10x-5=0 equation ,inverse operation,simplify,inverse operation,solution,check

Mathematics

1 answer:

sattari [20]2 years ago

8 0

Answer:

x=.5

Step-by-step explanation:

First, you need to isolate the variable term, so you have to move -5 over to the other side. Since it is subtraction on this side, you add 5 to both sides to cancel out the -5, and add it to the other side.

Now we have 10x=5. To solve for the variable, we have to divide by the number in the variable term. In this case, it is 10. 10/10 is 1, so now x is alone. We have to do the same thing on the other side. 5/10 is .5.

That's the answer! It's x=.5!

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Two perpendicular lines intersect at the origin. If the slope of the first line is -1/2, what is the equation of the second line

Dovator [93]

bearing in mind that perpendicular lines have <u>negative reciprocal</u> slopes.

now, they both intersect at 0,0, namely they both pass through it, we know the slope of the first one, so

$\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{1}\implies 2}}$

so, we're really looking for the equation of a line whose slope is 2, and runs through (0,0).

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=2(x-0)\implies y=2x$