Find the sum:
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The 38th term of the Arithmetic Progression (355, 348, 341, ...) will be 36.

As per the question statement, we are provided with a series of numbers such as (355, 348, 341, ...)

We are required to calculate the 38th term of the above mentioned series.

To solve this question, first we are required to identify the nature of the series. We can see that, the consecutive terms have a common difference between them, i.e.,

[tex](355-348)=7\\(348-341)=7[/tex]

Therefore, the given series is an Arithmetic Progression (A.P.). Thus, we need to know the formula to calculate a certain nth term of an A.P. which goes as

[tex]T_{n}=[a+(n-1)d][/tex],

Where, "Tₙ" is the nth term required,

"a" is  the first term of the A.P.,

And, "d" is the common difference between every pair of consecutive terms of the A.P.

In this case, (a = 355), (n = 38) and {d = (-7)}. Then, using these values in the above mentioned formula, we get,

[tex]T_{38}=[355+(38-1)(-7)]\\ or, T_{38}=355+[37*(-7)]\\or,T_{38}=355+(-259)\\or, T_{38}=(355-259)\\or,T_{38}=96[/tex]

Hence, the 38th term of the Arithmetic Progression (355, 348, 341, ...) will be 36.

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Answer:

AFB

Step-by-step explanation:

Answer:

AFB

Step-by-step explanation:

Vertical Angles are angles that are opposite of each other and are created by the same lines.

Answer:

1/2

Step-by-step explanation:

The formula for slope is (y2 - y1)/(x2-x1)

In this case, it is (2 - 1/2)/(4-1) which is 1.5 over 3. The slope is 1/2

Answer:

more details

Step-by-step explanation:

Answer: 82.40

Step-by-step explanation: I took the quiz

Answer:

Total Cost: $82.4

Step-by-step explanation:

80 × 3%

= 80 × 0.03

= $2.4

80 + 2.4

= $82.4

Answer:

0.14

Step-by-step explanation:

0.02 * 7 = 0.14

Answer:

quadrant I

Step-by-step explanation:

after the rotation will be in quadrant ll, then reflected back into  quadrant I

Answer:

690 miles

Step-by-step explanation:

Step one:

given data

For the first plane

the velocity is 300km/h

from noon (12:00) to 2pm is= 2 hours

the distance covered is expressed using the formula

velocity= distance/time

distance= velocity*time

distance= 300*2

distance= 600 miles

For the second plane

the velocity is 45km/h

from noon (12:00) to 2pm is= 2 hours

the distance covered is expressed using the formula

velocity= distance/time

distance= velocity*time

distance= 45*2

distance= 90 miles

Step two:

the total distance apart is the sum of the individual distances covered by the planes

= 600+90

=690 miles

Answer: x ≈ 44

because ΔHIJ is a right triangle at J

=> sin x = 47/68

=> x ≈ 44°

Step-by-step explanation:

Answer:

7 minutes per mile

Step-by-step explanation:

42/6=7

Answer:

c

Step-by-step explanation:

Answer:

9.8 x 7.45 = $73.01 ...

Step-by-step explanation:

Answer:

Step-by-step explanation:

Just apply the formula (x-3, y+3) to the points.

Point S: (1,-2) -----> (-2,1)

Point R: (3,1) ------> (0,4)

Point Q: (5,-3) -----> (2,0)

Point P: (3,-5) ---->(0,-2)

Answer:

P'(0, - 2) , Q'(2, 0) , R'(0, 4) , S'(- 2, 1)

Step-by-step explanation:

(x, y) ------> (x - 3, y + 3)

P (3, - 5) ------> P'(3 - 3, - 5 + 3) = (0, - 2)

Q (5, - 3) ------> Q'(5  - 3, - 3 + 3) = (2, 0)

R (3, 1) ------> R'(3 - 3, 1 + 3) = (0, 4)

S (1, - 2) ------> S'(1 - 3, - 2 + 3) = (- 2, 1)

Answer:

2x-3/y-5/37=0

Step-by-step explanation:

here, given equation of line is

y=3/2x+3

or,y(2x+3)=3

or,2x+3=3/y

or,2x-3/y+3=0...eqn(i)

equation of any line parallel to line (i) is

2x-3/y+k=0.. eqn(ii)

since, the line passes through (4,5)[replacing x=4 and y=5 in eqn(ii), we get]

2*4-3/5+k=0

or,8-3/5+k=0

or,40-3/5+k=0

or,k=-5/37

substituting the value of k=-5/37 in eqn(ii)

2x-3/y-5/37=0 is the required equation of line.

if he started working in 45 min he can make time for it

movie started at 2.55 pm

As per the question

Movie start at -2.55 pm

time take to drive the theatre - 10 min

So the time taking is

2.55-0.10=2.45 pm

(Let's take 10 min =0.10)

Marcus start the yard work at -2.00 pm

So the time take - start time

2.45-2.00 pm

= 45 minutes

If Marcus take the yard work for 45 minutes he can make it on time for movie

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Step-by-step explanation:

let the numbers be x and y

The system of equations is:

x+y=10

x-y=6

By elimination method,we can:

1. Add both equations to eliminate y and simplify

OR

2.Subtract both equations to eliminate x and simplify.

Going by the first approach

x+x+y+(-y)=10+6

2x+0=16

x=16/2=8

Plug x=8 into any equation,say equation 2

x-y=6

8-y=6

8-6=y

y=2

Answer

Step-by-step explanation:

[tex]a_n[/tex] is the n-th term in the sequence. So

• the first term (n = 1) is a₁ = 3 + 6•(1 - 1) = 3

• the second term (n = 2) is a₂ = 3 + 6•(2 - 1) = 9

• the third term (n = 3) is a₃ = 3 + 6•(3 - 1) = 15

• the fourth term (n = 4) is a₄ = 3 + 6•(4 - 1) = 21

• the fifth term (n = 5) is a₅ = 3 + 6•(5 - 1) = 27

The common difference between terms is what you get from subtracting consecutive terms in the sequence, or the number [tex]a_n-a_{n-1}[/tex]. Just by taking any two consecutive numbers from above, you have d = 6, since

9 - 3 = 6

15 - 9 = 6

and so on. More generally,

[tex]a_n-a_{n-1}=(3+6\cdot(n-1)) - (3+6\cdot(n-2))=6\cdot((n-1)-(n-2))=6[/tex]

Answer: 9

Step-by-step explanation:

[tex]\displaystyle\\6\div\frac{2}{3}=\\\\ 6*\frac{3}{2}=\\\\ \frac{(6)(3)}{2}=\\\\ \frac{(2)(3)(3)}{2} =\\\\(3)(3)=\\\\9[/tex]

Answer:

you didnt put a pic bro how can we answer

Step-by-step explanation:

the slope is (y coordinate change / x coordinate change) when going from on point on the line to another.

it does not matter in what direction we go, but it is important to keep the same direction for the x and for the y comparison.

so, because I prefer to go from left to right, let's go from

(-16, 8) to (-3, -4) :

x changes by +13 (from -16 to -3).

y changes by -12 (from 8 to -4).

so, the slope is

-12/+13 = -12/13

Answer:

It's 78.50 or either 78.54

Step-by-step explanation:

Answer:

m

Step-by-step explanation:

Answer:

750.88 (rounded to 2 d.p.)

Step-by-step explanation:

100% --- 731

100% + 7% --- [tex]\frac{100+7}{100}[/tex] × 731 = 782.17

100% --- 782.17

100% - 4% --- [tex]\frac{100-4}{100}[/tex] × 782.17 = 750.88 (rounded to 2 d.p.)

Answer:

A

Step-by-step explanation:

Answer:

the cosine of x is 60

Step-by-step explanation:

Answer:

c) x/z

Step-by-step explanation:

Answer

28 cm³ water entered the tank between 2 and 8 minutes;

Explanation

Rate of flow of water r(t) = dV/dt = 3√(t/2);

Flow of water between 2 and 8 minutes;

[tex]\int\limits dV = \int\limits^8_2 {3\sqrt{t/2} } \, dx[/tex]

[tex]V = 3/\sqrt{2} \int\limits^8_2 {\sqrt{t} } \, dt\\[/tex]

[tex]\\V = 2/\sqrt{2} (8^{3/2}- 2^{3/2} )\\[/tex]

V = 28 cm³

The flow rate of a liquid is how a whole lot fluid passes through a place in a specific time. float fee can be articulated in either in terms of velocity and cross-sectional place, or time and quantity. As liquids are incompressible, the price of circulate an area must be equal to the rate of waft out of an area.

How do I calculate flow rate?

Rate is the flow rate or speed of the water, using the unit “meters per second. “ For example: The object travels a 5 meter length of stream in 8 seconds. Divide 5 (length traveled) by 8 (time it took to travel the distance) for an answer of .

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