The legs of a right triangle xyz are 5 cm and 12 cm. triangle xyz is dilated to triangle x'y'z' by a scale factor of 2/3 . what is the area of triangle x'y'z'?

Assuming that the base is 5 cm and the height is 12 cm, so by dilating the legs by a scale factor of 2/3, the new dimensions are:

base = 5 cm * (2 / 3) = 10/3 cm

height = 12 cm * (2 / 3) = 8 cm

So the area of a right triangle is calculated using the formula:

A = b h / 2

A = (10/3) * 8 / 2

A = 13.33 cm^2

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)