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sveta [45]
1 year ago
10

stion 1 OT 5A researcher recorded the number of swans and the number of ducks in a lake every month. Function s represents the n

umber ofswans and function d represents the number of ducks in a lake after n months.s(n) = 2(1.1)" + 5d(n) = 4(1.08)" + 3Which function can be used to determine the total number of ducks and swans in the lake after n months?o++t(n) = 2 (1.1)” + + 2(1.0R)" + 4Ot(n) = 2[2(1.1)" + (1.08)" + 4t(n) = 4 (1.1)” + 2(1.08)” + 2)ot(n) = 2 (1.1)”. + 2(1.08)" + 2]++SubmitReset
Mathematics
1 answer:
Anon25 [30]1 year ago
8 0

Given functions are

s(n)=2(1.1)^n+5_{}d(n)=4(1.08)^n+3

The total number of ducks and swans in the lake after n months can be determined by adding the functions s(n) and d(n).

t(n)=s(n)+d(n)

t(n)=(2(1.1)^n^{}+5)+(4(1.08)^n+3)

t(n)=2(1.1)^n+5+4(1.08)^n+3

t(n)=2(1.1)^n+4(1.08)^n+5+3

t(n)=2(1.1)^n+4(1.08)^n+8

Taking 2 as common, we get

t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack

Hence The total number of ducks and swans in the lake after n months is

t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack

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Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS.
Rufina [12.5K]

Answer:

96 degrees

Step-by-step explanation:

STR + STQ=180 degree

Substitute

x+x-12=180

2x-12=180

2x=192

x=96

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3 years ago
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Aaron participates in a walkathon for charity. He has a sponsor who has pledged a base donation of $2 for the first mile he walk
tino4ka555 [31]

Answer:

total amount donated when aaron walks n miles = $2 + $3(n-1)

Step-by-step explanation:

Aaron participates in a walkathon for charity. He has a sponsor who has pledged a base donation of $2 for the first mile he walks and then a certain dollar amount for each additional mile he walks. Based on this pledge, if Aaron walks 8 miles, the sponsor will donate a total of $23 to the charity.

Write a formula that can be used to determine the amount of money this sponsor donates when Aaron walks n miles.

total amount sponsor pays = base donations + (additional miles walked after first mile x amount paid)

when Aaron walks 8 miles

additional miles = 8 - 1 = 7

23 = 2 + 7x

23 - 2 = 7x

x = 3

additional amount paid is $3

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3 years ago
Solve for x.<br> 7(1x - 3) = 4(x + 5)
alexandr1967 [171]

Answer:

x = 41/3

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

7(1x - 3) = 4(x + 5)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Simplify:                                        7(x - 3) = 4(x + 5)
  2. Distribute:                                     7x - 21 = 4x + 20
  3. Subtract 4x on both sides:          3x - 21 = 20
  4. Add 21 on both sides:                  3x = 41
  5. Divide 3 on both sides:                x = 41/3

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    7(1(41/3) - 3) = 4(41/3 + 5)
  2. Multiply:                        7(41/3 - 3) = 4(41/3 + 5)
  3. Subtract/Add:               7(32/3) = 4(56/3)
  4. Multiply:                        224/3 = 224/3

Here, we see that 224/3 is indeed equivalent to 224/3. ∴ x = 41/3 is a solution to the equation.

And we have our final answer!

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Circumference=2pir=<span>2∗3.14∗5.1</span><span>=30.028=30.03.</span>
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