Triangle ABC is shown below. Triangle A B C is shown. The length of side A B is 2 x, the length of side B C is 4 x minus 10, and
the length of side A C is 3 x minus 7. Angle A B C and B C A are congruent. What is the length of line segment AC?
2 answers:
Answer:the length of line segment AC is 14
Step-by-step explanation:
The diagram is shown in the attached photo
Since Angle A B C and B C A are congruent. It means that they are equal. An isosceles triangle is a triangle that has two equal sides and two equal base angles. Since Angle A B C and B C A are equal, it means that the triangle is an isosceles triangle. It also means that sides AC and AB are equal. The expression becomes
3x - 7 = 2x
3x - 2x = 7
x =7
To determine the length of line segment AC. We will substitute x = 7 into 3x - 7. It becomes
3×7 - 7 = 21 - 7 = 14
You might be interested in
Answer:
We conclude that young women are delaying marriage and marrying at a later age.
Step-by-step explanation:
We are given that the average age of brides marrying for the first time is 23.9 years with a population standard deviation of 4.2 years.
The sociologist randomly samples 100 marriage records and determines the average age of the first time brides is 24.9 years.
Let = <u><em>average age of brides marrying for the first time.</em></u>
So, Null Hypothesis, :
= 23.9 years {means that young women are not delaying marriage and marrying at a later age}
Alternate Hypothesis, :
> 23.9 years {means that young women are delaying marriage and marrying at a later age}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample average age of the first time brides = 24.9 years
= population standard deviation = 4.2 years
n = sample of marriage records = 100
So, <u><em>the test statistics</em></u> =
= 2.381
The value of z test statistics is 2.381.
<u>Now, at 1% significance level the z table gives critical value of and 2.326 for right-tailed test.</u>
Since our test statistic is more than the critical value of z as 2.381 > 2.326, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that young women are delaying marriage and marrying at a later age.
