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gtnhenbr [62]
3 years ago
6

In the figure below,

Mathematics
1 answer:
bogdanovich [222]3 years ago
8 0

Answer:

b

Step-by-step explanation:

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Can somebody prove this mathmatical induction?
Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

\sum \limits_{j=1}^k2^j=2(2^k-1)

3 step:

Check for n=k+1 whether the statement

\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)

is true.

Start with the left side:

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)

According to the 2nd step,

\sum \limits_{j=1}^k2^j=2(2^k-1)

Substitute it into the \ast

\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)

So, you have proved the initial statement

4 0
4 years ago
What is -2 = 5 / (2x+3)
LUCKY_DIMON [66]

Answer:

x = -11/4

Step-by-step explanation:

Given that:

-2 = 5 / (2x+3)

Multiplying both sides by (2x + 3)

-2(2x + 3) = 5

"-" sign will alter the inner signs

-4x -6 = 5

Adding 6 on both sides:

-4x -6 +6 = 5 + 6

-4x  = 11

Dividing both sides by -4

-4x/-4 = 11/-4

x = -11/4

i hope it will help you!

3 0
3 years ago
Amanda has at most $40 to spend on flowers. She wants to buy a pair of red rose flowers for $18 dollars and spend the rest on li
Mkey [24]

Answer:

x ≤ 2

Step-by-step explanation:

2 red rose cost  $ 18

x flowers cost $ 11x

"At most "  means ≤.

11x + 18 ≤ 40

11x ≤ 40 - 18

11x ≤ 22

x ≤ 2

5 0
3 years ago
Which expression is equivalent to 6x+8 PLZZZZZZZZZZZZ HEWLPPP!
Leto [7]
<h3>✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽</h3>

➷ Expand them all to see if you get the expression:

2(3x - 4) ==> 6x - 8

2(3x + 4) ==> 6x + 8

2(4x + 6) ==> 8x + 12

2(3x + 8) ==> 6x + 16

As you can see, the correct option is B. 2(3x + 4)

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ <u>ʜᴀɴɴᴀʜ</u> ♡

4 0
3 years ago
Read 2 more answers
Write two expressions that could be
N76 [4]

Answer:$80.24

Step-by-step explanation:68*0.18(18%)

12.24

68+12.24=$80.24

3 0
2 years ago
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