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2 years ago

If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a

Mathematics

1 answer:

PtichkaEL [24]2 years ago

6 0

Answer:

Step-by-step explanation:

$(a^2-1)x^2+(a-1)x+a^2-4a+3=0\\\\Calculate\ and\ identify\ the\ polynomials\\\\\Longleftrightarrow\ a^2x^2-x^2+ax-x+a^2-4a+3=0\\\\\Longleftrightarrow\ a^2x^2+ax+a^2-4a+3=x^2+x+0\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}a^2&=&1\\a&=&1\\a^2-4a+3&=&0\\\end{array} \right.\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}(a-1)(a+1)&=&0\\a-1&=&0\\(a-1)(a-3)&=&0\\\end{array} \right.\\\\\\We\ must\ exclude\ a=-1\ and\ a=3\ (not\ solution)\\\Longrightarrow\ a=1\\$

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A county's population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential

aliina [53]

Let t=number of years since 1991.
Then
P(t)=147 e^(kt) ... in millions
P(0)=147 e^(0)=147
P(7)=147 e^(7k)=153
e^(7k)=(153/147)
take ln both sides
ln(e^(7k))=ln(153/147)
7k=0.0400 => k=0.005715

Year 2017=>t=2017-1991=26
P(26)=147e^(26*.005715)=170.55
Answer: in 2017, the projected population is 170.55 millions.

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3 years ago

A kitten's weight increase by 12% each week for 4 mouths the little currently weighs 2.6 pounds which will not calculate how muc

krok68 [10]

Answer:

a. 2.6(0.12)

Step-by-step explanation:

Check all of the other answers: b. c. and d. are variations of equations that equal to 2.912. 2.6(0.12) is not the correct equation because it equals to 0.312. The kitten‘s weight must increase, so that is the incorrect equation.

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2 years ago

Round the whole number to the given place. 75,801,300 to the nearest million

valina [46]

Answer:

76,000,000

Step-by-step explanation:

Look at the 100,000 place and see whether to round up or down - 8 is larger than 5, therefore 75,000,000 gets rounded up to 76,000,000

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2 years ago

On a particular game show, there are 8 covered buckets and 2 of them contain a ball.

kobusy [5.1K]

Answer:

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

Step-by-step explanation:

The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

8 covered buckets, so N = 8.

4 buckets are selected, so n = 4.

2 contain a ball, which means that k = 2.

Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,8,4,2) = \frac{C_{2,2}*C_{6,2}}{C_{8,2}} = 0.2143$

0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.

7 0

2 years ago

PLESE HELP ASAP! WILL GIVE BRAINLIEST AND RATE!!

melisa1 [442]

The third option since they both will cross at 5-10 on the graph

3 0

2 years ago

If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a​

If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a