OK to solve this, we have to solve each system presented through elimination or substitution and find which one is equivalent to that of the teacher's!
First let's solve for the teacher's:
-2x+5y=10
-3x+9y=6
Solve by substitution (I think elimination might be easier to do for this one, but I don't really remember 100% sorry!)
Isolate the x (or y) variable in the first equation
-2x+5y=10
-2x=10-5y

Substitute x into the next equation and solve for y
-3(10-5y/2)+9y=6
3*10-5y/2+9y=6
(multiply both sides by 2)
3(10-5y)+18y=12
30-15y+18y=12
30+3y=12
3y=-18
y=-6
Substitute in x
x= -10-5(-6)/2
x=-20
TEACHER'S ANSWER (-20,-6)
GOKU
x-3y=-2
-2x+5y=-7
Do the same as above
Solve for x
x-3y=-2
x=3y-2
Plug in
-2(3y-2)+5y=-7
4-6y+5y=-7
4-y=-7
-y=-11
y=11
x=(3(11)-2)
x=31
GOKU'S ANSWER (31, 11)
SELINA:
-5x+14y=16
-3x+9y=12
One last time!! :)
-5x+14y=16
-5x=16-14y
x=(16-14y)/-5
-3(-(16-14y/5)+9y=12
3*16-14y/5+9y=12
3*16-14y+45y=60
48-42y+45y=60
48+3y=60
3y=12
y=4
x=-(16-14(4))/5
x=8
SELINA'S ANSWER
(8,4)
So neither Goku or Selina got the same answer as the teacher
Answer:
see explanation
Step-by-step explanation:
The circumference (C) is calculated as
C = πd ← d is the diameter
diameter = 2 × 9 = 18 in ( twice the top diameter ), thus
C = 18π in ← exact value ≈ 56.55 in ( to 2 dec. places )
Answer:
3c=273
c=91
2c= 212
C= 106
c= 91+ 106= 197
so they will need 197 canoes total
Why:
So first you have to determine a set variable to represent the number of canoes, I chose C. Then you make an equation to represent the number of canoes 273 people will use if they group into 3's, from this I got 3c=273. Solve for C and get 91.
The remainder of the group which is 485-273= 212 will use canoes in groups of 2's. To represent this, 2c=212. Solve for C and get 106. Combine 106 and 91 to get the total number of canoes.
The answer is: 30.4 cm³ .
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The volume = Base Area * height = (8 cm²) * (3.8 cm) = 30.4 cm³ .
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20*1.95 =39 girls
26girls/39girls =0.667
0.667*100 = 66.67%