Jay needs 19 quarts more paint for the outside of his barn than for the inside.If he uses 107 quarts in all,how many gallons of
1 answer:
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Answers:
Reason 3: Definition of Parallelogram
Reason 4: Alternate Interior Angles Theorem
Reason 5: Reflexive Property of Congruence
Reason 6: ASA Congruence Property
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Explanations:
Explanation for Reason 3: A parallelogram, by definition, has opposite sides that are parallel. It's built into the name more or less. Sides AB and CD are opposite one another in the parallelogram so they are parallel segments
Explanation for Reason 4: Angle ABD is congruent to angle CDB because they are alternate interior angles. They are on the inside of the "train tracks" that are formed by AB and CD. They lay on opposite sides of the transversal BD
Explanation for Reason 5: Any segment is congruent to itself; ie, the same length
Explanation for Reason 6: Using reasons 2,5 and 4, we can use ASA (angle side angle) to prove the two triangles ABD and CDB congruent. Reason 2 is the first "A" in ASA. Reason 5 is the S in ASA. Reason 4 is the other A in ASA. The side is between the two pairs of angles. See the attache image for a visual summary of how ASA is being used.
Reason 3: Definition of Parallelogram
Reason 4: Alternate Interior Angles Theorem
Reason 5: Reflexive Property of Congruence
Reason 6: ASA Congruence Property
------------------------------------------------------
Explanations:
Explanation for Reason 3: A parallelogram, by definition, has opposite sides that are parallel. It's built into the name more or less. Sides AB and CD are opposite one another in the parallelogram so they are parallel segments
Explanation for Reason 4: Angle ABD is congruent to angle CDB because they are alternate interior angles. They are on the inside of the "train tracks" that are formed by AB and CD. They lay on opposite sides of the transversal BD
Explanation for Reason 5: Any segment is congruent to itself; ie, the same length
Explanation for Reason 6: Using reasons 2,5 and 4, we can use ASA (angle side angle) to prove the two triangles ABD and CDB congruent. Reason 2 is the first "A" in ASA. Reason 5 is the S in ASA. Reason 4 is the other A in ASA. The side is between the two pairs of angles. See the attache image for a visual summary of how ASA is being used.
Answer:
B (6, 8)
C (1, 5)
see attached diagram (qu 1 is blue, qu2 is red)
Step-by-step explanation:
1.
A = (2, 3)
If B is 4 right and 5 up from point A, then
B = (2 + 4, 3 + 5) = (6, 8)
2. C = (9, 7)
If D is 8 left and 2 down from point C, then
C = (9 - 8, 7 - 2) = (1, 5)
A. False. Consider the identity matrix, which is diagonalizable (it's already diagonal) but all its eigenvalues are the same (1).
b. True. Suppose
is the matrix of the eigenvectors of 
, and 
is the diagonal matrix of the eigenvalues of :
Then
In other words, the columns of
are 
, which are identically 
, and these are the columns of 
.
c. False. A counterexample is the matrix
which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix
with eigenvalue
and eigenvector 
, where 
. But the matrix can't be diagonalized.
b. True. Suppose
Then
In other words, the columns of
c. False. A counterexample is the matrix
which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix
with eigenvalue