Simplify (12) 12). (1 point)

7, 9, 13 are the first three terms of a sequence with

ivann1987 [24]

(i) The simultaneous equations in a, b and c are a+b+c = 7 , 4a+2b+c = 9 & 9a+3b+c = 13

(ii) Expression for nth term = n²-n+7

The first three terms of the sequence are 7, 9, 13

nth term = an²+bn+c

If we put n = 1 then,

1st term = a(1)²+b+c

⇒ a+b+c = 7 ......(1)

If we put n = 2 then,

2nd term = a(2)²+b×2+c

⇒ 4a+2b+c = 9 ........(2)

3rd term = a(3)²+b×3+c

⇒ 9a+3b+c = 13 .......(3)

Multiplying 4 with (1) and subtract (2) from (1) we get,

(4a+4b+4c)-(4a+2b+c)=28-9

⇒ 4a+4b+4c-4a-2b-c=19

⇒ 2b+3c=19 .....(4)

Multiplying 9 with (1) and subtract (3) from (1) we get,

(9a+9b+9c)-(9a+3b+c)=63-13

⇒ 9a+9b+9c-9a-3b-c=50

⇒ 6b+8c=50

⇒ 3b+4c=25 .....(5)

Multiplying 3 with (4) and multiplying 2 with (5), then subtract (5) from (4),

3(2b+3c)-2(3b+4c)=57-50

⇒ 6b+9c-6b-8c=7

⇒ c = 7

From (5),

3b+28 = 25

⇒ 3b = -3

⇒ b = -1

From (1),

a+(-1)+7 = 7

⇒ a-1=0

⇒ a=1

So, nth term = n²-n+7

Learn more about sequence here :

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8 0

2 years ago

What is this answer ?

cluponka [151]

Answer:

Step-by-step explanation:

A isn't. You have that right. A sinusoidal wave is one that creates a sine curve.

Absolute value curves look sort of like a spear head.

7 0

3 years ago

Your friend attempted to factor an expression as shown. Find the error in your friends work. Then factor the expression correctl

loris [4]

Answer:

Third step is incorrect. The correct factored form is (x-1)(2x-5).

Step-by-step explanation:

The given expression is

$2x^2-7x+5$

We need to find the factored form of this expression.

Step 1: Given

$2x^2-7x+5$

Step 2: Splitting the middle term method, the middle term can be written as (-5x-2x).

$2x^2-5x-2x+5$

$(2x^2-5x)+(-2x+5)$

Step 3: Taking out common factors from each parenthesis.

$x(2x-5)-1(2x-5)$

Step 4: Taking out common factors.

$(x-1)(2x-5)$

Therefore, the third step is incorrect. The correct factored form is (x-1)(2x-5).

3 0

3 years ago

What should I buy? A study conducted by a research group in a recent year reported that 57% of cell phone owners used their phon

vovangra [49]

Answer:

Hence, the probability that seven or more of them used their phones for guidance on purchasing decisions is 0.7887

Step-by-step explanation:

We are given the following information in the question:

We treat people using phones in the store for guidance as a success.

P(People use phone for guidance) = 57% = 0.57

Then the number of people follows a binomial distribution, where

Formula:

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 14 and x = 7

We have to evaluate:

$P(x \geq 7) = P(x = 7) + P(x = 8) + P(x = 9) + P(x = 10) + P(x =11) + P(x = 12) + P(x = 13) + P(x = 14)\\= \binom{14}{7}(0.57)^7(1-0.57)^7 + \binom{14}{8}(0.57)^8(1-0.57)^6 + \binom{14}{7}(0.57)^9(1-0.57)^5 + \binom{14}{7}(0.57)^{10}(1-0.57)^4 + \binom{14}{7}(0.57)^{11}(1-0.79)^3 + \binom{14}{7}(0.57)^{12}(1-0.57)^2 + \binom{14}{7}(0.57)^{13}(1-0.57)^1 + \binom{14}{7}(0.57)^{14}(1-0.57)^0\\= 0.7887 = 78.67\%$

Hence, the probability that seven or more of them used their phones for guidance on purchasing decisions is 0.7887

5 0

3 years ago

When Jake's puppy was born she weighed 1.2 pounds in two months she weighed 11.15 pounds how much weight did Jack jacks pub agai

natulia [17]

They gained 9.95 pounds.

7 0

3 years ago

Read 2 more answers

Simplify (12) 12). (1 point)​

Simplify (12) 12). (1 point)