1 )
1st and 2nd equation (multiply 1st by -2 ):
-2x - 10 y + 8 z = 20
2 x - y + 5 z = -9
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- 11 y + 13 z = 11 / * ( -20 )
1st and 3rd:
- 2 x - 10 y + 8 z = 20
2 x - 10 y - 5 z = 0
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- 20 x + 3 z = 20 / * 11
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220 y - 260 z = -220
- 220 y + 33 z = 220
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z = 0, y = -1, x = - 5
2 )
2 x - y + 5 = -4
- 2 x + 3 y - 5 = - 10
Substitution: y = 2 x + 9
- 2 x + 3(2 x + 9 ) = -5
4 x = - 32, x = -8, y = -7, z = 5
3 )
x + y + z = 11
1.5 x+3 y +1.5 z = 21
x = 2 y
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3 y + z = 11 / * (-2)
6 y + 1.5 z = 21
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- 6 y - 2 z = -22
6 y + 1.5 z = 21
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-0.5 z = -1, z = 2, y = 3, z = 6
Answer: the store used 6 pounds of peanuts, 3 pounds of almonds and 2 pounds of raisins.
If
, then angle
is obtuse and triangle with sides a, b, c is obtuse triangle.
In an arbitrary triangle can be only one obtuse angle, and the side which lies opposite to the largest angle is the largest. Then since <span>angle
is opposite the side of length a</span> you can conclude that a>c and a>b.
Answer:
8x+y-13=0
Step-by-step explanation:
let the given point be
A(1,5)=(x1,y1)
slope(m)= -8
then,equation of straight line is,
(y-y1)=m(x-x1)
(y-5)= -8(x-1)
y-5= -8x+8
8x+y-5-8=0
therefore,8x+y-13=0 ..........(i) is the required equation.
Correct Answer: A. 2(n+8).
Actually, the answer is not A, if you're saying A is the first choice above. That's incorrect. You will need to use the Geometric mean for right triangles here to figure out what the value of a is. We will use this form:
. We have a value for YZ of 3; side a is XZ. That means in order to solve this we need WZ, which we can find using pythagorean's theorem. 3^2 + 4^2 = c^2 and 9 + 16 = c^2 and c = 5. Now we fill in accordingly:
. Cross-multiply to get 3XZ=25 and side XZ is
. XZ is 25/3 and YZ is 3, so 25/3 - 3 = XY. That means that XY (side a) = 16/3 or 5 1/3, choice B, or the second one down.