Unit 1
Write expressions: Two times the difference between a number and nine
2(n-9)
Find the domain
y=log3x
xy=log3x is x>0x>0.
Finding Slope from a Table:Given the following table of values for xx and yy, find the slope of the line connecting the points:
x| 1,4
y|3,7
The slope mm can be calculated using the formula m=change in ychange in xm=change in xchange in y. So, m=7−34−1=43m=4−17−3=34.
Writing Systems from a Situation: A bakery sells cookies for $2 each and brownies for $3 each. If a customer buys a total of 10 items and spends $25, how can you write a system of equations to represent this situation?
Let xx represent the number of cookies purchased and yy represent the number of brownies purchased. The system of equations is:
x+y=10
2x+3y=25
Exponent Rules: What is the product rule for exponents, and how does it apply when multiplying exponential expressions?
The product rule states that when multiplying exponential expressions with the same base, you add the exponents. For example, am×an=am+nam×an=am+n.
Write an inequalities:1 need 25 minutes or more to get ready .
X≥25
identifying function
x |4,4,5
y | 7,8,9
Yes
X & Y Intercepts: How do you find the x-intercept and y-intercept of a linear equation?
To find the x-intercept, set y=0y=0 and solve for xx. To find the y-intercept, set x=0x=0 and solve for yy.
Solving Systems by Substitution: What is the substitution method for solving systems of equations, and when is it most useful?
The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. It is most useful when one of the equations can be easily solved for one variable.
Rational Exponents & Radical Expressions: How do you convert a radical expression to an equivalent expression with rational exponents?
To convert a radical expression to an equivalent expression with rational exponents, use the property.
Solving equations : 3x +6= 11
X=1.6
Evaluating functions
f(X)=2x^2-3x+1
f(2)=
F(2)=3
Parallel Lines & their SlopeHow do you determine if two lines are parallel, and what relationship do their slopes have?
Two lines are parallel if they have the same slope. This means that the rate of change of both lines is equal, and they will never intersect.
Solving Systems by Elimination: Describe the elimination method for solving systems of equations, and explain when it is preferable over other methods.
The elimination method involves adding or subtracting equations in a system to eliminate one of the variables. It is preferable when the coefficients of one variable in the equations are multiples or opposites of each other.
Adding & Subtracting Polynomial: What is the process for adding and subtracting polynomials?
To add or subtract polynomials, combine like terms by adding or subtracting the coefficients of terms with the same variables and exponents.
Solving inequalities: -2x+7>-11
X<9
Arithmetic sequences
2,8,14,20,26,…
d=
D=6
Perpendicular Lines & their Slopes: What is the relationship between the slopes of perpendicular lines, and how can you determine if two lines are perpendicular?
The slopes of perpendicular lines are negative reciprocals of each other. If the product of the slopes of two lines is -1, then the lines are perpendicular.
Systems of Inequalities: What are systems of inequalities, and how do you graphically represent their solutions?
Systems of inequalities involve multiple inequalities with the same variables. Their solutions represent the regions in the coordinate plane where the shaded areas of each inequality overlap. Graphically, these solutions are represented by shaded regions that satisfy all inequalities simultaneously.
Multiplying Binomials: What method can you use to multiply two binomials together?
One method to multiply binomials is using the distributive property, also known as FOIL (First, Outer, Inner, Last), where you multiply each term of the first binomial by each term of the second binomial.
Literal equations :4x+8=x-1
X=-3
Geometric sequence
1,3,9,27
d=
D=3
Graphing Inequalities in Two Variables: How do you graph inequalities in two variables on a coordinate plane?
To graph an inequality in two variables, first graph the corresponding equation. Then, depending on the inequality symbol (>, <, ≥, ≤), shade the region above or below the line (for inequalities involving y) or to the right or left of the line (for inequalities involving x).
Solving Systems by Graphing: How do you solve a system of equations by graphing, and what does the solution represent?
To solve a system of equations by graphing, graph each equation on the same coordinate plane and identify the point(s) where the graphs intersect. The solution represents the point(s) of intersection, where the values of xx and yy satisfy both equations simultaneously.
Multiplying Polynomials: How do you multiply two polynomials together?
To multiply two polynomials, use the distributive property to multiply each term of one polynomial by each term of the other polynomial, then combine like terms. This process is often simplified by using the distributive property repeatedly.