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nika2105 [10]
3 years ago
11

-5(n + 3) = 6(n +4) + 5

Mathematics
2 answers:
laiz [17]3 years ago
6 0

Answer:

n = -4

Step-by-step explanation:

−5(n+3)=6(n+4)+5

Step 1: Simplify both sides of the equation.

−5(n+3)=6(n+4)+5

(−5)(n)+(−5)(3)=(6)(n)+(6)(4)+5(Distribute)

−5n+−15=6n+24+5

−5n−15=(6n)+(24+5)(Combine Like Terms)

−5n−15=6n+29

−5n−15=6n+29

Step 2: Subtract 6n from both sides.

−5n−15−6n=6n+29−6n

−11n−15=29

Step 3: Add 15 to both sides.

−11n−15+15=29+15

−11n=44

Step 4: Divide both sides by -11.

−11n

−11

=

44

−11

n=−4

monitta3 years ago
3 0

Answer:

n = -4

Step-by-step explanation:

-5(n + 3) = 6(n +4) + 5

First distribute by multiplying:

-5(n + 3) = 6(n +4) + 5 into:

-5n-15=6n+24+5

Combine Like Terms (CLT):

-5n-15=6n+24+5

-5n-15=6n+29

Inverse operation:

-5n-15=6n+29

     +15     +15

-5n=6n+44

-11n=44

_______

-11     -11

n = -4

                 

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Answer is 0.31. Hope this helps.
6 0
3 years ago
I’m slow and lazy and yeah sorry just at least help
Anna007 [38]

Answer:

2) x = 6    y = 7      3) x = -5    y= 2

Step-by-step explanation:

2) 10x - 8y = 4

   2(-5x + 3y = -9)

-10x + 6y = -18

 10x - 8y =   4      Add both equations together

         -2y = -14

         y = 7            Divide both sides by -2

10(x) - 8(7) = 4       Plug in 7 for the y to solve for x

10x - 56 = 4  

     + 56 + 56        Add 56 to both sides

10x = 60

x = 6                      Divide both sides by 10

3) Where the two lines intersect, that is the solution to x and y.

The lines intersect at (-5,2). x = -5      y = 2

3 0
3 years ago
This is a "water tank" calculus problem that I've been working on and I would really appreciate it if someone could look at my w
Sedaia [141]
Part A

Everything looks good but line 4. You need to put all of the "2h" in parenthesis so the teacher will know you are squaring all of 2h. As you have it right now, you are saying "only square the h, not the 2". Be careful as silly mistakes like this will often cost you points. 

============================================================

Part B

It looks like you have the right answer. Though you'll need to use parenthesis to ensure that all of "75t/(2pi)" is under the cube root. I'm assuming you made a typo or forgot to put the parenthesis. 

dh/dt = (25)/(2pi*h^2)
2pi*h^2*dh = 25*dt
int[ 2pi*h^2*dh ] = int[ 25*dt ] ... applying integral to both sides
(2/3)pi*h^3 = 25t + C
2pi*h^3 = 3(25t + C)
h^3 = (3(25t + C))/(2pi)
h^3 = (75t + 3C)/(2pi)
h^3 = (75t + C)/(2pi)
h = [ (75t + C)/(2pi) ]^(1/3)

Plug in the initial conditions. If the volume is V = 0 then the height is h = 0 at time t = 0
0 = [ (75(0) + C)/(2pi) ]^(1/3)
0 = [ (0 + C)/(2pi) ]^(1/3)
0 = [ (C)/(2pi) ]^(1/3)
0^3 =  (C)/(2pi)
0 = C/(2pi)
C/(2pi) = 0
C = 0*2pi
C = 0 

Therefore the h(t) function is...
h(t) = [ (75t + C)/(2pi) ]^(1/3)
h(t) = [ (75t + 0)/(2pi) ]^(1/3)
h(t) = [ (75t)/(2pi) ]^(1/3)

Answer:
h(t) = [ (75t)/(2pi) ]^(1/3)

============================================================

Part C

Your answer is correct. 
Below is an alternative way to find the same answer

--------------------------------------

Plug in the given height; solve for t
h(t) = [ (75t)/(2pi) ]^(1/3)
8 = [ (75t)/(2pi) ]^(1/3)
8^3 = (75t)/(2pi)
512 = (75t)/(2pi)
(75t)/(2pi) = 512
75t = 512*2pi
75t = 1024pi
t = 1024pi/75
At this time value, the height of the water is 8 feet

Set up the radius r(t) function 
r = 2*h
r = 2*h(t)
r = 2*[ (75t)/(2pi) ]^(1/3) .... using the answer from part B

Differentiate that r(t) function with respect to t
r = 2*[ (75t)/(2pi) ]^(1/3)
dr/dt = 2*(1/3)*[ (75t)/(2pi) ]^(1/3-1)*d/dt[(75t)/(2pi)] 
dr/dt = (2/3)*[ (75t)/(2pi) ]^(-2/3)*(75/(2pi))
dr/dt = (2/3)*(75/(2pi))*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)

Plug in t = 1024pi/75 found earlier above
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75(1024pi/75))/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (1024pi)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*(1/64)
dr/dt = 25/(64pi)
getting the same answer as before

----------------------------

Thinking back as I finish up, your method is definitely shorter and more efficient. So I prefer your method, which is effectively this:
r = 2h, dr/dh = 2
dh/dt = (25)/(2pi*h^2) ... from part A
dr/dt = dr/dh*dh/dt ... chain rule
dr/dt = 2*((25)/(2pi*h^2))
dr/dt = ((25)/(pi*h^2))
dr/dt = ((25)/(pi*8^2)) ... plugging in h = 8
dr/dt = (25)/(64pi)
which is what you stated in your screenshot (though I added on the line dr/dt = dr/dh*dh/dt to show the chain rule in action)
8 0
3 years ago
(64/8/ 4 + 7 – 2) • 5 =
maria [59]

Answer:

35

Step-by-step explanation:

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3 0
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Answer:

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Step-by-step explanation:

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6 0
2 years ago
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