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3 years ago

What is the solution of the equation? (√2x-1) + 2=x

Mathematics

1 answer:

Gwar [14]3 years ago

7 0

Answer:

x = 5

Step-by-step explanation:

√(2x − 1) + 2 = x

√(2x − 1) = x − 2

2x − 1 = (x − 2)²

2x − 1 = x² − 4x + 4

0 = x² − 6x + 5

0 = (x − 1) (x − 5)

x = 1 or 5

Check for extraneous solutions.

√(2(1) − 1) + 2 = 1

√(1) + 2 = 1

3 = 1

No solution

√(2(5) − 1) + 2 = 5

√(9) + 2 = 5

5 = 5

x = 5

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Answer: 6

Step-by-step explanation:

From the question, we are informed that a band expects to put 15 songs on their next CD and that the band writes and records 60% more songs than they expect to put on the CD. Therefore, the total songs will be:

= 15 + (60% × 15)

= 15 + (0.6 × 15)

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During the editing process, 75% of the songs are removed. The total number of songs that will be there on the final CD will be:

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3 years ago

The mean number of children among a sample of 15 low-income households is 2.8. The mean number of children among a sample of 19

gtnhenbr [62]

Answer:

Step-by-step explanation:

Let's put the data as below:

n1=15 x1=2.8 s1=1.6 and s1²=2.56

n2=19 x2=2.4 s2=1.7 and s2²=2.89

alpha= 0.05

To test the hypothesis:

H0= There is no sufficient evidence that low income household have fewer children

H1=There is sufficient evidence that low income household have fewer children

Assume that population variances are equal.

the t-static for two samples,

$t=\frac{x1-x2}{Sp\sqrt{\frac{1}{n1}-\frac{1}{n2} \\} } }$ ~t with min (n1-1,n2-1)df

The pooled variance estimate Sp equals:

$Sp^{2}=\frac{(n1-1)s1^{2}+(n2-1)s2^{2} }{n1+n2-2}$

Sp²=2.7456

Sp=1.65699

Degrees of freedom=n1+n2-2=32

Under null hypothesis:

$tcal=\frac{|2.8 - 2.4|}{1.6599\sqrt{\frac{1}{15}+\frac{1}{19} } }$

$tcal=0.6989$

The critical value ttab=2.0369 for alpha=0.05

So we reject our null hypothesis H0

So there is sufficient evidence that low income households have fewer children than high income households

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