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Elza [17]
3 years ago
14

Find a formula for an arithmetic sequence that begins 80, 83, 86, 89, ...​

Mathematics
1 answer:
mel-nik [20]3 years ago
3 0

Answer:

a_{n} = 3n + 77

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

Here a₁ = 80 and d = a₂ - a₁ = 83 - 80 = 3 , then

a_{n} = 80 + 3(n - 1) = 80 + 3n - 3 = 3n + 77

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Mr. Juarez opened a savings account with an initial deposit of $560 and will not make any additional deposits or withdrawals. Th
olga_2 [115]

Answer:

$576.80

Step-by-step explanation:

We have been given that Mr. Juárez opened a savings account with an initial deposit of $560 and will not make any additional deposits or withdrawals. The account earns 1% simple interest.

We are asked to find the total amount that Mr. Juárez will have in his account at the end of 3 years.

We will use simple interest formula to solve our given problem.

A=P (1+rt)

A = Final amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Let us convert 1% into decimal form,

1%=1/100=0.01

P=$560 and t=3

A=$560 (1+0.01(3))

A=$560 (1+0.03)

A= $560 (1.03)

A= $576.80

Therefore, Mr. Juárez will have $576. 80 in his account at the end of 3 years. Hope this helps!

5 0
3 years ago
Find the area of Pentagon ABCDE in which BL perpendicular to AC, CM perpendicular to AD, EN perpendicular to AD such that AC = 8
deff fn [24]

Answer:

Area ABCDE = 82 cm²

Step-by-step explanation:

ABCDE = ΔEAD + ΔDAC + ΔCAB

ABCDE = (12×5)/2 + (12×6)/2 + (8×4)/2 = 30+36+16 = 82

6 0
2 years ago
The points ( 2,4) and (5,y) lie on the same line. If the slope of the line is -IA, what is the value of y
raketka [301]

Answer:

<h3>y = 1</h3>

Step-by-step explanation:

Correct question

The points ( 2,4) and (5,y) lie on the same line. If the slope of the line is --1, what is the value of y

The formula for calculating slope of a line is expressed as;

m = y2-y1/x2-x1

Substitute the given point

y - 4/5-2 = -1

y-4/3 = -1

y-4 = -3

y = -3+4

y = 1

Hence the value of y is 1

4 0
3 years ago
What is the solution to this problem?
Lapatulllka [165]
I can tell you how to solve it I you want me too
3 0
3 years ago
Read 2 more answers
4) A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is walking away from the pole at a rate of 2 ft/sec. a
VARVARA [1.3K]

Answer:

A) 48/13 ft/sec

B) 22/13 ft/sec

Step-by-step explanation: Given that:

A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking away from the pole at a rate of 2 ft/sec.

A) At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?

Using similar triangles, we can say:

12/L = 55/(L - x)

Cross multiply to get:

12(l - x) = 5.5l

12l - 12x = 5.5l

6.5l = 12x

x = (6.5/12)l

Taking the derivative with respect to time we get:

dx/dt = (6.5/12)dl/dt or

dl/dt = (12/6.5)(dx/dt)

Since dx/dt = 2 so

dl/dt = (12/6.5)(2)

= 24/6.5

= 48/13 ft/sec

B) At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole ?

Subtract the rate the shadow is going from the rate the man is going. Therefore

48/13 - 2 = 22/13 ft/sec.

7 0
3 years ago
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