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

A consultant needs to make at least $720 this week. She earns $120 for each new written piece and $60 for each review. Which of the following inequalities represents the possible combinations of reviews and new written pieces that she must complete?A.B.C.D.

Valerie is ordering salads and drinks for her friends. Salads cost $7 each, drinks cost $3 each, and there is a $5 delivery charge per order. She has $50. She buys 3 salads, and wants to figure out the maximum number of drinks she can buy.If x = number of salads and y = number of drinks, which of the following inequalities could you use to answer the problem?

Juan wants to earn more than $71 trimming trees. He charges $8 per hour and pays $9 in equipment fees. What are the possible numbers of hours Juan could trim trees?Use t for the number of hours.Write your answer as an inequality solved for t.

Maya is taking her friends to a concert. Each ticket costs $25, and souvenir T-shirts are $12 each. There is a $4 service fee for the entire purchase. She has $130. If she buys 3 tickets, what is the maximum number of T-shirts she can buy?Solve the inequality 25x + 12y + 4 130, where x = number of tickets and y = number of T-shirts, to answer the question.A.5B.12C.3D.4

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. Michael 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: \[ x + y \geq 12 \] He spends at most 9 hours on weight training, which means: \[ y \leq 9 \] He spends at most 8 hours doing cardiovascular work, which means: \[ x \leq 8 \] 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 \( y \leq 9 \), draw a solid horizontal line at \( y = 9 \) and shade below, as all values of \( y \) must be less than or equal to 9. 3. For \( x \leq 8 \), draw a solid vertical line at \( x = 8 \) and shade to the left, as all values of \( x \) must be less than or equal to 8. 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 \( x + y = 12 \), \( x = 8 \), and \( y = 9 \). The vertices of this polygon will be at the points where these lines intersect, which are (8, 4) and (3, 9), and where each of the lines intersects the axes at (8, 0) and (0, 9). 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 \( x = 8 \), below \( y = 9 \), and above and to the right of the line \( x + y = 12 \). This shaded region represents all possible combinations of hours Michael can spend on cardiovascular work and weight training that satisfy the given conditions.