Mathematics, 28.07.2019 06:30 ashtonwishman

The square of 9 less than a number is 3 less than the number. what is the number? –12 or 7 –12 or –7 –7 or 12 7 or 12

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Answer from: kitttimothy55

D: 7 or 12.

Step-by-step explanation:

Given statement "The square of 9 less than a number is 3 less than the number."

Let us assume unknown number is = n

9 less than a number = (n-9)

Square of 9 less than a number = (n-9)^2

3 less than the number = n-3.

Therefore, we can setup an equation

(n-9)^2=n-3

Let us expand (n-9)^2=(n-9)(n-9) and now foil.

(n-9)(n-9) = n^2-9n-9n+81 = n^2-18n+81

Therefore,

n^2-18n+81 = n-3.

Adding 3 and subtracting n from both sides, we get

n^2-18n-n+81+3 = n-n-3+3.

n^2-19n+84 = 0

Factoring quadratic

n^2-12n-7n+84 = 0

(n^2-12n)+(-7n+84) = 0

n(n-12) -7(n-12) =0

(n-12)(n-7) =0

Applying zero product rule, we get

n-12=0 => n=12 or

n-7=0 => n= 7.

Therefore, correct answer is 7 or 12.

Answer from: Quest

If they nenenenenenene

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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