We can use linear combinations of the equations to eliminate variables.
3x - 4y = 1
-2x + 3y = 1
To eliminate y we'll make the linear combination of 3 times the first equation minus four times the second.
9x - 12y = 3
-8x + 12y = 4
Adding,
x = 7
We could solve for y directly but let's use another linear combination, twice the first plus three times the second:
2(3x - 4y) + 3(-2x + 3y)= 2(1)+3(1)
y = 5
Check: 3(7)-4(5)=1 good. -2(7)+3(5)=1 good.
Q18 Answer: (7,5)
y = -3x + 5
5x - 4y = -3
4y +1(5x - 4y) = 4(-3x + 5) + 1(-3)
5x = -12x + 20 -3
17 x = 17
x = 1
y = -3(1) + 5 = 2
Check: 5(1) - 4(2) = -3 good
Q19 Answer (1,2)
6x + 5y = 25
x = 2y + 24
6x = 12y + 144
5y = 25 - 12y - 144
17y = -119
y = -119/17= -7
x = 2y+24= 10
Check: 6(10)+5(-7)=25 good 2y+24=2(-7)+24=10=x good
Q20 Answer (10,-7)
3x + y = 18
-7x + 3y = -10
9x + 3y = 54
9x - -7x = 54 - -10
16x = 64
x=4
y = 18 -3x = 18-12=6
Check: 3(4)+6=18 good, -7(4)+3(6)=-10 good
Q21 Answer: (4,6)
Answer:
The quadratic curve has the best correlation to the given data.
Step-by-step explanation:
Enter the data into a spreadsheet or graphing calculator and try the different regression options to see which gives the highest R-value. Here, the quadratic regression does that.
Answer:
9/20
Step-by-step explanation:
1/3 * 3/5 * 2 1/4 =
1/3 * 3/5 * 9/4=
1/5 * 9/4 =
9/20
1) 1ml % 6 marbles = about 0.17ml so the volume per marble is 0.17ml 2) 10-(0.17x4) = 9.32 so that is the original volume 3) then 9.32 + (0.17 x 13) = 11.53ml 4) it is linear because for every marble placed inside the cylinder the volume increases by about 0.17ml the slope means amount of marbles placed vs. volume in cylinder
