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alina1380 [7]
3 years ago
14

Given that 99°, 153°, 162° are 3 of the interior angles of a n-sided polygon and that the remaining interior angles are 141° eac

h, find n.
Mathematics
1 answer:
Helen [10]3 years ago
8 0

Answer:

n = 9

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Given 3 angles and the remaining angle of 141° then there are

141(n - 3) angles of this size

Then

99 + 153 + 162 + 141(n - 3) = 180(n - 2) , that is

414 + 141n - 423 = 180n - 360

141n - 9 = 180n - 360 ( subtract 141n from both sides )

- 9 = 39n - 360 ( add 360 to both sides )

351 = 39n ( divide both sides by 39 )

9 = n

The polygon has 9 sides

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Perform the operation (9x^2+6x-7)+(-9x-5)
asambeis [7]

Answer:

9x^{2}-3x-12

9x^{2}+6x-7-9x-5

(Group liked terms)

9x^{2}+6x-9x-7-5

( subtract the numbers ) -7-5= -12

9x^{2}+6x-9x-12

( add similar elements ) 6x-9x=-3x

9x^{2}-3x-12

Step-by-step explanation:

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2 years ago
Wath the factorization of 8
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Factorization of 8
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alukav5142 [94]
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6 0
3 years ago
Need help with these 2 problems will give brainliest answer and worth 30 points!!
Elena L [17]
Question 1.
Step 1. Add the total cost of purchasing the luxury items:
TotalCost=35.95+34.65+15.30+6.99+42.96=135.85
You will spend $135.85 purchasing the luxury items.

Step 2. Add the total cost of purchasing the name brand items:
TotalCost=19.95+15.98+9.40+4.99+29.75=80.07
You will spend $80.07 purchasing the name brand items.

Step 3. Subtract the total cost of purchasing the name brand items from the total cost of purchasing the luxury items:
135.85-80.07=55.78

Answer to the original question:
We can conclude that you will spend $55.78 more by purchasing the luxury items.

Question 2:

Part 1. 
To find the how many months will take to pay the card debt, we are going to use the credit card equation: N=- \frac{1}{30}* \frac{ln(1+ \frac{b}{p}*(1+ \frac{r}{365})^{30}))  }{ln(1+ \frac{r}{365}) }
where
N is the months to pay the card
b is the balance 
p is the monthly payment 
r is the interest rate in decimal form 

We know from our problem that the balance of the credit card is $1,367.90 and the monthly payment is $400.00, so b=1367.90 and p=400. To find convert the interest rate to decimal form, we are going to divide the rate by 100% 
r= \frac{9.5}{100}=0.095.
Now that we have all we need, lets replace the values in our credit card equation: 
N=- \frac{1}{30}* \frac{ln(1+ \frac{b}{p}*(1+ \frac{r}{365})^{30})) }{ln(1+ \frac{r}{365}) }
N=- \frac{1}{30}* \frac{ln(1+ \frac{1367.90}{400}*(1+ \frac{0.095}{365})^{30})) }{ln(1+ \frac{0.095}{365}) }
N=3.4799

It will take you 3.5 months according to our calculation, but since you pay $400 each month on the due date, we can conclude that it will take you 4 months to pay off the card.

Part 2. To calculate the total amount paid including the interest, we just need to multiply the monthly payment by the number of payments.
We know from our problem that the monthly payment is $400. We also know from our previous calculations that the number of payments is 4, so lets multiply both quantities:
400*4=1600

We can conclude that the total amount paid including interest is $1,600


5 0
3 years ago
carol's father was 24 years old when carol was born, now he is 4 times as old a carol how old is carol
tensa zangetsu [6.8K]

Answer:

24 - 24 = 0 (carols age past tense)

24 x 4 = 96

96 - 24 = 72 (present tense)

carol is now 72 yr

8 0
3 years ago
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