To solve this problem, we need to translate the given information into a system of inequalities and then graph the solution on the coordinate plane provided. John exercises for at least 10 hours each week. This means the total time spent on cardiovascular work (x) and weight training (y) must be greater than or equal to 10 hours: \[ x + y \geq 10 \] He spends at most 12 hours doing cardiovascular work, which means: \[ x \leq 12 \] He spends at most 3 hours on weight training, which means: \[ y \leq 3 \] Now, let's graph these inequalities: 1. For \( x + y \geq 10 \), we draw a line where \( x + y = 10 \). We can find two points by setting \( x \) and \( y \) to 0: If \( x = 0 \): \[ 0 + y = 10 \] \[ y = 10 \] So one point is (0, 10). If \( y = 0 \): \[ x + 0 = 10 \] \[ x = 10 \] So another point is (10, 0). Draw a solid line through these points since the inequality includes the equal sign (\( \geq \)). The region above and to the right of this line will be shaded because it represents the values where \( x + y \) is greater than or equal to 10. 2. For \( x \leq 12 \), draw a solid vertical line at \( x = 12 \) and shade to the left, as all values of \( x \) must be less than or equal to 12. 3. For \( y \leq 3 \), draw a solid horizontal line at \( y = 3 \) and shade below, as all values of \( y \) must be less than or equal to 3. The solution to the system of inequalities is the region where all shaded areas overlap. This region will be a polygonal shape on the graph, bounded by the lines \( x + y = 10 \), \( x = 12 \), and \( y = 3 \). The vertices of this polygon will be at the points where these lines intersect, which are (12, 0), (7, 3), and (0, 3). Since I cannot physically shade the region on the image you provided, you would shade the region on your graph paper that is to the left of \( x = 12 \), below \( y = 3 \), and above and to the right of the line \( x + y = 10 \). This shaded region represents all possible combinations of hours John can spend on cardiovascular work and weight training that satisfy the given conditions.

To solve this problem, we need to translate the given information into a system of inequalities and then graph the solution on the coordinate plane provided. Elsa exercises for at least 12 hours each week. This means the total time spent on cardiovascular work (x) and weight training (y) must be greater than or equal to 12 hours: \[ x + y \geq 12 \] She spends at most 8 hours on weight training, which means: \[ y \leq 8 \] She spends at most 10 hours doing cardiovascular work, which means: \[ x \leq 10 \] Now, let's graph these inequalities: 1. For \( x + y \geq 12 \), we draw a line where \( x + y = 12 \). We can find two points by setting \( x \) and \( y \) to 0: If \( x = 0 \): \[ 0 + y = 12 \] \[ y = 12 \] So one point is (0, 12). If \( y = 0 \): \[ x + 0 = 12 \] \[ x = 12 \] So another point is (12, 0). Draw a solid line through these points since the inequality includes the equal sign (\( \geq \)). The region above and to the right of this line will be shaded because it represents the values where \( x + y \) is greater than or equal to 12. 2. For \( y \leq 8 \), draw a solid horizontal line at \( y = 8 \) and shade below, as all values of \( y \) must be less than or equal to 8. 3. For \( x \leq 10 \), draw a solid vertical line at \( x = 10 \) and shade to the left, as all values of \( x \) must be less than or equal to 10. The solution to the system of inequalities is the region where all shaded areas overlap. This region will be a polygonal shape on the graph, bounded by the lines \( x + y = 12 \), \( x = 10 \), and \( y = 8 \). The vertices of this polygon will be at the points where these lines intersect, which are (10, 2), (4, 8), and (2, 10), and where each of the lines intersects the axes at (10, 0) and (0, 8). Since I cannot physically shade the region on the image you provided, you would shade the region on your graph paper that is to the left of \( x = 10 \), below \( y = 8 \), and above and to the right of the line \( x + y = 12 \). This shaded region represents all possible combinations of hours Elsa can spend on cardiovascular work and weight training that satisfy the given conditions.

A woodworking artist makes two types of carvings: type X and type Y. He spends 3 hours making each type X carving and 2 hours making each type Y carving, and he can spend up to 30 hours each week making carvings. His materials cost him $5 for each type X carving and $7 for each type Y carving, and he must keep his weekly cost for materials to $105 or less. If x is the number of type X carvings he makes in a week and y is the number of type Y carvings he makes in a week, which of the following systems of inequalities models this situation?A.3x + 2y ≥ 30, 5x + 7y ≥ 105B.3x + 2y ≥ 30, 5x + 7y ≤ 105C.3x + 2y ≤ 30, 5x + 7y ≤ 105D.3x + 2y ≤ 30, 5x + 7y ≥ 105SUBMITarrow_backPREVIOUS

SolutionStep 1:We know the following.The surfboard costs $249$249.Adam has $50$50.His job pays $6.50$6.50 per hour.We want to know how many hours Adam needs to work to buy the surfboard.Let x=𝑥= the time expressed in hours.Let y=𝑦= Adam earningsThe equation of this line is: y=6.50x+50𝑦=6.50𝑥+50Step 2: We can solve this problem by making a graph that shows the number of hours spent working on the horizontal axis and Adam’s earnings on the vertical axis.Adam has $50$50 at the beginning. This is the Answer 1 Question 5: (0,50)(0,50).He earns $6.50$6.50 per hour. This is the Answer 2 Question 5 of the line.We can graph this line using the slope-intercept method. We graph the y𝑦−intercept of (0,50)(0,50), and we know that for each unit in the horizontal direction, the line rises by Answer 3 Question 5 units in the vertical direction. Here is the line that describes this situation.

Norman wants to spend some time drawing and using the computer before dinner.        Dinner will be ready in 45 minutes or less.        He wants to spend at least 25 minutes drawing.Which graph represents the amounts of time Norman can spend drawing and using the computer?

Graph the feasible region subject to the following constraints.6𝑥 − 8𝑦 ≤ 12 ; 3𝑥 + 4𝑦 ≥ 6 ; 𝑥 ≥ 0 ; 𝑦 ≥ 0