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:
11
Step-by-step explanation:
So if he already biked 25 miles we can subtract 80 and 25 which will get a total of 55. if we divided 55 miles to the rest of the 5 days he will have to bike 11 miles each day
Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
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<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
Step-by-step explanation:
your friend is closer to the school (b)
it's graph covers less area..
Answer:
<u>Range = 1 1/4</u>
Step-by-step explanation:
Range = Maximum - Minimum
Arranging the data in ascending order :
- <u>1/2, 5/8, 3/4, 1 1/4, 1 1/2, 1 3/4</u>
<u />
Solving for range :
- Range = 1 3/4 - 1/2
- Range = 1 3/4 - 2/4
- Range = 7/4 - 2/4
- Range = 5/4
- <u>Range = 1 1/4</u>
