FREE BPP Mathematics Questions and Answers
He produced important advances in partition theory, combinatorics, number theory, invariant theory, matrix theory, and invariant theory.
James Joseph Sylvester was an English mathematician who made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He was also a cofounder of invariant theory, along with Arthur Cayley, and a pioneer of algebraic invariant theory. He coined many mathematical terms, such as graph, discriminant, matrix, and syzygy. He was a professor at several universities in England and the United States, and he founded the American Journal of Mathematics. He received many honors and awards for his work, such as the Royal Medal, the Copley Medal, and the De Morgan Medal
Factors of AC that add up to get B
To factor a quadratic equation of the form ax^2 + bx + c = 0, you need to find two factors of ac that add up to b. For example, if you have x^2 + 5x + 6 = 0, then ac = 6 and b = 5. You need to find two numbers that multiply to 6 and add to 5. These are 2 and 3, because 2 × 3 = 6 and 2 + 3 = 5. Then you can write the equation as (x + 2)(x + 3) = 0.
Bring the constant back over after finishing the square, and don't forget to add the slope before the parenthesis.
To the right side of the equation, move all Constants. To both sides of the equation, add ((B/2)2). Calculate the square roots of the left side factor.
Completing the square is a method for solving quadratic equations by transforming them into the form of (x+d)^2 + e = 0, where x is the variable, d and e are constants, and then taking the square root of both sides. The steps you described are the general procedure for completing the square.
Y=mx*b
Y = mx + b is the slope-intercept form of a linear equation, where y and x are the variables, m is the slope, and b is the y-intercept. This form is useful for graphing a line, finding the slope and y-intercept of a line, or writing the equation of a line given the slope and y-intercept or two points on the line.
Negative Reciprocal of the slope
Take the Absolute Value by itself, Make two issues and consequently two solutions by changing everything to the right to plus or minus.
(y-y1)=m(x-x1)
(y-y1) = m(x-x1) is the point-slope form of a linear equation, where y and x are the variables, m is the slope, and (x1, y1) is a point on the line. This form is useful for finding the equation of a line given the slope and a point on the line, or finding the slope and a point on the line given the equation of a line.
Increase in Y above decrease in X
Change in y over change in x is the formula for slope. Slope is a measure of how steep a line is. It is calculated by dividing the difference in the y-coordinates of two points on the line by the difference in the x-coordinates of those same points. For example, if we have two points (x1, y1) and (x2, y2) on a line, the slope of the line is given by:
Slope = (y2 - y1) / (x2 - x1)
The slope can be positive, negative, zero, or undefined, depending on the direction and shape of the line. A positive slope means that the line is rising from left to right, a negative slope means that the line is falling from left to right, a zero slope means that the line is horizontal, and an undefined slope means that the line is vertical.
Square root Both sides
Taking square roots is a method for solving equations that involve a variable raised to the power of two, such as x^2 = 9. To take the square root of both sides of an equation, you need to apply the square root function to both sides and simplify the result.