The properties or relationship between the angles m∠1, m∠2, and m∠3 can be used to determine the statement that must be true
The correct option that gives the statement that must be true to prove that m∠1 + m∠2 + m∠3 = 180°, is the first option
A. m ║ n
Reason:
Which statement must be true to prove that m∠1 + m∠2 + m∠3 = 180°?
A. m ║ n
B. m∠1 + m∠2 = 180° - m∠3
C. m∠1 + m∠2 = 90°
D. m∠1 = m∠2 = m∠3
Given that m∠1 + m∠2 + m∠3 = 180°, we have;
m∠ACD + m∠2 + m∠3 = 180° by angles on a straight line
Therefore;
m∠ACD = m∠1 by addition property of equality
m∠ACD ≅ m∠1 by definition of congruency
m∠ACD and m∠1 are alternate interior angles formed between lines <em>m</em> and <em>n</em> and their common transversal AC
Which gives;
<em>m</em> ║ <em>n</em>, by alternate interior angles theorem which states that alternate interior formed between parallel lines are congruent
Therefore;
The statement that must be true to prove that m∠1 + m∠2 + m∠3 = 180° is <u><em>m</em></u><u> ║ </u><u><em>n</em></u>
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Answer:
The correct group of answer is D) 3 + (−4) = −1, because −1 is 4 units to the left of 3
Step-by-step explanation:
Consider the provided information.
Point P on the number line shows Lara's score after the first round of a quiz:
Point P is shown on 3.
That means after the first round her total was 3.
In round two, she lost 4 points.
Therefore, she score −4 points in 2nd round
To find the total points at the end of round 2, we need to add -4 to 3.
3+(−4)=−1
Here −1 is 4 units to the left of 3.
Hence, the correct group of answer is D) 3 + (−4) = −1, because −1 is 4 units to the left of 3
9514 1404 393
Answer:
1,222,200
Step-by-step explanation:
A search using a computer program found ...
5432 × 225 = 1,222,200
__
1000 mod 225 = 100
4 × 225 = 900
This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.
Answer: the current of the river is 3 mph.
Step-by-step explanation:
Let x represent the current of the river.
The boat travels 2.4 miles downstream. Assuming it travelled with the current of the river. If the boat travels at an average speed of 21 miles per hour in the still water, it means that the total speed at which the boat travelled downstream is
(21 + x) mph
Time = distance/speed
Time taken to travel downstream is
2.4/(21 + x)
it travels 1.8 miles upstream. Assuming it travelled against the current of the river. it means that the total speed at which the boat travelled upstream is
(21 - x) mph
Time taken to travel upstream is
1.8/(21 - x)
Since the time taken to travel upstream and downstream is the same, then
2.4/(21 + x) = 1.8/(21 - x)
Cross multiplying, it becomes
2.4(21 - x) = 1.8(21 + x)
50.4 - 2.4x = 37.8 + 1.8x
2.4x + 1.8x = 50.4 - 37.8
4.2x = 12.6
x = 12.6/4.2
x = 3 mph
Answer:
With what? I don't see the question.....
