All categories

3 years ago

A triangle in the coordinate plane has vertices ????(0,10), ????(−8,8), and ????(−3,5). Is it a right triangle? If so, at which

Mathematics

1 answer:

GaryK [48]3 years ago

5 0

Answer:

It is a right triangle, the right angle is at the point (-3, 5)

Step-by-step explanation:

The first step is to locate the points of the vertices in a plane, in this case they are (0.10), (-8.8) and (-3.5). The desmostration of this is shown in the attached image.

As we can see it is formed a right triangle (the figure outlined in red), and the rigth angle is the one at the point (-3,5).

You might be interested in

The accompanying data on x = current density (mA/cm2) and y = rate of deposition (m/min)μ appeared in a recent study.

gtnhenbr [62]

Answer:

a) $r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857$

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

b) $m=\frac{64.5}{2000}=0.03225$

Now we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50$

$\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425$

$b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27$

So the line would be given by:

$y=0.3225 x -0.27$

Step-by-step explanation:

Part a

The correlation coeffcient is given by this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=4 $\sum x = 200, \sum y = 5.37, \sum xy = 333, \sum x^2 =12000, \sum y^2 =9.3501$

$r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857$

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

Part b

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=12000-\frac{200^2}{4}=2000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=333-\frac{200*5.37}{4}=64.5$

And the slope would be:

$m=\frac{64.5}{2000}=0.03225$

Now we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50$

$\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425$

And we can find the intercept using this:

$b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27$

So the line would be given by:

$y=0.3225 x -0.27$

4 0

3 years ago

Factor completely -5x 2 y + 10xy - 15xy 2

victus00 [196]

-5x^2 y + 10xy - 15xy^2

= -5xy(x - 2 + 3y)

8 0

3 years ago

Read 2 more answers

Using whichever equation you prefer (part a, b, or c), find the speed of light in meters per second if a mass of 3 kilograms con

pav-90 [236]

$Given:\\m=3kg\\E=2.7\cdot 10^{17}J\\\\Find:\\c=?\\\\Solution:\\\\E=mc^2\\\\c^2= \frac{E}{m} \\\\c= \sqrt{\frac{E}{m}} \\\\c= \sqrt{ \frac{2.7\cdot 10^{17}J}{3} } = (2.7\cdot 10^{16} \frac{m^2}{s^2} )^{ \frac{1}{2} }=3\cdot 10^{8} \frac{m}{s}$

6 0

3 years ago

Which of the following forms of I.D. is not an acceptable form of I.D. for opening a savings account?

larisa86 [58]

Answer: [A]: "library card".
____________________________________
Explanation: One would need a valid, government-issued photo ID card (i.e. that has not expires).

Although SOME library cards include one's picture, library cards do not constitute "valid ID's" because they are not "government-issued" and would, theoretically, be easy to be made fraudulently (e.g. not have security-issued seals and features).

Even "school ID's"; or "college ID cards"; even if "current" (e.g. currently enrolled" with a photo ID) would not be considered "official" and would only be considered "secondary ID".
_____________________________________________

6 0

3 years ago

Read 2 more answers

Can you pls help me it’s timed

Lerok [7]

Answer:

The median is 22

Step-by-step explanation:

6 0

3 years ago