4 to both sides: 7x < 4. Now, divide both sides by 7: x < rac{4}{7}. This tells us that the solution set contains […]
Which number line represents the solution set for the inequality 4x < 3 - 2x?
To solve the inequality 4x < 3 – 2x, we first need to isolate the variable on one side. We can start by adding 2x to both sides: 4x + 2x < 3 This simplifies to: 6x < 3 Next, we will divide both sides by 6: x < rac{3}{6} Which reduces to: x < […]
Find the equation of the plane whose x intercept, y intercept, and z intercept are 2, 3, and 1 respectively.
To find the equation of a plane given its intercepts on the x, y, and z axes, we can use the intercept form of the equation of a plane. The general form is: 1/x + 1/y + 1/z = 1 Where: x-intercept = 2 y-intercept = 3 z-intercept = 1 Substituting the intercept values into […]
If x is a number that is 7 more than y how do you express x as a function of y?
To express x as a function of y, we start by understanding the relationship described. The statement ‘x is a number that is 7 more than y’ can be translated into a mathematical equation. We can write this relationship as: x = y + 7 Here, we take the value of y and add 7 […]
Read the numbers and decide what the next number should be: 8, 6, 9, 5, 10, 4, 11
The pattern in this sequence alternates between two distinct sequences. The first sequence consists of numbers that are increasing: 8, 9, 10, 11. The second sequence consists of numbers that are decreasing: 6, 5, 4. To find the next number, we can continue both sequences. Continuing the increasing sequence, after 11, the next number is […]
What’s the equation of a line that passes through points (0, 1) and (2, 3)?
To find the equation of a line that passes through the points (0, 1) and (2, 3), we’ll first determine the slope (m) of the line using the formula: m = (y2 – y1) / (x2 – x1) Here, we can take (x1, y1) as (0, 1) and (x2, y2) as (2, 3). Plugging these […]
What is the solution for n n 1 4n 8?
To approach the expression n n 1 4n 8, we first need to interpret its structure. It seems to be a combination of variables and numbers, but without clear operators or context, it’s a bit ambiguous. If we assume n represents a variable and following that assumption, we might translate this to an equation to […]
What are the solutions to the quadratic equation 4x² + 22x + 36?
To find the solutions to the quadratic equation 4x² + 22x + 36 = 0, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In our equation, the coefficients are: a = 4 b = 22 c = 36 First, we need to calculate the discriminant, which is b² […]
In the formula for yearly compounding, what does n represent?
In the formula for yearly compounding, the variable n represents the number of times that interest is compounded in a year. Typically, for yearly compounding, n is equal to 1 since the interest is calculated and added to the principal balance once every year. To explain further, the compounding formula is generally written as: A […]
What is the sum total of the interior angles of any quadrilateral?
The sum total of the interior angles of any quadrilateral is 360 degrees. This can be understood by using the fact that any quadrilateral can be divided into two triangles. Since the sum of the interior angles of a triangle is always 180 degrees, two triangles would have a combined sum of: 180 degrees + […]