pick out the rational numbers in this sequence:
5, 1/7, -37, 6.88, 0
All numbers in this sequence are rational.
Why? Rational numbers include all numbers except numbers that goes on and on without pattern, such as pi.
100
The lengths of a triangle are consecutive even numbers. What is the length of the shortest side if the perimeter of the whole thing is 90?
Let n= even integer
n+2= 2nd even
n+4= 3rd even
n+n+2+n+4=90
3n+6=90
-6 -6
3n=84
/3 /3
1n=28
lengths: 28,30, 32 shortest side=28
100
What is the domain and range of a sequence of relation?
The domain is the set of x coordinates. The range is the set of y coordinates.
100
what letter is used to define slope?
m
100
Unit 4-
How do you calculate the rate of change?
You divide the change in Y by the change in X.
200
True or false.
All negative numbers are integers.
False.
Why? -1.2 or any mixed negative numbers aren't integers, only rational
200
Ian is 7 years older than Bailee. 3 years ago, he was twice her age. Find Bailee's age.
Let b= Bailee's age
I= Ian's age
b+7=2b-3
-b -b
7=b-3
+3 +3
b=10
....
I-3=2(i-7-3)
I-3=2i-20
-I -I
-3=I-20
+20 +20
I=17
Bailee is 10. Ian is 17.
200
Is the relation a function? (1,2),(2,3),(1,4),(3,1)
No it is not a function.
Why? Because there is a repeat in the domain.
200
Are the slope and constant rate of change ever the same?
Yes
Why? Because the slope and constant rate of change are the same only when data is linear.
200
Unit 1-
What is the rational number?
a. 1
b. 1/3
c. -9
d. all of the above
The answer is all of the above.
Why? Because a rational number is any number that can be written in the form a/b, where a and b are integers. (b cannot equal 0)
300
Simplify this term:
8rs+2x-15rs+9x^2
8rs-15rs+2x+9x^2
-7rs+2x+9x^2
Why? because the only like terms (8rs and -15rs) were grouped together and since 9x has an exponent of 2, they are not alike because they are not raised to the same power
300
A tv cost $700 and is on sale for 25% discount. How much would it cost?
700-->525
25
x/700=25/100
100x=17500
/100 /100
1x=175...700-175=525
The tv now costs $525
300
In a relation, what is the dependent and independent variable?
In every relation the output (y) is the dependent and the input (x) is the independent.
Why? because y depends on x.
300
How many point do you need to calculate the slope?
You need 2 points
Why? Because you find the difference between the X1 and X2 and Y1 and Y2. Change in Y over change in X.
300
Unit 3-
When you have discrete data do you connect the dots?
No
Why? Because you cannot have a fraction of the independent variable.
400
Write an expression for this verbal phrase, then simplify using distributive property:
The product of 9 and the quantity 32 minus z.
9(32-z)
288-9z
Why? because product meaning multiplication, you multiply 9 times 32 and 9 times z. 9*32=288 and 9*z=9z
400
a building casts a shadow 8 feet long. a boy 6 feet tall cast a shadow 4 feet long. how tall is the tree?
l l
__l 6 ____l x Let x=height of building
4 8
4/8=6/x
4x=48
/4 /4
x=12
The building is 12 feet tall.
400
What is the domain and range of every inverse graph?
All real numbers except 0 for both.
Why? because inverse graphs never touch either axis.
400
What are the ways to calculate slope?
1. Make a table (change in Y over change in X)
2. Subtraction (Y2 - Y1 over X2 - X1)
3. Formula (Y2 - Y1 over X2 - X1)
400
Unit 1-
What property does this equation illustrate?
(10x11)x12=10x(11x12)
a. Associative(+)
b. Identity(x)
c. Associative(x)
d. Inverse (x)
The answer is c.
Why? Because the numbers are the same in each equation, but the grouping of the numbers is different.
500
Explain the property happening in each step of the equation; (deductive reasoning)
8x-6+3(x-2)=5x+6+4x+5
=5x+4x+6+5
=5x+4x+(6+5)
=5x+4x+11
= 9x+11
1. distributive property- distributing the variables and non-variable integers in an equation form
2. commutative of addition- moving like terms together but you end up with the same answer
3. associative of addition- grouping together to emphasize grouping singular numbers together first
4. combine like term- adding together like terms ex. 7+8=15 but 6x+8=6x+8 because they are unlike terms
5. combine like terms- combing the two numbers with the variables together
500
Andy bought 4 shirts for a total of $20. Some cost $5.50 and some cost 3.50. How many of each did he buy?
Let s=# of shirts bought at 3.50....3.50s
7-s= 5.50(4-s)
3.50s+5.50(4-s)=20
3.50s+22-5.50s=20
-2s+22=20
-22 -22
-2s=(-2)
-2 /-2
1s=1
Andy bought 1 shirt for $3.50 and 3 shirts for $5.50
500
What happens to this parent function when it goes from:
f(x)=|x| to f(x)=|x|+3 ?
The function will shift up 3 units on the graph.
Why? because you are adding 3 units to the x value so it increases
500
What is the slope of horizontal and vertical lines?
Horizontal is 0 because there is no increase
Vertical is undefined because it's always a number over 0, which would be a divide by zero error.
500
Unit 3-
What is the common difference in this set of numbers?
5, 10, 15, 20, 25, 30
The answer is 5.
Why? Because you add 5 to each previous number to get the next number.