Mathematics 3 Flashcards
what is the formula for the axis of symmetry of a parabola?
x = -b/2a
What is step one of solving a quadratic equation by completing the square?
express as x squared + px = q
What is step two of solving a quadratic equation by completing the square?
Add the square of half the coefficient of x to both sides
What is step three of solving a quadratic equation by completing the square?
Replace the perfect trinomial square by its binomial squared
What is step four of solving a quadratic equation by completing the square?
Take the square root of both sides
Don’t forget square roots can usually be positive or negative
What is the quadratic formula?
x = -b +- sqroot of b2 - 4ac all over 2a
Every quadratic equation has two roots.
If the product of two factors is zero, then one or the other factors or both must equal zero.
What is a reciprocal of a number?
1 divided by the number
Rule 1 of Reciprocals
The fractions a/b and b/a are reciprocals of each other, that is, the reciprocal of a fraction is the fraction inverted
Rule 2 of Reciprocals
The product of two reciprocals is 1
Rule 3 of reciprocals
To divide by a number or a fraction, multiply by it’s reciprocal
Rule 4 of Reciprocals
To solve an equation for an unknown having a fractional coefficient, multiply both members by the reciprocal fraction.
Thus if 2/3x = 10 multiply both sides by 3/2. x = 30/2 x = 15
If a fraction means division, what does 3/4 mean?
3 divided by 4
The numerator is the dividend and the denominator is the divisor.
If x and y vary inversely as each other, and a value of either x or y is multiplied by a number, then the corresponding value of the other is ________ by the same number.
Divided
If the length of a rectangle is doubled and the width is halved, its area _______.
Remains constant
What is the formula for an inverse variation with a constant?
xy = k
What follows from xy = k?
X and y vary inversely as each other
x and y are inversely proportional to each other, that is x2/x1 = y1/y2
what follows from y = kx
x and y var directly as each other
x and y are directly proportional to each other, that is x2/x1 = y2/y1
A variable in algebra is a letter which may represent
any number of a set of numbers under discussion when the set contains more than one number
In algebra, a constant is any letter or number which
has a fixed value that does not change under discussion. The letter k is used to represent a constant while the letters x, y, and z represent variables.
What is an adjacent angle?
Angles sharing the same vertex and a common side between them
What are complementary angles
Two angles the sum of whose measures equals 90 degrees
supplementary angles
two angles the sum of whose measure equals 180 or a straight angle
What is a proportion?
An equality of two ratios
2:5 = 4:10 or 2/5 = 4/10
The fourth term of a proportion is the ____________
fourth proportional to the other three taken in order
The means of a proportion are its
middle terms, that is, its second and third terms
The extremes of a proportion are its ____________.
outside terms, that is, its first and fourth terms
If a:b = c:d, what follows?
ad = bc
In any proportion, the ________ are equal
cross products
In any proportion, the product of the __________ the product of the extremes.
means equals
