We are given that m∠AEB = 45° and ∠AEC is a right angle. The measure of ∠AEC is 90° by the definition of a right angle. Applying
the gives m∠AEB + m∠BEC = m∠AEC. Applying the substitution property gives 45° + m∠BEC = 90°. The subtraction property can be used to find m∠BEC = 45°, so ∠BEC ≅ ∠AEB because they have the same measure. Since divides ∠AEC into two congruent angles, it is the angle bisector.
2 answers:
Answer:
The proof is given below.
Step-by-step explanation:
Given m∠AEB = 45° and ∠AEC is a right angle. we have to prove that EB divides ∠AEC into two congruent angles, it is the angle bisector.
Given ∠AEC=90° (Given)
∠AEC=∠AEB+∠BEC
⇒ 90° = 45° +∠BEC (Substitution Property)
By subtraction property of equality
⇒ ∠BEC = 90° - 45° = 45°
Hence, both angles becomes equal gives ∠AEB≅∠BEC
Since EB divides ∠AEC into two congruent angles, ∴ EB is the angle bisector.
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Answer:
The second statement is Correct.
Step-by-step explanation:
Consider the provided information.
It is given that Antonio uses a calculator to find and gets a result of –10.
So, the first statement is incorrect.
2nd statement: Antonio found the answer for
The second statement is Correct.
Third statement: Antonio found the answer for
So, the third statement is incorrect.
Fourth statement: Antonio found the answer for
So, the fourth statement is incorrect.
Hence, the second statement is Correct.
Answer:
We conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.
Step-by-step explanation:
We are given that a particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8000.
From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles.
<u><em>Let </em></u><u><em> = average miles for deluxe tires</em></u>
So, Null Hypothesis, :
50,000 miles {means that deluxe tire averages at least 50,000 miles before it needs to be replaced}
Alternate Hypothesis, :
< 50,000 miles {means that deluxe tire averages less than 50,000 miles before it needs to be replaced}
The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean lifespan = 46,500 miles
= population standard deviation = 8000 miles
n = sample of tires = 28
So, <u><em>test statistics</em></u> =
= -2.315
The value of the test statistics is -2.315.
Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is less than the critical value of z as -2.315 < -1.6449, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that deluxe tire averages less than 50,000 miles before it needs to be replaced which means that the claim is not supported.