Math Algebra Final Exam
solve by substitution: x-5y=17 2x-7y=22
(-3,-4)
Solve by elimination: 2y+x=9 3x-2y=7
(4,5/2)
Power property
(x(to the power of a))To the power of b=x (to the power of ab) To raise a power to a power, multiply the exponents (Sorry I know thats a confusing way to put it idk how to put exponents on quizlet :( Just look on pg 328 in the chart in the text book for it)
Tailwind
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downstream
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Headwind
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Upstream
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Simplify: 4abc(-3a(to the power of 3)bc)
-12a(to the power of 4)c(to the power of 2)
Remember! Anything to the power of 0 is always...
1
Steps for solving a system of inequalities
1. Graph all inequalities on the same set of axes 2. Find the solution set where the shaded regions intersect 3. Check
What are the steps for solving a system by substitution?
1. Solve either equation for either variable, its best to choose the easiest variable to solve 2. Substitute that value into the other equation 3. Solve for the remaining variable 4. Take the value of that variable and substitute it into one of the equations to solve for the 2nd variable 5. you must write the solution as an ordered pair 6. Check the solution in each equation
Steps for solving a system by elimination
1. multiply both sides of one or both equations so that the coefficients of one of the variables have the same absolute value 2. Add or subtract the equations to eliminate a variable 3. solve the resulting equation 4. find the value of the eliminated variable by a. substituting the result into an original equation and solving or b. eliminating the other variable (Write solution as an ordered pair and check!!)
Express in scientific notation: 390,000,000
3.9x10(to the power of 8)
What is the slope of (5,7) (1,-3)
5/2
what is the standard form of a linear equation?
Ax+By=C
Third?
Choose a test point that is not on the line and substitue it into the inequality (If it is true, shade the side containing the test point if not shade the other side)
FOIL is...
First Outside Inside Last
How do you write polynomials in standard form?
First simplify if needed, the put terms in proper order Descending order based on the degree of the "x" (If there is no x then choose variable thats first in alphabetical order)
Second?
Graph the corresponding linear equation
What type of line is 0?
Horizontal
When is the line solid?
If it is greater than or equal to or less than or equal to
When is the line dashed?
If it is greater than or less than
Perpendicular lines?
Meets at a right angle
What is the name of a polynomial with 1 term? 2? 3?
Monomial Binomial Trinomial (anything above is just a polynomial)
What are the two properties of exponents?
Product property Power property
What is the first step of graphing an inequality?
Solve for y and identify the slope and y-int of the corresponding equality
What are parallel lines?
The lines in the same plane that have no points in common
What is the x-intercept?
The point where the graph intercepts the x-axis
What is the y-intercept?
The point where the graph intersects the y-axis
Dividing polynomials
To divide a polynomial by a monomial you divide each term by the monomial
What type of line is undefined?
Vertical
What is a polynomial?
an expression with terms connected with addition or subtraction symbols *cannot have a variable in the denominator or a negative exponent*
Multiply (c-3)(c+8)
c(squared) +5c-24
In scientific notation, the first number must be...
greater than or equal to than 1 but less than 10 (Put it into decimal form between the first and second digits)
What is the slope formula?
m= rise/run= y2-y1/x2-x1
Perpendicular lines have slopes that are...
negative reciprocals of each other
If the line is going up to the right it is...
positive
Add or subtract the wind or current in the...
rate
Motion Problems (Personally my worst) but remember this basic formula:
rt=d
When adding or subtracting polynomials...
simplify and write in standard form then combine like terms
Parallel lines have the same...
slope
How do u change a linear equation to slop intercept form?
solve the linear equation for y then arrange the terms on the right side with variable term first
To find equation of a line with the slope and y-int known,...
subsitute the values into slope-intercept form equation
What is slope?
the ratio of the rise (vertical change) to the corresponding run (horizontel change) slope=m
What is the degree of a term?
the sum of the exponents of its variables
What is the slope of (-1,7) (-1,2)
undefined
Quotient Property of Exponents
x(to the power of a)/x(to the power of b)=x(to the power of a-b) for x is not equal to 0 To divide with like bases, subtract the exponents (pg. 333)
Product property
x(to the power of a)multiply x(to the power of b)= x(to the power of a plus b) To multiply powers with like bases add the exponents
what is the x and y intercept of x-3y=-3
x=-3 y=1
What is the point-slope form?
y-y1=m(x-x1)
Use the point slope form to write the slope intercept form of the line parellel to the given line and passing through the given point: 4x+y=9 (-2,5)
y=-4x-3
Change this linear equation into a slope-intercept equation: 8x-3y=9
y=8/3x-3
Write the equation of the line passing thro the given point with the given slope : (-3,2) m=8
y=8x+26
What is the slope intercept form of a linear equation?
y=mx+b
