Logic & Proof
If "triangle ABCABC is isosceles" is a false statement and "Elizabeth goes to the beach when it's nice out" is a false statement, evaluate the truth of the statement "triangle ABCABC is isosceles and Elizabeth goes to the beach when it's nice out."
False.
And statements are true if all "atomic" or constituent statements are true.
Find the slope of a line parallel to the line whose equation is 6x+y=−3. Fully simplify your answer.
Slope of a parallel line: −6
In ΔVWX, m∠V=(x+8)∘, m∠W=(5x+9), and m∠X=(3x+10). Find m∠X..
61
A line, segment, or ray that divides a segment into two equal parts and is perpendicular to the segment.
Perpendicular Bisector
What is the national animal of Scotland?
Unicorns
If p is false and q is true, find the truth value of:
¬p∧¬q
False
Which equation represents a line which is parallel to the line x+4y=−20
Correct Equation: y=−1/4x−1
Quadrilateral YLPS≅ quadrilateral VHTK. If m∠Y=57∘ and m∠S=18∘, find m∠K.
m∠K= 18
A segment that connects a vertex of a triangle to the midpoint of the opposite side.
Median
What ranking did UGA receive in the College Football Playoff bracket?
Write the statement that is the contrapositive of the following statement:
If a triangle is isosceles, then it has congruent base angles.
Contrapositive: If a triangle doesn't have congruent base angles, then it isn't isosceles.
Which equation represents a line which is perpendicular to y=0?
Correct Equation: x=−1
In ΔBCD, m∠B = 61° and m∠C = 90°. Which list has the sides of ΔBCD in order from shortest to longest?
Order from smallest to largest:
BC,CD,DB
A segment that connects a vertex of a triangle to the opposite side so that it is perpendicular to that side.
Altitude
What was the most-streamed song on Spotify for 2024?
Expresso - Sabrina Carpenter
State whether the Law of Detachment or the Law of Syllogism was used to conclude the given statements. If it's an invalid conclusion, write invalid.
Given: If two lines are parallel, then they never intersect.
Given: If two lines never intersect, then they have the same slope.
Conclusion: If two lines are parallel, then they have the same slope.
Law of Syllogism
What is an equation of the line that passes through the point (6,−4) and is perpendicular to the line 2x−y=4?
Final answer:
y=−1/2x−1
Camden is 1.35 meters tall. At 12 noon, he measures the length of a tree's shadow to be 19.35 meters. He stands 14.2 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The tree is 5.07 m tall.
Which "center of a triangle" relationship cannot be created by solving for the midpoint and/or perpendicular slope?
Incenter
What were God's first recorded words in the Bible?
"Let there be light."
State whether the Law of Detachment or the Law of Syllogism was used to conclude the given statements. If it's an invalid conclusion, write invalid.
Given: If the Patriots win their next game, then they will win their division.
Given: If the Patriots win their next game, then they will go to the playoffs.
Conclusion: If the Patriots win their division, then they will go to the playoffs.
Invalid
Use the point-slope form to write the equation of a line that passes through the point (20,−10) with slope 13/8.
y+10=13/8(x−20)
Dominic is 1.75 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 37.95 meters. He stands 33.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The tree is 15.63 m tall.
List the terms in order. Number for credit.
1) Intersection of Perpendicular Bisectors
2) Intersection of Angle Bisectors
3) Intersection of Medians
4) Intersection of Altitudes
1) Circumcenter
2) Incenter
3) Centroid
4) Orthocenter
How old was Queen Elizabeth the Second when she was crowned the Queen of England?
27