Which function in vertex form is equivalent to f(x) = x² – 6x + 3?
To convert the quadratic function from standard form to vertex form, we can complete the square. The function given is: f(x) = x² – 6x + 3 First, we focus on the x² and -6x terms. To complete the square, we take the coefficient of x (which is -6), divide it by 2 (giving us […]
Which expression is equivalent to 4 6i²?
The expression 4 6i² can be simplified using the property of imaginary numbers. Specifically, we know that i² = -1. So, let’s break it down: First, we can rewrite the expression as 4 + 6i². Now, substituting i² with -1 gives us: 4 + 6(-1). This simplifies to: 4 – 6. Finally, performing the arithmetic […]
How do you find the height of a triangle with an area of 30 square units and a base of 12 units?
To find the height of a triangle when the area and the base are known, we can use the formula for the area of a triangle: Area = (Base x Height) / 2 In this case, we know the area is 30 square units and the base is 12 units. We can rearrange the formula […]
How to Solve for x in the Equation 2x² = 128?
To solve the equation 2x² = 128, we first need to isolate x. Here’s how we can do it step by step: Start with the original equation: 2x² = 128 Next, divide both sides of the equation by 2 to simplify it: x² = 64 Now, we need to find x by taking the square […]
What is 64×6 27 written as a sum of cubes 4x 3 33 4×2 3 33 4×2 3 93 4×3 3 33?
To express the product of 64 and 6, which is 384, using sums of cubes, we need to break it down into its component cubes. The expression you’re referencing seems a bit jumbled, but we can clarify it step by step. First, we recognize that 64 can be expressed as 4^3 (since 4 x 4 […]
What is the percent increase of the price of a hair piece that was increased from 500 to 550?
To calculate the percent increase of the price, you can use the formula: Percent Increase = [(New Value – Old Value) / Old Value] x 100 In this case, the old value is 500 and the new value is 550. Plugging the numbers into the formula: Percent Increase = [(550 – 500) / 500] x […]
If you flip a fair coin 10 times what is the probability of getting at least one tail?
To find the probability of getting at least one tail when flipping a fair coin 10 times, it can be easier to first calculate the probability of the opposite event—getting no tails at all (which means getting all heads)—and then subtract that from 1. 1. The probability of getting heads in a single flip of […]
A Number Divisible by 8: What Other Numbers Will It Be Divisible By?
When a number is divisible by 8, it means that when you divide that number by 8, there is no remainder. However, this also tells us about other numbers that the number will be divisible by. The key concept here is that 8 can be factored into smaller divisors. The prime factorization of 8 is […]
How do you solve the equation 62x + 42 = 2x + 4?
To solve the equation 62x + 42 = 2x + 4, we will first aim to isolate the variable x. 1. Start by getting all terms with x on one side of the equation and constant terms on the other side. To do this, subtract 2x from both sides: 62x – 2x + 42 = […]
In the rectangular coordinate system, the vertical number line is called the
In the rectangular coordinate system, the vertical number line is called the y-axis. This axis runs up and down on a graph and is perpendicular to the horizontal number line, known as the x-axis. The origin point, where the two axes intersect, is designated as (0,0). The y-axis allows us to represent values on a […]