Interesting High School Math Quiz

Explanation
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. To find the slope of the given line, we can rearrange the equation into the slope-intercept form y = mx + b, where m is the slope. By isolating y, we get y = (3/2)x - 3. The slope of the given line is 3/2. To find the slope of a line perpendicular to this, we take the negative reciprocal, which is -2/3. Therefore, the slope of a line perpendicular to 3x - 2y = 6 is -2/3, which is approximately -0.6666666666666666.

Explanation
The lines connecting the foci in an ellipse are called the major axis. The major axis is the longest diameter of the ellipse and passes through the two foci. It divides the ellipse into two equal halves, known as the major semiaxes. The major axis is an important characteristic of an ellipse and helps determine its shape and orientation.

Explanation
Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. They do not terminate (end) or repeat (have a recurring pattern) when expressed as decimals. Examples of irrational numbers include the square root of 2 (√2), pi (π), and e.

Explanation
The solution to the given system of equations is (4, 2). This can be found by solving the equations simultaneously. By adding the two equations, we get 2x = 8, which means x = 4. Substituting this value of x into either of the original equations, we can solve for y. Substituting x = 4 into the first equation, we get 4 + y = 6, which means y = 2. Therefore, the solution is (4, 2).

Explanation
The absolute value of a number is the distance of that number from zero on the number line. In this case, the absolute value of x is given as 3. This means that x can be either 3 or -3, as both numbers are 3 units away from zero in opposite directions. Therefore, the correct answer is 3 & -3.

Explanation
When two equations intersect at one point, we call that system consistent. This means that there is a unique solution to the system of equations. If the system was inconsistent, it would mean that the equations do not intersect at any point and there is no solution. Dependent systems have infinitely many solutions and coincident systems refer to equations that are essentially the same.

Explanation
When two graphed equations produce the same line, we call them coincident. This means that the two equations have the same slope and y-intercept, resulting in identical lines on the graph. In other words, the equations represent the exact same relationship between the variables and have an infinite number of solutions in common.

Explanation
The equation y = 3 represents a horizontal line because the value of y remains constant at 3 regardless of the value of x. In a horizontal line, the slope is always zero, indicating that the line does not rise or fall. Therefore, the line y = 3 is a horizontal line that is parallel to the x-axis.

Explanation
The answer to the question "What is tan 18 degrees?" is 0.3249. This value represents the tangent of the angle 18 degrees. The tangent function calculates the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. In this case, when the angle is 18 degrees, the tangent is positive and equal to 0.3249.

Explanation
The values of x that will make the equation x^2 = 16 true are 4 and -4. This is because when we square 4, we get 16, and when we square -4, we also get 16. Therefore, both 4 and -4 satisfy the equation x^2 = 16.

Explanation
To complete the square for the equation x^2 - 8x = 0, we need to add half of the coefficient of x, squared, to both sides of the equation. In this case, the coefficient of x is -8, so half of it is -4. Squaring -4 gives us 16. Therefore, to complete the square, we add 16 to both sides of the equation.

Explanation
The slope-intercept form of an equation is y = mx + b, where m represents the slope and b represents the y-intercept. Therefore, the equation that can be written given a slope and a y-intercept is the slope-intercept form.