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ELEN [110]
3 years ago
8

The total number of degrees, D, in an n-sided polygon is given by the formula D=180(n-2). When Janelle solves for n, she gets n=

D+360/180. Sophie solved the same equation for n and got an equivalent equation. Which of the following could be Sophie’s equation?
n=D/180 +2


n=D/180 -2


n=D-178


n=D-182
Mathematics
2 answers:
Rus_ich [418]3 years ago
3 0
<span>D = 180 * (n -2)
D = 180n -360
180n = D +360
n = (D / 180) + 2

So, the answer is "A"
And we can test this with a square, sum of angles = 360
n = (D / 180) +2
n = (360 / 180) +2
number of sides = 4
correct

Source:
http://www.1728.org/polygon.htm



</span>
Maksim231197 [3]3 years ago
3 0
D=180(n-2)
Solving for n. Dividing both sides of the equation by 180:
D/180=180(n-2)/180
D/180=n-2
Adding 2 both sides of the equation:
D/180+2=n-2+2
D/180+2=n
n=D/180+2

Answer: First Option n=D/180+2

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Nonamiya [84]

Combine the terms by multiplying into a single fraction.

\bf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14   }

Find the common denominator.

\bf{\dfrac{5x}{2}-7=\dfrac{3}{4}x+14   }

Combine fractions with the lowest common denominator.

\bf{\dfrac{5x(-7)}{2}=\dfrac{3}{4}x+14   }

Multiply the numbers.

\bf{\dfrac{5x-14}{2}=\dfrac{3}{4}x+14   }

Combine the multiplied terms into a single fraction

\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+14   }

Find the common denominator.

\bf{\dfrac{5x-14}{2}=\dfrac{3x}{4}+\dfrac{4\cdot14}{4}    }

Combine fractions with the lowest common denominator.

\bf{\dfrac{5x-14}{2}=\dfrac{3x+4\cdot14}{4}   }

Multiply the numbers.

\bf{\dfrac{5x-14}{2}=\dfrac{3x+56}{4}   }

Eliminate the denominators of the fractions.

\bf{4\cdot\dfrac{5x-14}{2}=4\cdot\dfrac{3x+56}{4}   }

Cancel the multiplied terms that are in the denominator.

\bf{2(5x-14)=3x+56}

To distribute.

\bf{10x-28=3x+56 }

Add 28 to both sides.

\bf{10x-28+28=3x+56+28 }

Simplify

\bf{10x=3x+84 }

Subtract 3x from both sides.

\bf{10x-3x=3x+84-3x }

Simplify

\bf{7x=84 }

Divide both sides by the same factor.

\bf{x=\dfrac{84}{7} }

Simplify

\bf{x=12 \ \ \ === > \ \ \ Answer}

↓

<h3>Verification</h3>

Let x=12.

  1. \bf{\dfrac{5}{2}\times12-7=\dfrac{3}{4}\times12+14   }
  2. \bf{\dfrac{5\times12}{2}-7=\dfrac{3}{4}\times12+14   }
  3. \bf{\dfrac{60}{2}-7=\dfrac{3}{4}\times12+14   }
  4. \bf{30-7=\dfrac{3}{4}\times12+14   }
  5. \bf{30-7=\dfrac{3\times12}{4}+14   }
  6. \bf{30-7=\dfrac{36}{4}+14   }
  7. \bf{30-7=9+14   }
  8. \bf{23=9+14 }
  9. \bf{23=23}

Checked ✅

3 0
2 years ago
Which strategies can be used to solve this problem?
Y_Kistochka [10]
DUse logical reasoning. Combine the totals for cars painted in the first two years (5,000 + 7,213). Subtract 8,201 (cars painted in the third year) from the sum to get the answer.
7 0
3 years ago
Please help ill give brainiest answer
trapecia [35]

Answer:

1: AAS, RQC 2: ASA, SRP

Step-by-step explanation:

(1) We are shown that two angles and one side are congruent in the order of AAS. Make sure you write the letters in terms of the corresponding angles. The angles and sides are congruent because the problem labels it for us. For example, B,A,C=R,Q,S. Answers: AAS, RQC.

(2) We are shown that two angles and one side are congruent in the order of ASA. Make sure you write the letters in terms of the corresponding angles again. For example, P,Q,R=P,S,R. The angles are congruent because the problem labels it for us. Side PR is congruent to side PR by reflexive property. Answers: ASA, SRP.

I hope this helped :) Good luck

4 0
3 years ago
Suppose you have a ​$8-off coupon at a fabric store. You buy fabric that costs ​$7.50 per yard. Write an equation that models th
zhannawk [14.2K]

Answer:

= 7.5x-8

Step-by-step explanation:

Total cost = cost per yard * yard of fabric - coupon

total cost = 7.5 x - 8

y = 7.5x-8

8 0
3 years ago
Read 2 more answers
The length of a rectangle has a measure of x and the width of a rectangle has a measure of (x-2). Find x if the area is 35.
Oliga [24]

Answer:

length = 7

pls mark me the brainliest

Step-by-step explanation:

A = Lw

35 = x (x -2)

35 = x2 - 2x

x2 -2x -35 = 0

(x-7)(x+5) = 0  

x-7=0

x=7       (we won't use the other factor since it would give us a negative length

so length = 7

4 0
3 years ago
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