Find the missing number so that the equation has no solutions. __x+ 3 = 5x+19

Mathematics

1 answer:

cricket20 [7]3 years ago

7 0

Answer:

Step-by-step explanation:

The given equation is:__x+ 3 = 5x+19

Let the missing number be k, then

$kx + 3 = 5x + 19$

Combine like terms to get:

$kx - 5x = 19 - 3$

$(k - 5)x = 16$

For the equation to have no solution, the coefficient of x must be zero.

$k - 5 = 0$

$k = 5$

Therefore the missing number is 5

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A circle centered at the origin contains the point (0,-9). Does (8, sqr 17) also lie on the circle?

Reptile [31]

Check the picture below.

since the circle is centered at the (0,0) origin, and a point on it is at (0, -9), its radius is simple the distance between those two, or r = 9.

if the second point is also on the circle, it must also be 9 units away from the origin.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{\sqrt{17}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(8-0)^2+(\sqrt{17}-0)^2}\implies d=\sqrt{8^2+(\sqrt{17})^2} \\\\\\ d=\sqrt{64+17}\implies d=\sqrt{81}\implies d=9~~\textit{\Large \checkmark}$