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sukhopar [10]
3 years ago
7

What should be the value of x so that the three consecutive terms will be in GP 2x+2, 16 and 64x. Also find the sum of first 10

terms if the starting term is 2x+2.
Mathematics
1 answer:
Alexxandr [17]3 years ago
5 0

Answer:

<em>x = 1 and -2</em>

<em>Sum of the first ten terms = 1,398,100</em>

Step-by-step explanation:

Given the geometric progression 2x+2, 16, 64x...

Since they are in GP, their common ratio is expressed as;

16/2x+2 = 64x/16

16/2(x+1) = 4x

8/x+1 = 4x

Cross multiply

4x(x+1) = 8

4x²+4x = 8

4x²+4x - 8 = 0

divide through by 4

x²+x - 2 = 0

Factorize

x²+2x-x- 2 = 0

x(x+2)-1(x+2) = 0

(x-1)(x+2) = 0

x = 1 and -2

Hence the values of x are 1 and -2

Get the common ratio;

r = 16/2x+2

Since x = 1

r = 16/2(1)+2

r = 16/4

r = 4

Sum of the first n terms is expressed as;

Sn = a(rⁿ-1)/r-1

a = 2x+2

a = 2(1)+2

a = 4

Substitute;

S10 = 4(4^10 - 1)/4 - 1

S10 = 4(1,048,576-1)/3

S10 = 4,194,300/3

S10 = 1,398,100

Hence the sum of the first ten terms is 1,398,100

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balandron [24]

Answer:

40 minutes

Step-by-step explanation:

Given 1 mile = 8 minutes

5 miles = (5 × 8) minutes

5 miles = 40 minutes

It would take 40 minutes to run 5 miles

7 0
3 years ago
If G is the midpoint of FH, FG= 14x + 25 and GH = 73- 2x, find FH
Alenkinab [10]
Given that G is the midpoint of FH, then:
FG=GH
hence;
14x+25=73-2x
solving for x we get:
14x+2x=73-25
16x=48
x=48/16
x=3
therefore the length FG=14x+25 will be:
14*3+25
=67
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4 0
3 years ago
Devin is buying 2 concert tickets. The concert tickets have a regular price of $40 each. Devin has a coupon that gives a 5% disc
Svetach [21]

Given :

Devin is buying 2 concert tickets. The concert tickets have a regular price of $40 each.

Devin has a coupon that gives a 5% discount off of the regular price of the tickets. He will then pay a 10% purchasing fee on the discounted price of the tickets.

To Find :

Devin's total cost of the two tickets after the discount and the fee.

Solution :

Discount on price, D = 40×0.05 = $2 .

Price of product after discount, P = $( 40 - 2 ) = $38 .

Now, total price after adding purchasing fee is :

T = P + (P×0.10)

T = 38 + (38×0.10)

T = 38 + 3.8

T = $41.8

Therefore, Devin's total cost of the two tickets after the discount and the fee is $41.8 .

Hence, this is the required solution.

5 0
3 years ago
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Use the method of ELIMINATION to solve the system. You must SHOW ALL WORK. Make sure you have an answer for both x and y.
jekas [21]

Answer:

<h3>Required <u>Answer</u><u>:</u><u>-</u></h3>

\sf 4x+8y=10\dots\dots (1)

\sf -4x+2y=-30\dots\dots (2)

  • by adding eq (1) and eq (2) we get

{:}\longrightarrow\sf 4x+8y=20

{:}\longrightarrow\sf -4x+2y=-30

<h2>__________________________</h2>

{:}\longrightarrow\sf 10y=-10

{:}\longrightarrow\sf y={\dfrac {-10}{10}}

{:}\longrightarrow{\underline{\boxed{\bf y=-1}}}

  • Substitute the value in eq (2)

{:}\longrightarrow\sf -4x+2 (-1)=-30

{:}\longrightarrow\sf -4x-2=-30

{:}\longrightarrow\sf -4x=-30+2

{:}\longrightarrow\sf -4x=-28

{:}\longrightarrow\sf x={\dfrac {-28}{-4}}

{:}\longrightarrow{\underline{\boxed{\bf x=7}}}

\therefore{\underline{\boxed{\bf (x,y)=(7,-1)}}}

6 0
3 years ago
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