Question

Question 1 (Multiple Choice Worth 2 points)

Answer 1

1. 4c + 6a < = 120
    4c + 4a < = 100
    if u sub in 20 for c and 6 for a, u will find that the answer is : No,because the bike order does not meet the restrictions of 4c + 6a < = 120 and 4c + 4a < = 100. 
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2. 2x + y < 10
    2x - 4y > 8
    answers are : E,F,G
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3. y < = -2x + 3
    y < = x + 3
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4. y > = -3x + 1
    y < = 1 / 2x + 3
    answer : Both lines are solid. 1 lines passes thru (-2,2) and (0,3), shaded below the line. Other line passes thru (0,1) and (1,-2) and is shaded above the line....I am not 100% sure on this one
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5.y < -3x + 3
   y < x + 2
   answer is (1,-5)
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6. y < = 2x - 2
    y > -x + 3
    
   
    
    

Answer 2

The correct answers are:

#1) No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100;

#2) E, F and G;

#3) y ≤ −2x + 3 and y ≤ x + 3;

#4) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.;

#5) (1, -5); and

#6) y ≤ 2x − 2 and y > −x + 3.

Explanation:

#1) The first inequality, representing the number of hours it takes to build the bikes, is 4c+6a ≤ 120. This is because each child bike takes 4 hours to build and each adult bike takes 6 hours to build, and they have up to 120 hours to build bikes.

The second inequality, representing the number of hours it takes to test, is 4c+4a ≤ 100. This is because each child bike takes 4 hours to test and each adult bike takes 4 hours to test, and they have up to 100 hours to test bikes.

Using 20 for c and 6 for a, the first inequality gives us 4(20)+6(6)≤120; 80+36≤120; 116≤120. This is true.

The second inequality gives us 4(20)+4(6)≤100; 80+24≤100; 104≤100. This is not true.

#2) Substituting the x-values in for x and the y-values in for y, we have:

E: 2x + y < 10 and 2x − 4y > 8; 2(4)+-2<10 and 2(4)-4(-2)>8; 8+-2<10 and 8--8>8; 6<10 and 16>8. Both of these are true statements.

F: 2x + y < 10 and 2x − 4y > 8; 2(1)+-6<10 and 2(1)-4(-6)>8; 2+-6<10 and 2--24>8; -4<10 and 26>8. Both of these are true.

G: 2x + y < 10 and 2x − 4y > 8; 2(-3)+-10<10 and 2(-3)-4(-10)>8; -6+-10<10 and -6--40>8; -16<10 and 34>8. Both of these are true.

None of the other points work when substituted in.

#4) The slope of the line through (-2,2) and (0,3) is m=(3-2)/(0--2)=1/2. The y-intercept is one of the points given, (0, 3). This makes the equation y=1/2x+3. Since it is graphed below the line, the inequality is y≤1/2x+3.

The slope of the line through (0, 1) and (1, -2) is m=(-2-1)/(1-0)=-3/1=-3. The y-intercept is one of the points given, (0, 1). This makes the equation y=-3x+1. Since it is graphed above the line, the inequality is y≥-3x+1.

#5) Substituting our x-values in for x and y-values in for y, we have:

y < −3x + 3 and y < x + 2; -5<-3(1)+3 and -5<1+2; -5<-3+3 and -5<3; -5<0 and -5<3. Both of these are true.

#6) The slope of the line through (0, -2) and (1, 0) is m=(0--2)/(1-0)=2/1=2. The y-intercept is one of the points given to us, (0, -2). This makes the equation y=2x-2. Since the graph is shaded below and has a solid line, this makes it y≤2x-2.

The slope of the line through (0, 3) and (3, 0) is m=(0-3)/(3-0)=-3/3=-1. The y-intercept is one of the points given to us, (0, 3). This makes the equation y=-1x+3. Since the graph is shaded above the line and has a dashed line, this makes it y>-1x+3.