Q1. The answer is x = 1, y = 1, z = 0
<span>(i) -2x+2y+3z=0
</span><span>(ii) -2x-y+z=-3
</span>(iii) <span>2x+3y+3z=5
</span><span>_________
Sum up the first and the third equation:
</span>(i) -2x+2y+3z=0
(iii) 2x+3y+3z=5
_________
5y + 6z = 5
Sum up the second and the third equation:
(ii) -2x-y+z=-3
(iii) 2x+3y+3z=5
_________
2y + 4z = 2
(iv) 5y + 6z = 5
(v) 2y + 4z = 2
________
Divide the fifth equation by 2
(iv) 5y + 6z = 5
(v) y + 2z = 1
________
Multiple the second equation by -3 and sum the equation
(iv) 5y + 6z = 5
(v) -3y - 6z = -3
________
2y = 2
y = 2/2 = 1
y + 2z = 1
1 + 2z = 1
2z = 1 - 1
2z = 0
z = 0
-2x-y+z=-3
-2x - 1 + 0 = -3
-2x = -3 + 1
-2x = -2
x = -2/-2 = 1
Q2. The answer is x = -37, y = -84, z = -35
<span>(i) x-y-z=-8
(ii) -4x+4y+5z=7
(iii) 2x+2z=4
______
</span>Divide the third equation by 2 and rewrite z in the term of x:
(iii) x+z=2
z = 2 - x
______
Substitute z from the third equation and express y in the term of x:
<span>x-y-(2-x)=-8
x - y - 2 + x = 8
2x - y = 10
y = 2x - 10
______
Substitute z from the third equation and y from the first equation into the second equation:
</span><span>-4x + 4y + 5z = 7
-4x + 4(2x - 10) + 5(2 - x) = 7
-4x + 8x - 40 + 10 - 5x = 7
-x -30 = 7
-x = 30 + 7
x = -37
y = 2x - 10 = 2*(-37) - 10 = -74 - 10 = -84
z = 2 - x = 2 - 37 = -35</span>
(AAA) Corresponding angles are congruent.
Therefore, the sides of the triangles are proportional:
cross multiply
use distributive property
subtract 100 from both sides
divide both sides by 100
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(SAS)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
Therefore we have the equation:
The perimeter of △PQR:
Substitute the value of y to the expression:
It's looking for the measures
m<F + m<G = 180°
(4x)° + (8x)° = 180°
12x = 180°
÷12 ÷12
x = 15
check your work
m<F + m<G = 180°
(4x)° + (8x)° = 180°
4(15)° + 8(15)° = 180°
60° + 120° = 180°
D. I think because you would get a negative
Let us check series : -10 /-2 = 5 -50/-10 = 5
so it is a geometric series with a= -2 and r= 5
sum formula for n terms of geometric series = a ( r^n -1 ) /( r-1)
here we find S5 that is n= 5 = -2 ( 5^ 5 - 1) /( 5-1)
= -2 ( 3125 -1) / 4 = -1562
second series is : 1.5/1 = 1.5 2.25/1.5 = 1.5
this is also geometric series but n = 12 a= 1 and r= 1.5
we use same formula
S12 = 1 ( (1.5) ^12 -1) /( 1.5-1) =
128.74 / 0.5 = 257.49
Last is 2/1= 2 4/2 = 2 8/4 = 2 so r = 2 a = 1 and n = 12
we use same formula 1 ( 2^12 - 1) / (2-1)
= 4095
Answers : -1562 , 257.49 , 4095
