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3 years ago

Prove that the altitude to the base of an isosceles triangle is also the median to the base

1 answer:

4 0

The base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent. The Isosceles Triangle Theorem states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle.

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It’s linear so you map out the first differences and then put it into y=Mx+b form. For the you gotta find the y intercept

Alika [10]

$▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

Let's find the slope (m) :

$\dfrac{y2 - y1}{x2 - x1}$

$\dfrac{16 - 11}{9 - 6}$

$\dfrac{5}{3}$

slope of given line is 5/3

now, let's plug the value of coordinates of a point lying on the line ( for example : (6 , 11) and slope (m) to find the y - intercept (c) :

$y = mx + c$

$11 = \bigg(\dfrac{5}{ 3} \times 6 \bigg) + c$

$11 = (5 \times 2) + c$

$11 = 10 + c$

$c = 11 - 10$

$c = 1$

value of y - intercept (c) = 1, so our equation will be :

$y = mx + c$

$y = \dfrac{5}{3}x + 1$

6 0

2 years ago

What is the numerical expression for 3 - 0 x 5 - 0 ?

Sav [38]

I gotten this question before the answer is 3

7 0

2 years ago

Experian would like to test the hypothesis that the average credit score for an adult in Virginia is different from the average

aliya0001 [1]

Answer:

a. We fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

b. The 95% confidence interval for the true difference of means is -2.2468 and 36.2468. There is a probability of 95% that the true difference of means $\mu_{1}-\mu_{2}$ is between -2.2468 and 36.2468. This confidence interval contains the number 0, this is consistent with the results we got in a. Because we fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

Step-by-step explanation:

Let $\mu_{1}-\mu_{2}$ be the true difference between the average credit score for an adult in Virginia and the average credit score for an adult in North Carolina. We have the large sample sizes $n_{1} = 40$ and $n_{2} = 35$ , the unbiased point estimate for $\mu_{1}-\mu_{2}$ is $\bar{x}_{1} - \bar{x}_{2}$ , i.e., 699-682 = 17.

The standard error is given by $\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}$ , i.e.,

$\sqrt{\frac{(44)^{2}}{40}+\frac{(41)^{2}}{35}}$ = 9.8198.

a. We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative). The rejection region is given by RR = {z | z < -1.96 or z > 1.96} where -1.96 and 1.96 are the 2.5th and 97.5th quantiles of the standard normal distribution respectively. The test statistic is $Z = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}}$ and the observed value is $z_{0} = \frac{17}{9.8198} = 1.7312$ . Because 1.7312 does not fall inside RR, we fail to reject the null hypothesis.

b. The endpoints for a 95% confidence interval for $\mu_{1}-\mu_{2}$ is given by $17\pm (z_{0.05/2})9.8198$ , i.e., $17\pm (z_{0.025})9.8198$ where $z_{0.025}$ is the 2.5th quantile of the standard normal distribution, i.e., -1.96, so, we have 17-(1.96)(9.8198) and 17+(1.96)(9.8198), i.e., -2.2468 and 36.2468. There is a probability of 95% that the true difference of means $\mu_{1}-\mu_{2}$ is between -2.2468 and 36.2468. This confidence interval contains the number 0, this is consistent with the results we got in a. Because we fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

3 0

4 years ago

Explain why some geometric shapes don't roll

shutvik [7]

Answer: some don’t have constant width that allows the top and bottom to be the same distance away from each other (which is what helps shapes to roll)

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

8.4 = 3 x m what is the value of m

nataly862011 [7]

M= 2.8

Alternate form:

14/5 or 2 4/5

5 0

3 years ago