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IRINA_888 [86]
2 years ago
6

((Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Mathematics
1 answer:
defon2 years ago
8 0

Answer:

C

Step-by-step explanation:

The first term = 1500

2nd term = 900

3rd term = 540

The series is a GP.

r = 900/1500 = 0.6

The sum of the first 10 term, S₁₀, is as calculated below.

Sn = a(1-rⁿ)/(1-r)

S₁₀ = 1500(1 - 0.6¹⁰)/(1 - 0.6)

      = 1500 × 0.9939/0.4

       = 3,727.125 m

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6, 12, 18 and 24 are the first four multiples of 6.<br><br> What are the next 2 multiples?
kondor19780726 [428]

Answer:

30 and 36

Step-by-step explanation:

six times two equals 12

6 * 3 = 18

and six times four equals 24.

to get the next two multiples, You need to multiply 6 by 5, and then 6

6 * 5 = 30 and 6 * 6 = 36

3 0
2 years ago
What is the perimeter, in terms of x, of the rectangle shown here?​
MaRussiya [10]
8x^2+10x-18
The explanation is in the picture below if needed

3 0
2 years ago
Which of the following is equivalent to (5)^7/3? 5^-4<br> 5^4<br> ^7squroot5^3<br> ^3squroot5^7​
kvv77 [185]

Answer:

^7 squroot5^3

Step-by-step explanation:

5x2= 10

7÷ 3= 2.5

8 0
3 years ago
Determine if the two figures are congruent and explain your answer using transformations.
IRISSAK [1]

Answer:

Comparing each pair of lines,

AB and EF,

BC and FG,

CD and GH,

DA and HE.

For, AB and EF,

If we take a look at both the lines they are the mirror image of each other, the distance between point A and B is 1 unit upwards, and 2 unit sidewise, similarly between point E and F the distance is 1 unit upwards, and 2 unit sidewise. therefore, the length of both the lines is the same.

Also, we can use the formula, for the distance between two points on a coordinate plane,

,

As we can see in the image,

A = (-1, 1),

B = (-3, 2),

C = (-4, 4),

D = (-2, 6),

E = (2, 0),

F = (4, 1),

G = (5, 3),

H = (3, 5),

Solving using the formula,

AB = EF = √5,

BC = FG = √5,

CD = GH = √8,

DA = HE = √26,

Therefore, the length of all the sides of the polygon are the same,

Hence, the two figures are congruent.

Step-by-step explanation:

7 0
2 years ago
Find m∠STU and m∠TUA
PIT_PIT [208]

Answers:

  • angle STU = 65 degrees
  • angle TUA = 123 degrees

=========================================================

Explanation:

Let's find the expression for angle TUS in terms of x

Angle TUA has the expression 11x+2. It will add to angle TUS to get 180 degrees

(angle TUS) + (angle TUA) = 180

angle TUS = 180 - (angle TUA)

angle TUS = 180 - (11x + 2)

angle TUS = 180 - 11x - 2

angle TUS = -11x + 178

Now focus on the interior angles of triangle TUS. We have these three angles

  • T = 5x+10
  • U = -11x+178
  • S = 58

For any triangle, the interior angles always add to 180, so,

T+U+S = 180

(5x+10) + (-11x+178) + (58) = 180

(5x-11x) + (10+178+58) = 180

-6x + 246 = 180

-6x = 180-246

-6x = -66

x = -66/(-6)

x = 11

Use this x value to find the angle measures we're after:

  • angle STU = 5x+10 = 5*11+10 = 55+10 = 65 degrees
  • angle TUA = 11x+2 = 11*11+2 = 121+2 = 123 degrees

--------------------------

As an alternative route, you can apply the remote interior angle theorem. This says that adding two interior angles leads to the exterior angle that isn't adjacent to either one.

In this case, we would say

(angle STU) + (angle TSU) = angle TUA

that leads to the equation

(5x+10) + (58) = 11x+2

Solving this should lead to x = 11 to generate the angles mentioned earlier.

6 0
2 years ago
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