Unit 1
−3/4 + 3/8 =
-3/8
What is a linear equation?
Can be described by slope and y-intercept
3x= 180
60
what is Inductive reasoning
is the process of reaching a
conclusion based on a pattern of examples.
“If a quadrilateral has four congruent sides, then it is a square.”
A rhombus has four congruent sides but is not necessarily a square.
What is a line?
A set of points extending infinitely in opposite directions
35 + x= 90
X=55
How many points are needed to define a plane?
3 non-collinear points.
A student says, “Every prime number is odd.”
is a prime number that is even.
if a number ends in 5, it is divisible by 10
Counterexample: 35 ends in 5 but is not divisible by 10.
2.3 + ( − 1.4)
0.9
− 40.5 + 3.07
−37.43
Line k has slope –1/2.
Question: What is the slope of a line perpendicular to it?
2
Write the conditional statement in “if–then” form:
“Four-sided shapes are quadrilaterals.”
If a shape has four sides, then it is a quadrilateral.
Write the converse of the conditional:
“If a figure is a square, then it has 4 right angles.”
If a figure has 4 right angles, then it is a square.
(x + 6 )+ 3x = 90
21
(3x + 1) + (2x − 6) = 180
37
Determine if the biconditional is true:
“A number is even if and only if it is divisible by 2.”
True
2, 4, 6, 8.
Give a counterexample that shows this conjecture is not necessarily true.
A possible next term could be 9, which is odd
Determine if the biconditional is true:
“A number is even if and only if it is divisible by 2.”
true
Ms. Takanawa has three bank accounts.
The balances in the accounts are $436.12, $1178.05, and −$0.05.
How much money does she have altogether in these accounts?
$1614.12
The difference between the weight of
3 gallons of liquid and 5-pound brick is 19 pounds.
Write an equation to represent this situation. What
is the weight of 1 gallon of the liquid?
3g−5 = 19; 8 lb
Angles C and D are complementary. Angle C = 40°.
Find angle D.
90 – 40 = 50°
Given:
All squares are rectangles.
All rectangles have 4 right angles.
Question: What can you deduce about squares?
Squares have 4 right angles.
Angles A and B are vertical angles. If angle A = 65°, what is angle B?
Angle B = 65°