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Hunter-Best [27]
3 years ago
13

two times the least of three consecutive odd integers exceeds three times the greatest by 25. what are the integers?

Mathematics
1 answer:
Slav-nsk [51]3 years ago
6 0
2(2n+1)=3(2n+5)+25\\
4n+2=6n+15+25\\
2n=-38\\
n=-19\\\\
2n+1=2\cdot(-19)+1=-37\\
2n+3=2\cdot(-19)+3=-35\\
2n+5=2\cdot(-19)+5=-33\\\\
\boxed{-37,-35,-33}
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I'd really appreciate some help on these questions, I'm really struggling
nikklg [1K]
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)

6 0
3 years ago
Marcus needs to bike at least 80 miles this week for his training.If he has already biked 25 miles this week ,then how many mile
Orlov [11]

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

5 0
2 years ago
How do I solve this?
Readme [11.4K]

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

_____

A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.

_____

<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))

4 0
3 years ago
Help me on this please I’d appreciate it
guajiro [1.7K]

Step-by-step explanation:

your friend is closer to the school (b)

it's graph covers less area..

4 0
2 years ago
NoT YellInG ThIS IS JuSt TO AtTRaCT AtTeNTiOn 50 POiNtS PLeaSE ANswER I Am NoT WasTiNg PoInTS!!! Find the range of 1 1/4, 5/8, 3
Arada [10]

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>
5 0
2 years ago
Read 2 more answers
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