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3 years ago

For what values of k will the pair of equations kx + 3y = k-3 , 12x + ky = k have no solution

1 answer:

5 0

$\left\{\begin{array}{ccc}kx+3y=k-3\\12x+ky=k\end{array}\right\\\\ W=\left|\begin{array}{ccc}k&3\\12&k\end{array}\right|=k^2-3\cdot12=k^2-36\\\\W_x=\left|\begin{array}{ccc}k-3&3\\k&k\end{array}\right|=k(k-3)-3k=k^2-6k\\\\W_y=\left|\begin{array}{ccc}k&k-3\\12&k\end{array}\right|=k^2-12(k-3)=k^2-12k+36\\\\System\ of\ equals\ hasn't\ solution\ when\:\\W=0\ and\ (W_x=0\ or\ W_y=0)$

$W=0\iff k^2-36=0\to k^2=36\to k=-6\ or\ k=6\\\\W_x=0\iff k^2-6k=0\to k(k-6)=0\to k=0\ or\ k=6\\\\W_y=0\iff k^2-12k+36=0\to(k-6)^2=0\to k=6$

$Answer:\\\\for\ k=6\ the\ system\ has\ infinity\ solutions\\\\for\ k=-6\ system\ has\ no\ solution.$

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Lauren has a bouquet of flowers. 1/5 of the flowers are red. 3/10 of the flowers are white. The rest are yellow. Lauren’s bouque

ss7ja [257]

Answer:

36 flowers

Step-by-step explanation:

Given

$Red = \frac{1}{5}$

$White = \frac{3}{10}$

$Yellow = 18$

Required

Determine the number of flowers

First, we need to determine the fraction of flowers that are yellow;

$R + W + Y = 1$

$\frac{1}{5} + \frac{3}{10} + Y = 1$

$\frac{2+ 3}{10} + Y = 1$

$\frac{5}{10} + Y = 1$

$Y = 1 - \frac{5}{10}$

$Y = \frac{10 -5}{10}$

$Y = \frac{5}{10}$

$Y = \frac{1}{2}$

Let the number of flowers by N;

The yellow flowers can be represented as;

$18 = \frac{1}{2} * N$

Solve for N

$N = \frac{18 * 2}{1}$

$N = \frac{36}{1}$

$N = 36$

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3 years ago

n office will randomly select one computer to check for viruses and other problems. Five of the office computers are less than o

Margaret [11]

The answer is 5/18

Your welcome!

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3 years ago

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g A random sample of size 16 taken from a normally distributed population revealed a sample mean of 50 and a sample variance of

Angelina_Jolie [31]

Answer:

The upper limit is

$k = 52.94$

Step-by-step explanation:

From the question we told that

The sample size is $n = 16$

The sample mean is $\= x = 50$

The sample variance is $\sigma ^2 = 36$

For a 95% confidence interval the confidence level is 95%

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table(reference- math dot armstrong dot edu), the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

Here $\sigma$ is the standard deviation which is mathematically evaluated as

$\sigma = \sqrt{\sigma^2}$

substituting values

$\sigma = \sqrt{36}$

=> $\sigma = 6$

$E = 1.96 * \frac{6}{\sqrt{16} }$

$E = 2.94$

The 95% confidence interval is mathematically represented as

$\= x - E < \mu < \= x + E$

substituting values

$50 -2.94 < \mu$

$47.06 < \mu$

The upper limit is

$k = 52.94$

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3 years ago

If the measure of angle 5 is (11 x minus 14) degrees and x = 6, which expression could represent the measure of angle 2? 3 lines

ella [17]

Answer:

(A) (8 x + 4) degrees

Step-by-step explanation:

$m \angle 5 =(11x-14)^\circ\\x=6\\m \angle 5 =(11(6)-14)^\circ=(66-14)^\circ=52^\circ\\m \angle 5 =m \angle 2$ (Vertically Opposite Angles)$

Out of the options, the one which gives a result of 52 degrees could represent the measure of angle 2.

$(A)(8 x + 4)^\circ=(8(6) + 4)^\circ=(48+4)^\circ=52^\circ\\(B)(9x+2)^\circ=(9(6) + 2)^\circ=(54+2)^\circ=56^\circ\\(C)(20x + 8)^\circ=(20(6) + 8)^\circ=(120+8)^\circ=128^\circ\\(D)(18 x + 20)^\circ=(18(6) + 20)^\circ=(108+20)^\circ=128^\circ$

We can see that only Option A gives a result of 52 degrees. Therefore, it can represent the measure of angle 2.

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pav-90 [236]

Answer:

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