Answer:
2
-1
x=4,y=11 (same in both equations)
First picture:
2 and 7 are alternate exterior angles, which when added together need to equal 180 degrees.
Angle 7 = 180 - 146 = 34
Answer is B.34
Second picture:
Angle 8 = 48
Angle 8 + angle 7 = 180
Angle 7 = 180 - 49 = 131
Angle 5 and angle 7 are vertical angle, so angle 5 = angle 7 = 131
Angle 6 is a vertical angle to angle 8 so = 49
Angle 1 = angle 5 = 131
Angle 2 = angle 6 = 49
Angle 3 = angle 7 = 131
Angle 4 = angle 8 = 49
3x + 7 = x
First, subtract 3x from both sides. / Your problem should look like: 7 = x - 3x
Second, simplify x - 3x to -2x. / Your problem should look like: 7 = -2x
Third, divide both sides by -2. / Your problem should look like:
![\frac{7}{-2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B-2%7D%20)
= x
Fourth, simplify
![\frac{7}{-2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%7D%7B-2%7D%20)
to
![-\frac{7}{2}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B7%7D%7B2%7D%20)
/ Your problem should look like:
![- \frac{7}{2}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B7%7D%7B2%7D%20)
= x
Fifth, switch sides. / Your problem should look like: x =
![-\frac{7}{2}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B7%7D%7B2%7D%20)
Answer as fraction:
![-\frac{7}{2}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B7%7D%7B2%7D%20)
Answer as decimal: -3.5
To obtain the total surface we have to calculate the surface of the 4 triangles and add up the areas (remember that the area of a triangle is (b*h)/2 , b is the base, h is the height ).
We will caculate first the area of the base triangle for that we considerer the fact that it is an equilateral triangle with sides of lenght 6 cm, now we calculate the height, I am going to draw please wait a moment
using the pythagorean theorem we have that
![\begin{gathered} h^2=6^2cm^2-3^2\operatorname{cm}=27cm^2 \\ h=\text{ }\sqrt[]{27\text{ }}cm \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%5E2%3D6%5E2cm%5E2-3%5E2%5Coperatorname%7Bcm%7D%3D27cm%5E2%20%5C%5C%20h%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B27%5Ctext%7B%20%7D%7Dcm%20%5Cend%7Bgathered%7D)
Then, the area of the triangle is 6*h/2 = 3h = 15.59 cm^2.
Now we calculate the area of the other 3 triangles, notice that those triangles have the same base and height so we will calculate for one of them and multiply by 3. From the image we know that the height is 15cm and the base is 6 cm so the area is 45cm^2, and 45*3 cm^2 = 135cm^2.
Finally we add up all the areas:
Answer: The mean increases by 3
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The original data set is
{50, 76, 78, 79, 79, 80, 81, 82, 82, 83}
The outlier is 50 because it is not near the group of values from 76 to 83 which is where the main cluster is.
The original mean is M = (50+76+78+79+79+80+81+82+82+83)/10 = 77
If we take out the outlier 50, the new mean is N = (76+78+79+79+80+81+82+82+83)/9 = 80
So in summary so far
old mean = M = 77
new mean = N = 80
The difference in values is N-M = 80-77 = 3
So that's why the mean increases by 3