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3 years ago

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

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

Separate the solutions

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

The equation has complex roots

Separate the real and imaginary parts

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)

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