Mathematics, 17.09.2019 17:20 kad3n

On a coordinate plane, 2 straight lines are shown. the first solid line has a positive slope and goes through (0, 3) and (3, 4). everything above the line is shaded. the second dashed line has a positive slope and goes through (0, negative 2) and (1, 1). everything to the right of the line is shaded. which system of linear inequalities is represented by the graph? y > one-thirdx + 3 and 3x – y > 2 y > one-halfx + 3 and 3x – y > 2 y > one-thirdx + 3 and 3x + y > 2 y > one-thirdx + 3 and 2x – y > 2

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Answer from: briiiii7410

$y\geq\dfrac{1}{3}x+3\\\\3x-y2$

Step-by-step explanation:

Equation of line passes through points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Given : The first solid line (≤ or ≥) has a positive slope and goes through (0, 3) and (3, 4).

$(y-3)=\dfrac{4-3}{3-0}(x-0)\\\\\Rightarrow\ y-3=\dfrac{1}{3}x\\\\\Rightarrow\ y-\dfrac{1}{3}x=3$

Also, Everything above the line is shaded .

i.e. the inequality represents the first graph: $y\geq\dfrac{1}{3}x+3$

The second dashed line (< or >) has a positive slope and goes through (0, - 2) and (1, 1).

$(y-(-2))=\dfrac{1-(-2)}{1-0}(x-(0))\\\\\Rightarrow\ y+2=\dfrac{1+2}{1}x\\\\\Rightarrow\ 3x-y=2$

Everything to the right of the line is shaded.

i.e. inequality represents the second graph : 3x-y2

Hence, the system of linear inequalities is represented by the graph :

$y\geq\dfrac{1}{3}x+3\\\\3x-y2$

Answer from: natishtaylor1p8dirz

On a coordinate plane, when two straight line are drawn the, the slope of the line will be the derivative and the values of the points on the line will be given by the shaded region.

The system of linear inequalities is represented by the graph is:

$y\geq \frac{1}{3}x+3$

3x-y 2

Given information:

Two straight lines are given,

The first solid line has a positive slope.

The points (0,3) and (3,4)

Now, the equation of line passes through points (a,b) and (c,d) is given by:

$(y-b)=\frac{d-b}{c-a}(x-a)$

Now ,

On putting the values in above equation:

$(y-3)=\frac{4-3}{3-0}(x-0)\\(y-3)=\frac{1}{3}x\\y-\frac{1}{3}x=3$

Also, the shaded region id above this line

Hence, the inequality represents the graph is $y\geq \frac{1}{3}x+3$

Now for the second point:

The equation can be written as:

$(y-(-2))=\frac{1-(-2)}{1-0}(x-0)\\(y+2)=\frac{3}{1}x\\3x-y=2$

As, the shaded region is right to the line

Hence, inequality represents the second graph is 3x-y 2

Hence, The system of linear inequalities is represented by the graph is:

$y\geq \frac{1}{3}x+3$ 3x-y 2

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Answer from: Quest

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

Answer from: Quest

X= 2 he can buy 2 packs of cards for $12 and an action figure for $3 so he would spend $15 in total plus the free poster

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