Find the values for a, b, and c that complete the simplification.

a = 6, b = 4, and c = 2

Step-by-step explanation:

The given expression is

\sqrt{x^{12}y^{9}z^{5}}=(x^{a}y^bz^c)\sqrt{yz}           (1)

It can be written as

\sqrt{x^{12}\cdot y^{8}\cdot y\cdot z^{4}\cdot z}

\sqrt{x^{12}\cdot y^{8}\cdot z^{4}\cdot y\cdot z}

\sqrt{(x^{6})^2\cdot (y^{4})^2\cdot (z^{2})^2\cdot y\cdot z}     [\because (a^m)^n=a^{mn}]

\sqrt{(x^{6}y^4z^2)^2\cdot y\cdot z}          [\because a^xb^x=(ab)^x]

(x^{6}y^4z^2)\sqrt{yz}               (2)       [\because \sqrt{x^2}=x]

0.02040816326

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form