Mathematics, 05.12.2019 12:31 proutyhaylee

Explain y u got the answer you very much.

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ANS: power of a quotient property

(x/y)^n = x^n / y ^n ( power of quotient )

x^m/x^n = x^(m-n) (Quotient of power)

x^m x^n = x^(m+n) (Product of powers) < Same base >

x^(m^n) (Power of Power)

In your case you have (2/5)^3 -> 2/5 is called a quotient ( fraction ) when you raise it to power ( ^3) it's power of quotient

Power = multiple repetitions of multiplication

(2/5)^3 = 2/5 multiplied by itself 3 times = 2/5 * 2/5 * 2/5

$\frac{2}{5} \frac{2}{5} \frac{2}{5}$

in multiplication you simply multiply all terms in the denominator times each other and all terms in the nominator times each other
$\frac{2 * 2 * 2}{5 * 5* 5}$

we know that repetitive multiplication = power , we have 3 terms in the denominator 2 2 2

so = 2^3 ( 3 because it's repeated 3 times )

same for the denominator we get 5^3

$\frac{2^3}{5^3}$

2^3 = 2 x 2 x 2 = 8

5^3 = 5 x 5 x 5 = 125

= 8/125

Proving such property in general requires the use of Proof by induction in which you have 3 basic steps < basic step (proof for 1 or 0) , assume true for n , proof for n + 1 or simple induction start from 0 repeat until you have a pattern and induce the general formula)

x/y * x/y = x^2/y^2 = (x/y)^2

x/y * x/y * x/y = x^3/y^3 = (x/y)^3

......

x/y * x/y * x/y * ...... n = (x/y)^n

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

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

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

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).

$1=-0+4$

$1=4$

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 $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

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

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

a .4y4

hope this !

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