Abrace for a shelf has the shape of a right triangle. it’s hypotenuse is 12 inches long and the two legs are equal in length. how long are the legs of the triangle

The sides of a right triangle can be represented by the equation a^2+b^2=c^2, where c is the hypotenuse and a and b are the legs.  

Since both legs are the same in this equation, we can pick one variable to combine both and add the terms.  The equation would become:

x^4=c^2

We know c=12 so we can plug in and solve for x:

x^4=12^2

x^4=144

x=3.4641

The legs of the triangle are about 3.4641 in long.

Hope this helps!!

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is