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Math
Algebra
Math Exam Definitions Soleiman
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Terms in this set (54)
Variable
symbol that represents a number
equal sign
Difference between an expression and equation
domain
is a set of numbers that a variable could be
solution
any value of a variable that turns an open sentence into a true statement
no it can have multiple
does an equation only have one solution
integers
the set consisting of the positive integers, negative integers, and zero
whole numbers
set consisting of zero and of all the positive integers
grouping symbols
device such as a pair of parentheses used to enclose an expression that should be simplified first
commutative property
a + b= b + a
associative property
(a + b) + c= a + (b + c)
unique
when there is only one answer
closure property
a + b= unique, real number
property of equality
what you do to one side you must do to the other
reflexive
a=a
symmetric
a=b, b=a
transitive
a=b, b=c, a=c
identity property of addition
a + 0= a
property of opposites
a + -a= 0
property of the opposite of the sum
-(a + b)= -a + -b
definition of subtraction
a - b= a + -b
distributive property
a(b + c)= ab + ac
identity property of multiplication
a x 1= a
identity property of addition
identity property of multiplication is related to what property
multiplicative property of zero
a x 0= a
multiplicative property of -1
a x -1= -a
property of opposites in products
-a x b= -ab
property of reciprocals
a x 1over a = 1
property of the reciprocal of the opposite of a number
one over -a= negative one a
property of the reciprocal of a product
one over ab= one over a times one over b
definition of division
a divided by b= a times one over b
3 consecutive even variables
x, x+2, x+4
3 consecutive odd variables
x, x+2, x+4
3 consecutive variables
x, x+1, x+2
no
can you divide by zero
neither
is division commutative or associative
cost
number of items x price per item
total value
number of items x value per item
income
hours worked x wage per hour
theorem
a statement that is shown to be true using logical reasoning
how many times a number is multiplied
what does an exponent represent
monomial
is a single term or expression thats a number, a variable, or a product of a variable
polynomial
sum of monomials
find the power of each factor and then multiply
to find the power of a product
because the monomials have the same base
why do you add exponents when multiplying monomials
multiply te exponents
when you find a power of a power
transformation
a step in solving an equation
formula
a set equation
distance
rate x time
distributive property and rules of exponenets
when multiplying a monomial by a polynomial what two pieces of information do you use
not enough info and leads to an unrealistic result
two reasons why a problem may not have a solution
binomials
the foil method is limited because it only works for
constant
5 is a
linear term
5x is a
quadratic term
7x to the second is a
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Verified questions
algebra
Geneve is designing a video display for an aircraft instrument panel. One of her design requirements is that it must have full high-definition capability. However, space on the panel is very limited because of the many other critical instruments required for flying, so she would like the video display to be as small as practically possible. She collected data from manufacturers about available video screens currently used for phones and computers. For each screen she recorded the number of light emitting pixels on the screen in millions (y) and the distance measured diagonally across the rectangular screen in inches (x). a. Make a scatterplot of the data. b. A curved relationship is apparent. Before doing any analysis using your calculator or other graphing technology, which type of curve do you think will be a better fit: exponential or quadratic? Why? c. Use your calculator or other graphing technology to determine exponential and quadratic regression equations and add the exponential and a quadratic regression curves to your scatterplot. d. Geneve learns that full HD resolution requires about 2.1 million pixels on the screen. Use your regression equation to determine what would be a reasonable estimate of the screen diagonal in inches required for full HD. e. Explain at least one factor that may be causing this data to not fit your curved model exactly. $$ \begin{matrix} \text{Diagonal (in)} & \text{Pixels (millions)}\\ \text{3.5} & \text{0.6144}\\ \text{3.7} & \text{0.3840}\\ \text{4.3} & \text{0.3840}\\ \text{3.1} & \text{0.1536}\\ \text{6.0} & \text{0.4800}\\ \text{3.3} & \text{0.1306}\\ \text{3.5} & \text{0.1536}\\ \text{17} & \text{2.3040}\\ \text{9.7} & \text{0.7864}\\ \text{4.3} & \text{0.1306}\\ \text{15.4} & \text{1.2960}\\ \text{30} & \text{4.0960}\\ \end{matrix} $$
algebra
The table shows the amount of water remaining in a swimming pool as it is being drained. $$ \begin{matrix} \text{Time (h)} & \text{Amount of Water (L)}\\ \text{0} & \text{18 750}\\ \text{1} & \text{17 280}\\ \text{2} & \text{15 870}\\ \text{3} & \text{14 520}\\ \text{4} & \text{13 230}\\ \text{5} & \text{12 000}\\ \text{6} & \text{10 830}\\ \text{7} & \text{9 720}\\ \text{8} & \text{8 670}\\ \text{9} & \text{7 680}\\ \text{10} & \text{6 750}\\ \end{matrix} $$ a) Determine the average rate of change of the volume of water for consecutive hours. b) Compare the values in part a). When is the rate of change the greatest? the least? c) Create a table of finite differences for the data. Use the finite differences to determine the type of polynomial function that best models this situation. d) Is there a relationship between the finite differences and the average rates of change? Explain. e) Enter the data in a graphing calculator. Use the regression feature to obtain the equation of the curve of best fit for the data. f) Graph the equation in part e). g) How long will it take the pool to fully drain? Justify your answer.
algebra
The half-life of palladium-100 is 4 days. After 20 days a sample has been reduced to a mass of 0.375 g. What is the mass after 3 days?
algebra
Any sinusoid can be modeled by both a sine function and a cosine function. Therefore, you can choose the type of function that is more convenient. Explain which type of function you would choose to model a sinusoid whose y-intercept occurs at the minimum value of the function.
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