Solve the following equation: 6y – 20 = 2y + 4
To solve the equation 6y – 20 = 2y + 4, we first want to get all the terms involving y on one side of the equation and the constant terms on the other side. 1. Start by subtracting 2y from both sides: 6y – 20 – 2y = 2y + 4 – 2y This […]
What values of x make the equation x² – 18x + 81 = 0 true?
To solve the equation x² – 18x + 81 = 0, we can factor the quadratic. First, we need to identify two numbers that multiply to 81 (the constant term) and add up to -18 (the coefficient of x). In this case, the numbers -9 and -9 satisfy these conditions, since: -9 × -9 = […]
What is 80 percent as a fraction?
To convert 80 percent into a fraction, start by remembering that percent means ‘per hundred.’ Therefore, 80 percent can be written as: 80% = 80/100 Next, we simplify the fraction. Both the numerator (80) and the denominator (100) can be divided by their greatest common divisor, which is 20: 80 ÷ 20 = 4 100 […]
Does a runner taking part in the 200m dash need to run around the end of a track?
No, a runner taking part in the 200m dash does not need to run around the end of a track in the traditional sense. In most outdoor tracks, the standard 200m race is run on a circular track, which typically means that the runners will start on a straight section and turn to complete the […]
Find the vertex of the parabola whose equation is y = 2x² + 8x + 5
To find the vertex of the parabola represented by the equation y = 2x² + 8x + 5, we first note that this is a quadratic equation in the standard form y = ax² + bx + c, where: a = 2 b = 8 c = 5 The vertex of a parabola in this […]
The sum of three consecutive even integers is 30, what are the integers?
To find three consecutive even integers that sum up to 30, we can start by defining the integers. Let’s represent the first even integer as x. The next two consecutive even integers can then be expressed as x + 2 and x + 4. Now, we can set up an equation based on the information […]
What is the slope of the line represented by the equation y = x + 7?
The slope of the line represented by the equation y = x + 7 is 1. This can be explained by looking at the standard form of a linear equation, which is generally written as y = mx + b, where m represents the slope and b is the y-intercept. In the equation y = […]
Which of the following is a solution of x² + 2x + 2?
To find the solutions of the quadratic equation x² + 2x + 2 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In this case, the coefficients are: a = 1, b = 2, and c = 2. First, we calculate the discriminant […]
What is 125×9 64y12 written as a sum of cubes?
To express the expression 125×9 + 64y12 as a sum of cubes, we can utilize the formula for a sum of cubes, which is given by: a3 + b3 = (a + b)(a2 – ab + b2) In our case, we can identify the components: a = 5×3 (since (5×3)3 = 125×9) b = 4y4 […]
What is 1/2 of 1 3/4?
To find 1/2 of 1 3/4, we first need to convert the mixed number into an improper fraction. 1 3/4 is the same as 1 + 3/4, which can be converted as follows: 1 = 4/4, so 1 3/4 = 4/4 + 3/4 = 7/4. Now, we need to find 1/2 of 7/4. To do […]