Systems of Equations by substitution, elimination, or graphing
Which of the following is NOT a method for solving Systems of Equations?
A. graphing B. Substitution C. Elimination D. Using Protractors
What is D.
Solve for s in the literal equation P = 4s
What is P/4 = s
1. You can isolate the variable s on both sides.
P = 4s
2. Divide both sides by 4.
P/4 = 4s/4
3. Simply. Done!
P/4 = s
Exponential growth and decay graphs look like opposites an can sometimes be mirror images. True or false.
What is True
two functions can be "reverse images" of each other in the sense that the values for the functions are reciprocals
When solving multi-step inequality as with solving equations, we must use: _____ of _____
What is Order of Operations
What is the slope-intercept formula.
What is y=mx+b
Fill in the blank: A systems of Equations is a group of _____ equations that contain the same set of variables.
What is 2 or more
Solve this literal equation m=x-y/3
What is 3m+y=x
1. Start by multiplying both sides by 3.
3(m=x-y/3)3
2. simplify to get rid of the denominator.
3m=x-y
3. Add both sides by y.
3m+y=x-y+y
4. Simplify.
3m+y=x
What is the general form of an exponential function?
What is y=a(b)^x
A=initial value B=growth factor
The inequality symbol in a multi-step equation should be reversed if: you reverse the sides of the equation or ___________
What is you multiply or divided both sides by a negative number
What's the first rule of Order of Operations with Exponents?
A. Simplify all operations inside the parentheses
B. Do all multiplications and divisions, working from left to right
C. Do all additions and subtractions, working from left to right.
What is A
Fill in the blank: ______ equations yield straight lines and only contain only variables, coefficients and constants
What is linear.
Solve for L in this two step literal equation P=2L+2W
What is L=P-2W/2
1. Flip the equation to isolate the variable on the left side.
2L+2W=P
2. Subtract both side by 2W
2L+2W-2W=P-2W
3. Simplify.
2L=P-2W
4. Divide both sides by 2.
2L/2=P-2W/2
5. Simply.
L=P-2W/2
If a bank account starts with $100, has an annual rate of 4%, and the money is left in the account for 12 years, What's the balance?
What is $160.12
P(t)=100(1+.04)^12
P(t)=$160.12
Solve the inequality 6x-5>10
What is x<5/2
6x-5>10 Add 5 to both sides: 6
x-5+5<10+5 Simplify:6
x<15 Divide both sides by 6
6x/6<15/6
Alex is buying shoes and wants to spend $200 or less on his purchase. The shoes he likes best cost $50. How many pairs of shoes can he purchase?
What is x>=4
Let x equal the number of pairs.
(number of pairs)(prices of pairs)>=200 or 50x>=200
Solve using Elimination
2x-3y=-2
4x+y=24
what is x=5, y=4
2x-3y=-2
4x+y=24
1. multiply the first row by 2
4x-6y=-4
4x+y=24
2. Subtract the second row by the first row, then solve for y.
-7y=-28, y=4
3. Substitute y=4 into any of the two equations above. (4x-6y=-4)
4x-6(4)=-4
4. solve for x.
x=5
Solve for C in the literal equation F=9C/5+32
What is 5(F-32)/9=C
1. Start by subtract both sides by 32
F-32=9C/5+32-32
2. simplify.
F-32=9C/5
3. Multiply both sides by 5.
5(F-32=9C/5)5
4. Simplify and divide both sides by 9.
5(F-32)=9C
5(F-32)/9=9C/9
5. 5(F-32)/9=C
Why is (2x-1)^2=4 not an exponential equation?
Because there is no variable in an exponent
Which is the most logical first step for solving for the variable in the inequality: 8x+7 < 3(2x+1)
A.Reverse the inequality sign B.Use the distributive property to clear the parentheses by multiplying each of the terms by 3 C.Subtract 2x from both sides of the inequality D.Divide both sides of the inequality by 3
What is B
The distributive property clears the parentheses so you can isolate the variable
What is the rule for adding exponents?
What is both the exponents and variables should be the same.
Only terms that have the same variables and powers are added.
Solve using substitution:
5=x+y
2y+x=7
x = 3, y = 2
1) solve x in 5=x+y
x=5-y
2) substitute x=5-y into 2y+x=7
y+5=7
3) solve for y in y+5=7
y=2
4) Substitute y=2 into x=5-y
x=3
5) So, x=3, y=2
Solve for h in the literal equation 3h + g = 5h − hg
What is g/2-g=h
1. subtract both sides by 3h.
3h-3h+g=5h-3h-hg
2. simplify
g=2h-hg
3. Factor the h out.
g=h(2-g)
4. Divide both sides by (2-g)
g/2-g=h(2-g)/(2-g)
5. Cancel.
g/2-g=h
Fill in the blank: An exponential function of the form y=b^x, where b is a positive number not equal to one, an x is any _____.
What is any real number.
Solve the following inequality:
4x-2(3x-9)<=-4(2x-9)
What is x<=3
Simplify the parenthesis: 4-6
x+18<=-8+36
Collect like terms: -2
x+18<=-8+36
Add 8x to both sides: -2x+8x+18<=-8x+8x=36
Simplify:6
x+18<=36
Subtract 18<=36
Subtract 18 from both sides:6
x+18-18<=36-18
Simplify:6
x<=18
Divide both sides by 6:
6x/6<=18/6
Simplify: x<=3
What is the Power rule?
It tells us that to raise a power to a power, just multiply the exponents.