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  1.Given the inequalities  I. 3x-y<5  II.2x-3y>-2...

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jakielegs | Student, Grade 11 | eNoter

Posted October 3, 2010 at 11:14 PM via web

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1.Given the inequalities
 I. 3x-y<5
 II.2x-3y>-2
III.x-6y(_>)-28
     (2,5) satisfies
2. can a graph be plotted for the inequality 3x-4y-8(>_)0?(thank you)
 
3.State an ordered pair that satisfies the inequality 3x-4y(<_)-4?
 
4. Snow Rider Winter Sports Co. makes skis and snowboards. In any given month, the total number of skis and boards produced is 300. Draw the correct graph that best describes this situation? 

 

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william1941 | College Teacher | Valedictorian

Posted October 3, 2010 at 11:24 PM (Answer #1)

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The inequalities given in the question are:

3x-y<5

2x-3y>-2

x-6y(_>)-28

Now the coordinates of the point (2,5) if substituted in 3x- y gives 6 - 5 = 1 which is less than 5. So the inequality has been satisfied.

Substituting (2,5) in 2x - 3y = 4 - 15 = -11 which is not greater than -2. So the second inequality is not satisfied.

Substituting (2,5) in x- 6y = 2 - 30 = -28. Now by (_>) if you mean greater than or equal to the relation is satisfied.

2. For plotting the graph first express the equation as y in terms of x. Now find the values of x that satisfy it and mark those points.

3. An ordered pair that satisfies 3x-4y(<_)-4 is (0, 1)

4. Take the number of skis as x and snow boards as y . Now x+y =300. This is the equation that you have to draw the graph for.

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neela | High School Teacher | Valedictorian

Posted October 4, 2010 at 12:01 AM (Answer #2)

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1.Given the inequalities  I. 3x-y<5  II.2x-3y>-2 III.x-6y(_>)-28      (2,5) satisfies Ans:  We substitute the given coordinates on the LHS  find the values. Coparing the value with right side of the inequality, we conclude whether the inequality is satishied : (I)3x-y = 3*2-5 = 10-5 = 5. 5< 5 is not correct . So (2, 5) does not satisythe inequality. (II) 2*2-3*5 = 4-15 = -11 <-2 is true. So (2,5) satisfy the inequality. (III) 2-6*5 = 4-30 = -26 > -28. True satisfies.

2. can a graph be plotted for the inequality 3x-4y-8(>_)0?(thank you)  We draw the graph for 3x-4y-8 = 0. 3x-4y-8 > 0 is  same as: 3x-8> 4y. Or 4y < 3x-8. So all the points below the line (not the points  on the  are on the line) satisfy this inequality.    3.State an ordered pair that satisfies the inequality 3x-4y(<_)-4?

 3x-4y < -4 :  x =  (0, 2) , as 3*0-4*2 = -5 which is < -4.

  4. Snow Rider Winter Sports Co. makes skis and snowboards. In any given month, the total number of skis and boards produced is 300. Draw the correct graph that best describes this situation?    Sorry no facility with us to  draw the graph. We give few ordered pairs.   X axis represents skips. Y axis represents snowboards. Please plot them:   x :        50          100         150        200 y:        250         200         150        100 The required equation is x+y = 300. which has slope of  -1 , as you can write this equation in  the slope intercept form :y = -1*x+300. The equation (or graph) makes x intercept at  -300 on xaxis. and y intercept at y = 300 on Y axis. 

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giorgiana1976 | College Teacher | Valedictorian

Posted October 3, 2010 at 11:28 PM (Answer #3)

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To verify if the point (2,5) is the solution of the system of inequalities, we'll simply substitute x by 2 and y by 5 in each inequality, as it follows:

3*2 - 5<5

6 - 5 < 5

1 < 5

So, (2,5) verify the first inequality.

II. 2*2 - 3*5 > -2 4 - 15 > -2 -11 > -2 As we can notice, -11 < -2, so the interval (2,5) doesn't verify the second inequality. III. 2 - 6*5(_>)-28 2 - 30 = -28 -28 = -28 The interval  (2,5) verify the 3rd inequality.

To plot the graph, we'll have to re-write the inequality.

3x-4y-8 >= 0

We'll isolate -4y to the left side. For this reason, we'll subtract 3x - 8 both sides:

-4y >= -3x + 8

We'll multiply by -1 and we'll change the direction of the inequality:

4y =< 3x - 8

We'll divide by 4:

y =< 3x/4 - 2

Now, we'll input values for x and we'll find values for y.

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