Mathematics, 19.11.2019 22:31 Itsjazzyyy001

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describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern. state which situation is linear and which is nonlinear.

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Answer from: alyea231

Step-by-step explanation:

The sum of the ages of a Mother and her son is 78 , three years ago the mother is five times as old as the son, what is their present ages?

To solve this , let the age of the mother be x and the age of the son be y , from the first statement :

x + y = 78

Three years ago , the mother will be x- 3 and the son will be y - 3 , from the second statement:

x - 3 = 5 ( y-3)

x- 3 = 5y - 15

x - 5y = -12

The resulting equations are

x + y = 78

x - 5y = -12

This is called a simultaneous linear equation , that means it is a linear equation.

The side of a square is xcm , if the difference between the area and the perimeter is 12 , find the legth of its side.

Interpretation:

The formula for the area of a square is $l^{2}$ and the perimeter is 4l , from the question , we have

$x^{2}$ - 4x = 12

This is not a linear equation , it is simply a quadratic equation , so the situation is non linear

Answer from: Quest

What are the options

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

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