Answer:
<h2>The perimeter of the cross section is 30 centimeters.</h2>
Step-by-step explanation:
In this problem we have the intersection of a rectangular prism an a plane.
The dimensions of the rectangular plane are
Assuming the plane is cutting the prism horizontally, the cross section would have dimensions
Because only the height would be cut.
So, the perimeter of the rectangle cross-section is
Therefore, the perimeter of the cross section is 30 centimeters.
Answer:
13 sides.
Step-by-step explanation:
(n - 2) = 1980 / 180 = 11.
n = 13
When the sum of the interior angles is 1980 degrees, the convex polygon will have 13 sides.
i hope this helps and is right! p.s. i really need brainliest :)
Answer:
Step-by-step explanation:
<u>Given expression:</u>
<u>This is undefined when the denominator is zero:</u>
Correct choice is B
Step 1. Multiply first equation with -3 and the second one with 2. You'll get:
Step 2. Add both equations together. You'll get:
, which gives x = -2
Step 3. Replace x = -2 in the first equation and calculate y.
The solution is: x=-2, y=5
The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>