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Reil [10]
3 years ago
8

M<KGH=x+161,m<FGK=x+41,and m<FGH=180° Find x

Mathematics
1 answer:
Butoxors [25]3 years ago
4 0

Answer: x = -11   ∠FGK = 30°   ∠KGH = 150°

<u>Step-by-step explanation:</u>

∠FGK + ∠KGH = ∠FGH    <em>Segment Addition Postulate</em>

x + 41 + x + 161 = 180       <em>Substitution</em>

2x + 202 = 180  <em>               Simplify (added like terms)</em>

2x = -22                            <em>Subtraction Property of Equality</em>

x = -11                               <em>Division Property of Equality</em>

 

∠FGK = x + 41     = (-11) + 41    = 30

∠KGH = x + 161   = (-11) + 161   = 150

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Dustin has only nickels and quarters in his piggy bank. He was 49 total for combined value of $8.85. How many of each type of co
Troyanec [42]
Let's use the variables N and Q for the number of nickels and the number of quarters.

We know there are 49 total coins, so we can write the following equation:

N + Q = 49

We can solve this equation for one variable which will help in the next step. Let's solve for N:

N = 49 - Q

Next, we know that nickels are worth $0.05 and quarters are worth $0.25. We can use these values along with the total value of $8.85 to create another equation.

0.05N + 0.25Q = 8.85

Now we can use substitution to solve our system out equations. We solved the first equation for N, so we can plug 49 - Q in for N.

0.05(49-Q) + 0.25Q = 8.85

Distribute and combine like terms.

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Plug 32 in for Q in N + Q = 49 to find the number of nickels.

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Dustin has 32 quarters and 17 nickels.


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3 years ago
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