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>
Answer:
60%
Step-by-step explanation:
If I get you right, you're asking for the percentage gain to the nearest percentage, right?
Now to do this, we need to get the amount of profit she made. That's quite easy, we only need to subtract the cost price from the selling price. And that equals $15 - $9.38 that equals $5.62.
Now, we divide this value by the cost price and multiply by 100% to get the percentage gain.
I.e 5.62/9.38 × 100%.
That gives 59.9% , which equals 60% when approximated to the nearest percentage.
12x +13 equal to or not equal to 12x - 6 + 8 or 12x +2
No, these expressions are not equivalent.
Hope this helps!
Answer: x = 31
Step-By-Step:
<u>To Find x:</u>
<u />
(Angle Sum Property Of Triangles)
(Remove the brackets)
<u />
<u />
(Group Accordingly)
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= 
= 
= 
= 
= 
= 
<u>Therefore</u> x = 31
So,
Angle A = x + 10 = 31 + 10 = 41
Angle B = 2*x + 20 = 2*31 + 20 = 82
Angle C = 2*x - 5 = 62 - 5 = 57
