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olga nikolaevna [1]
3 years ago
15

If y + 2q = 15, q + 2p = 5 and p + 2y = 7, then find the value of p + q + y.

Mathematics
1 answer:
notsponge [240]3 years ago
5 0
y+2q=15\\
y=15-2q\\\\
p+2y=7\\
p+2(15-2q)=7\\
p+30-4q=7\\
-3q+30=7\ \ \ |Subtract\ 30 \\
-3q=-23\ \ \ |Divide\ by\ -3\\
q=\frac{23}{3}\\\\
y=15-2q=15-2(\frac{23}{3})=15-\frac{29}{3}=15-7=8\\\\
p=7-2y\\
p=7-2*8\\
p=7-16=-9\\\\
\textbf{p+q+y=}-9+\frac{23}{3}+8=-1+7\frac{2}{3}=\boxed{6\frac{2}{3}}

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The product of twice a number and two is the same as the difference of three times the number and 1/2. find the number.
Daniel [21]
The equation would be 2n x 2 = 3n - 1/2.

So, combine like terms to make it 4n = 3n - 1/2. Subtract to get n = -1/2.

Your answer is -1/2.
4 0
3 years ago
Abby filled her goodie bags with 4 cookies and 3 candy bars and spent a total of $10.25 per bag. Marissa filled her goodie bags
Paladinen [302]
Let's start by writing a system of linear equations:
c -> cookies 
cb -> candy bars
(You can use any abbreviations to your preference)

Abby:
4 cookies 
3 candy bars
$10.25 per bag
The equation would be:
4c+ 3cb = $10.25

Marissa:
2 cookies
7 candy bars
$14.75 per bag
The equation would be:
2c + 7cb = $14.75

So our linear equation system would be:
<span>4c+ 3cb = $10.25
</span><span>2c + 7cb = $14.75

I would try to get rid of one variable so I can solve for the other variable. In this case, it is easier to get rid of c since I can multiply the second equations by 2. Then it would subtract the two equations.

(2c + 7cb = $14.75) 2 = 4c + 14 cb = $29.50

      4c + 3cb = $10.25
   -  4c+14 cb = $29.50                    (4c would get canceled.)
---------------------------------
             -11 cb = - $19.25                (Divide by -11 to solve for cb)
</span>             ---------   -------------
              -11           -11
            
             cb = $1.75

Now we know cb (candy bar) cost, we would substitute this value into cb into one of the equations. It doesn't matter which equation you put it in. I will substitute it in the first equations. 

  4c + 3 (1.75) = $10.25
  4c + 5.25 = $10.25                       (Multiply 3 by 1.75)
       -5.25       -5.25                         (Subtract 5.25 on both sides)
             4c = 5                                 (Divide by 4 on both sides to get c)
             ----   ---
              4      4
         
         c= 1.25

Check the work:
4(1.25) + 3(1.75) 
  = $10.25

2(1.25) + 7(1.75)
   = $14.75

Total cost:
cookies = $1.25
candy bars = $ 1.75

Hope this helps! :)

6 0
4 years ago
Find the slope of the line through each pair of points.<br> (-2, -12) and (-18, -12)
Jobisdone [24]

Answer:

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Step-by-step explanation:

you use the equation y2-y1/x2-x1 so -12-(-12) which is 0 then do -18-(-2)=-16 so the slope is 0/-16

4 0
3 years ago
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Tcecarenko [31]
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To find the slope, use the formula: rise over run —> y2 - y1/x2 - x1
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Hope I helped:)
6 0
3 years ago
526 divided by 18 show your work
Damm [24]

Answer:

Step-by-step explanation:

4 0
3 years ago
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