Properties of Real Numbers
This property says if ab=0 then either a=0 , b=0 , or both a=b=0
What is the zero property of real numbers?
What is "identify the variable"?
The factorization of this is (A+B)(A-B).
What is the difference of squares?
The mathematical symbol translation of "x is at least 5".
What is x\geq 5?
In a variation equation, we may change y\propx to y=kx because k is called this.
What is the constant of proportionality?
This property says that if x=5 and x+2=7 , then you may also say 5+2=7 and not change the validity of the statement.
What is the substitution property of real numbers?
Simple interest formulas require the percentage is converted to this form when doing calculations.
What is "decimal form"?
Simplify
(x^2-1)/(x^2+x-2)
What is (x+1)/(x+2) ?
This inequality 3 \le x \leq 10 can be written as two inequalities which is this. Make sure you use the correct conjunction.
What are 3 \le x and x \le 10?
A variation equation appearing as y=kx^n .
What is direct variation?
This property allows us to conclude that there are an infinity number of values between any two real numbers.
What is the density property of real numbers?
This concept from geometry and triangles is often used to find the height of an object without trigonometry or Pythagorean's Theorem.
What are similar triangles?
True or False: (a+b)^2=a^2+b^2 .
What is False?
It is correct to rewrite " x \le 4 or x \ge 10 " as 10 \le x \le 4 .
What is "No"?
A variation equation of this type has one value increase while the other value decreases.
What is inverse variation?
According to the identity property of real numbers, one (1) is also called this.
What is the multiplicative identity?
A rental truck company charges $65 a day and 40 cents a mile for the rental of one of their trucks. A truck was rented for 3 days and the total rented charge was $283. How many miles was the truck driven?
What is 220 miles?
True or False: The following is correct:
2/(1+1) = 2/1 + 2/1=2+2=4
What is False?
The solution in interval notation for
1/6 < (2x-13)/12 \le 2/3
What is (\frac{15}{2}, \frac{21}{2}] ?
The translation to "if y varies directly with x and inversely with z".
What is y=kx/z ?
According to the additive inverse property, any real number added to this gives the additive identity.
What is "its opposite value"?
Two friends work together to wash a car. If one takes 25 minutes to wash the car and the other takes 35 minutes to wash the car, how long does it take the two friends when they work together? Given the answer in minutes and seconds.
What is 14 minutes and 35 seconds?
This is the domain of 1/sqrt(x-1) .
What is (1,\infty)?
The solution in interval notation for
7|x+2|+5>4
What is (-infty, infty)?
The cost of printing a magazine is jointly proportional to the number of pages in the magazine and the number of magazines printed. Find the printing cost for 5000 copies of a 92-page article, if it costs $60,000 for 4000 copies of a 120-page magazine.