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vfiekz [6]
3 years ago
11

Write the number 0.5 in the form mc003-1.jpg, using integers, to show that it is a rational number.

Mathematics
1 answer:
Tasya [4]3 years ago
6 0
If x=0.5, then 10x=5, and so x=\dfrac5{10}=\dfrac5{5\times2}=\dfrac12.
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Solve the equation: k^2+5k+13=0
mr_godi [17]

Step-by-step explanation:

k² + 5k + 13 = 0

Using the quadratic formula which is

x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}  \\

From the question

a = 1 , b = 5 , c = 13

So we have

k =  \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(1)(13) } }{2(1)}  \\  =  \frac{ - 5 \pm \sqrt{25 - 52} }{2}  \\  =  \frac{ - 5 \pm \sqrt{ - 27} }{2}  \:  \:  \:  \:  \:  \:  \\  =  \frac{ - 5  \pm3 \sqrt{3}  \: i}{2}  \:  \:  \:  \:  \:  \:

<u>Separate the solutions</u>

k_1 =  \frac{ - 5 + 3 \sqrt{3} \: i }{2}  \:  \:  \:  \: or \\ k_2 =  \frac{ - 5 - 3 \sqrt{3}  \: i}{2}

The equation has complex roots

<u>Separate the real and imaginary parts</u>

We have the final answer as

k_1 =  -  \frac{5}{2}  +  \frac{3 \sqrt{3} }{2}  \: i \:  \:  \:  \: or \\ k_2 =  -  \frac{5}{2}  -  \frac{3 \sqrt{3} }{2}  \: i

Hope this helps you

8 0
3 years ago
4 hours to 30 minutes
arlik [135]

Answer:

3 hours and 30 minutes

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
How many solutions does have 3x-6=3(x-2)<br>​
Anarel [89]

Answer:

Infinite.

Step-by-step explanation:

3x-6=3\left(x-2\right)

Expand:

3x-6=3x-6

Add 6 to both sides:

3x-6+6=3x-6+6

3x=3x

Subtract 3x from both sides:

3x-3x=3x-3x

0=0

No matter what x is, it doesn't affect the answer. Thus, the equation is true for all values of x.

3 0
3 years ago
15600=x (x+1)(x+2) What is x?
Andrew [12]
The answer is x = 24
4 0
3 years ago
Read 2 more answers
insurance company checks police records on 559 accidents selected at random and notes that teenagers were at the wheel in 91 of
ss7ja [257]

Answer: (13.22\%,\ 19.34\%)

Step-by-step explanation:

Given : Sample space : n= 559

Sample proportion : \hat{p}=\dfrac{91}{559}=0.162790697674\approx0.1628

=16.28\%

Significance level : \alpha= 1-0.95=0.05

Critical value : z_{\alpha/2}=1.96

Confidence level for population proportion:-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.1628\pm (1.96)\sqrt{\dfrac{0.1628(1-0.1628)}{559}}\\\\=0.1628\pm0.030604971367\\\\\approx 0.1628\pm0.0306=(0.1322,\ 0.1934)=(13.22\%,\ 19.34\%)

Hence, 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.= (13.22\%,\ 19.34\%)

7 0
3 years ago
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