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3 years ago

graph the solution to the following system of inequalities y<-2x+7, y greater than or equal to 2x - 3

Mathematics

1 answer:

Alex777 [14]3 years ago

6 0

Answer:

See attached diagram

Step-by-step explanation:

Graph the solution of the inequality $y$ First, draw the dotted line $y=-2x+7$ (dotted because the sign of the inequality is <). Then determine wich part of the coordinate plane should be shaded. Since the origin's coordinates satisfy the inequality, then this point should belong to the region (red part on the diagram).

Graph the solution of the inequality $y\ge 2x-3.$ First, draw the solid line $y=2x-3$ (solid because the sign of the inequality is ≥). Then determine wich part of the coordinate plane should be shaded. Since the origin's coordinates satisfy the inequality, then this point should belong to the region (blue part on the diagram).

The intersection of both regions is the solution of the system of two inequalities.

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<h3>Answer:</h3>

$\boxed{\pink{\sf \leadsto Yes \ there \ is \ a \ solution \ of \ the \ given \ inequality .}}$

<h3>Step-by-step explanation:</h3>

A inequality is given to us and we need to convert it into standard form and see whether if it has a solution . So let's solve the inequality.

The inequality given to us is :-

$\bf\implies |2y + 3 | - 1 \leq 0 \\\\\bf\implies |2y+3|\leq 1 \\\\\bf\implies (|2y+3|)^2 \leq 1^2 \\\\\bf\implies (2y+3)^2 \leq 1 \\\\\bf\implies (2y)^2+3^2+2(2y)(3) \leq 1 \\\\\bf\implies 4y^2+9+12y - 1 \leq 0 \\\\\bf\implies 4y^2+12y+8 \leq 0 \\\\\bf\implies 4( y^2 + 3y + 2 ) \leq 0 \\\\\bf\implies y^2+3y +2 \leq 0 \:\:\bigg\lgroup \purple{\bf Standard \ form \ of \ inequality }\bigg\rgroup \\\\\bf\implies y^2y+2y+y+2 \leq 0 \\\\\bf\implies y(y+2)+1(y+2)\leq 0 \\\\\bf\implies ( y+2)(y+1)\leq 0 \\\\\bf\implies \boxed{\red{\bf y \leq (-2) , (-1) }}$

Let's plot a graph to see its interval . Graph attached in attachment .

Now we can see that the Interval notation of would be ,

$\boxed{\boxed{\orange \tt \purple{\leadsto}y \in [-2,-1] }}$

<h3>Hence the standard form of inequality is y²+3y +2 ≤ 0 and the Solution set of the inequality is [ -2 , -1 ] .</h3>

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The data set represents the total number of pencils each student in a class needs to sharpen.

Firdavs [7]

Given:

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0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

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The correct statement that represents the box plot of the data correctly.

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We have,

0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

Divide the data in 2 equal parts.

(0, 1, 1, 1, 2), 3, (4, 4, 6, 6, 9)

Divide each parenthesis in 2 equal parts.

(0, 1), 1, (1, 2), 3, (4, 4), 6, (6, 9)

Here,

Minimum value = 0

First quartile = 1

Median = 3

Third quartile = 6

Maximum value = 9

A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 1 to 6. A line divides the box at 3.

Therefore, the correct option is D.

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3 years ago

graph the solution to the following system of inequalities y<-2x+7, y greater than or equal to 2x - 3 ​

graph the solution to the following system of inequalities y<-2x+7, y greater than or equal to 2x - 3