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3 years ago

Find the point, M, that divides segment AB into a ratio of 3.1 if A is at (-4,-2) and B is at (4. -10).

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

7 0

Answer:

The coordinates of M are (2,-8)

Step-by-step explanation:

The coordinates of the point that divides the line segment joining

$A(x_1,y_1)$ to $B(x_2,y_2)$ in the ratio m:n is given by:

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

If A is at (-4,-2) and B is at (4. -10) and the ratio is 3:1.

Then

$(\frac{3(4)+1(-4)}{3+1},\frac{3(-10)+1(-2)}{3+1})$

$(\frac{8}{4},\frac{-32}{4})$

The coordinates of M are (2,-8)

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A balance can measure up to 0.001 g.when using such a balance, how many decimal places should your answer have?

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Places skied 3 and 1 de decimal point

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3 years ago

Secants AC and DB intersect at point E inside the circle. Given that the measure of arc CD = 40o, arc AB = 60o, and arc BC = 160

s344n2d4d5 [400]

Answer:

C. $130^{\circ}$

Step-by-step explanation:

Please find the attachment.

We have been given that secants AC and DB intersect at point E inside the circle. Given that the measure of arc $CD = 40^o$ , arc $AB = 60^o$ , and arc $BC = 160^o$ . We are asked to find the measure of angle AED.

We know that the measure of angle formed by two intersecting secants is half the sum of measure of the arcs by intercepted by the angle and its vertical angle.

$\angle AED=\frac{\widehat{BC}+\widehat{AD}}{2}$

Let us find measure of arc AD by subtracting measure of given arcs from 360 degrees as:

$\widehat{AD}=360^{\circ}-(60^{\circ}+40^{\circ}+160^{\circ})$

$\widehat{AD}=360^{\circ}-(260^{\circ})$

$\widehat{AD}=100^{\circ}$

$\angle AED=\frac{160^{\circ}+100^{\circ}}{2}$

$\angle AED=\frac{260^{\circ}}{2}$

$\angle AED=130^{\circ}$

Therefore, measure of angle AED is 130 degrees and option C is the correct choice.

6 0

3 years ago

Otra forma de representar 42/9

Oksi-84 [34.3K]

Answer:

(84/18, 14/3). These are the same as 42/9

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3 years ago

What angle corresponds to angle AFG?

viva [34]

Look at the image below :)

In case you didn't know, corresponding angles are equal to each other and are on the same side of the traversal

Therefore the answer is angle CGH

Hope this helped!

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3 years ago

Read 2 more answers

Suppose you are interested in the effect of skipping lectures (in days missed) on college grades. You also have ACT scores and h

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Answer:

a) For this case the intercept of 2.52 represent a common effect of measure for any student without taking in count the other variables analyzed, and we know that if HSGPA=0, ACT= 0 and skip =0 we got $colGPA=2.52$

b) This value represent the effect into the ACT scores in the GPA, we know that:

$\hat \beta_{ACT} = 0.015$

So then for every unit increase in the ACT score we expect and increase of 0.015 in the GPA or the predicted variable

c) If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_i = 0$

Alternative hypothesis: $\beta_i \neq 0$

Or in other wouds we want to check if an specific slope is significant.

The significance level assumed for this case is $\alpha=0.05$

Th degrees of freedom for a linear regression is given by $df=n-p-1 = 45-3-1 = 41$ , where p =3 the number of variables used to estimate the dependent variable.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_i}{SE_{\beta_i}}$

And replacing we got:

$t = \frac{-0.5}{0.0001}=-5000$

And for this case we see that if we find the p value for this case we will get a value very near to 0, so then we can conclude that this coefficient would be significant for the regression model .

Step-by-step explanation:

For this case we have the following multiple regression model calculated:

colGPA =2.52+0.38*HSGPA+0.015*ACT-0.5*skip

Part a

(a) Interpret the intercept in this model.

For this case the intercept of 2.52 represent a common effect of measure for any student without taking in count the other variables analyzed, and we know that if HSGPA=0, ACT= 0 and skip =0 we got $colGPA=2.52$

(b) Interpret $\hat \beta_{ACT}$ from this model.

This value represent the effect into the ACT scores in the GPA, we know that:

$\hat \beta_{ACT} = 0.015$

So then for every unit increase in the ACT score we expect and increase of 0.015 in the GPA or the predicted variable

(c) What is the predicted college GPA for someone who scored a 25 on the ACT, had a 3.2 high school GPA and missed 4 lectures. Show your work.

For this case we can use the regression model and we got:

$colGPA =2.52 +0.38*3.2 +0.015*25 - 0.5*4 = 26.751$

(d) Is the estimate of skipping class statistically significant? How do you know? Is the estimate of skipping class economically significant? How do you know? (Hint: Suppose there are 45 lectures in a typical semester long class).

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_i = 0$

Alternative hypothesis: $\beta_i \neq 0$

Or in other wouds we want to check if an specific slope is significant.

The significance level assumed for this case is $\alpha=0.05$

Th degrees of freedom for a linear regression is given by $df=n-p-1 = 45-3-1 = 41$ , where p =3 the number of variables used to estimate the dependent variable.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_i}{SE_{\beta_i}}$

And replacing we got:

$t = \frac{-0.5}{0.0001}=-5000$

And for this case we see that if we find the p value for this case we will get a value very near to 0, so then we can conclude that this coefficient would be significant for the regression model .

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3 years ago