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Nikolay [14]
2 years ago
15

(A) If the 13th and 38th terms of an arithmetic sequence are -53 and -128,

Mathematics
1 answer:
grigory [225]2 years ago
7 0

9514 1404 393

Answer:

  (A) -2018

  (B) 5/36

Step-by-step explanation:

(A) The rate of change between any pair of terms in an arithmetic sequence is the same:

  (a668 -a38)/(668 -38) = (a38 -a13)/(38 -13)

  a668/630 = a38/630 +(a38 -a13)/25 . . . . add a38/630 to both sides

  a668 = a38 +630/25(a38 -a13) = -128 +25.2(-128 -(-53)) = -128 -1890

  a668 = -2018

__

(B) The sum of an infinite geometric series is ...

  S = a1/(1 -r) . . . . . . for first term a1 and common ratio r

We are given S = 6, a1 = 5, so we can find r to be ...

  6 = 5/(1 -r)

  1 -r = 5/6

  1 -5/6 = r = 1/6

Then the 3rd term is ...

  a3 = 5×(1/6)^(3 -1) = 5/36

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Given the figure below, find the values of x and z.
aleksandrvk [35]

Answer: x = 2 and z=78

Step-by-step explanation:

Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent (equal in measure). Z is Opposite to 78 angle, so z=78.

Adjacent angles add up to 180 degrees, and 78 and (5x + 92) are adyacents so:

5x + 92 + 78 = 180

5x + 170 = 180

5x = 180 - 170

5x = 10

x = 10/5

x = 2

7 0
3 years ago
-4b - 5 + 2b =10. Can I have some help solving this.
kramer

Answer:

-7.5

Step-by-step explanation:

Simplify

-4b - 5 + 2b = 10

-2b - 5 = 10

-2b = 15

b = -7.5

5 0
3 years ago
Read 2 more answers
Suppose that 10 years ago you bought a home for $160,000, paying 10% as a down payment, and financing the rest at 9% interest fo
Goshia [24]

Answer:

Current monthly payment on their existing mortgage would be $1158.66

Step-by-step explanation:

Total cash value = $160,000

Down payment = 10% of 160,000

Down Payment = $16,000

Balance amount = 160,000 - 16,000 = $144,000

Monthly payment formula:

P=\dfrac{r(PV)}{1-(1+r)^{-n}}

where,

PV is present value of home, PV=$144,000

r is rate per period , r=\frac{9}{1200}=0.0075

n is number of period, n=30x12 = 360

P=\dfrac{0.0075\times 144000}{1-(1+0.0075)^{-360}}

P=\$ 1158.66

Monthly payment would be same for 30 years.

Thus, Current monthly payment on their existing mortgage would be $1158.66

5 0
2 years ago
A leaky faucet in kali's house drips water at a rate of 42 gallons per week. How many gallons does the faucet drip in three days
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Amount of water that the faucet leaks in 1 week = 42 gallons

That means Amount of water that the faucet in Kali's house leaks in                 7 days = 42 gallons So The amount of water that the faucet in Kali's house leaks in 1 day = (42/7) gallons  = 6 gallons Then The amount of water that the faucet in Kali's house leaks in 3 days = 6 * 3 gallons = 18 gallons

So it can said from the above deduction that the amount of water leaked by the faucet in Kali's house is 18 gallons.

hope this help .-.

5 0
3 years ago
Okie is a low western lowland gorilla living at the frankline park zoo near boston, ma. he loves to fingerpaint. many of his pai
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13500-1500= 12000/5=2400

12000-2400= 9600

$9600 most expensive painting

5 0
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