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inysia [295]
3 years ago
15

Identify the 42nd term of an arithmetic sequence where a_1=-12 and a_27=66

Mathematics
2 answers:
baherus [9]3 years ago
7 0

Answer:

111

Step-by-step explanation:

Arithmetic sequences are linear. That means no matter the pair of points use to calculate slope, or common difference, that number remains constant.

We are given points (1,-12) and (27,66) are on the line.

Calculating slope by subtracting points and then putting 2nd number over 1st.

(27,66)

(1, -12)

-----------subtracting

26 , 78

The slooe or the common difference is 78/26=3.

So now we want to know n such that (42,n) is on this same line.

Let's use the slope formula again with (42,n) and (1,-12).

(42,n)

( 1,-12)

----------subtracting

41 , n+12

The slope is (n+12)/41 but we have also calculated it to be 3 so these expressions are equal.

(n+12)/41=3

Multiply both sides by 41:

n+12=123

Subtract 12 on both sides.

n=111

Wittaler [7]3 years ago
3 0

Answer:

a₄₂ = 107

Step-by-step explanation:

The nth term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₂₇ = 66 , then

a₁ + 26d = 66 , that is

- 12 + 26d = 66 ( add 12 to both sides )

26d = 78 ( divide both sides by 26 )

d = 3

Then

a₄₂ = - 16 + (41 × 3) = - 12 + 123 = 111

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aivan3 [116]

Answer:

Length of the lake is 97.30 m

Step-by-step explanation:

We have given Caleb starts at one end of the lake and walk 95 m

So d_1=95m

And then he turns at an angle of 60°

So \Theta =60^{\circ} and then again walk 8 m

So d_2=8m

We have to fond the total length of the lake , that is d

Total length of the lake is given by d=\sqrt{d_1^2+d_2^2+2d_1d_2cos\Theta }=\sqrt{95^2+8^2+2\times 95\times 8\times cos60^{\circ}}=97.30m

So length of the lake is 97.30 m

3 0
3 years ago
(NEED EVIDENCE, NOT ONLY ANSWER)
bearhunter [10]
Area of rectangle = width * length

So,
A = 75 * 18
A= 1350 inch^2

Convert inches to feet
1350 * 0.0833 = 112.5 ft^2
6 0
2 years ago
Brittany and Ashley can paint a room in 7 hours if they work together. If Ashley were to work by himself, it would take him 2 ho
stich3 [128]

Answer:

Step-by-step explanation:

Brittany paints the room in x hours, completing 1/x of the room per hour.

Ashley paints the room in x+2 hours, completing 1/(x+2) of the room per hour.

Working together, they complete 1/x + 1/(x+2) = ⅐ of the room per hour.

7(x+2) + 7x = x(x+2)

14x + 15 = x^2 + 2x

x^2 - 12x - 15 = 0

x = [12 ±√(12²+60)]/2= 6±√51

6-√51 is an extraneous solution.

x = 6+√51 ≈ 13.14

Brittany paints the room in 12.14 hours

3 0
3 years ago
Christine, Dale, and Michael sent a total of 71 messages during the weekend. Dale sent 9 fewer messages than Christine. Michael
Alisiya [41]

Answer:

Micheal sent 40 messages, Christine sent 20, and Dave sent 11.

Step-by-step explanation:

Christine, Dale, and Michael sent a total of 71 messages

C + D + M = 71

Dale sent 9 fewer messages than Christine

D = C - 9

Michael sent 2 times as many messages as Christine

M = 2C

Plug-in the numbers.

C + C - 9 + 2C = 71

4C - 9 = 71

4C = 80

C = 20

Now, plug in to other equations for other results.

D = (20) - 9

D = 11

M = 2(20)

M = 40

Micheal sent 40 messages, Christine sent 20, and Dave sent 11.

Verify?

40 + 20 + 11 = 71.

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