answer：First, I need to understand the problem. A farmer used a total of 1,034 acres of land for beans, wheat, and corn in the ratio of 5:2:4, respectively. I need to find out how many acres were used for corn.To solve this, I'll start by determining the total number of parts in the given ratio. The ratio is 5:2:4, which means there are 5 parts for beans, 2 parts for wheat, and 4 parts for corn. Next, I'll calculate the total number of parts by adding them together:5 (beans) + 2 (wheat) + 4 (corn) = 11 partsNow, I know that the total land of 1,034 acres is divided into these 11 parts. To find out the size of one part, I'll divide the total acres by the total number of parts:1,034 acres ÷ 11 parts = 94 acres per partSince corn has 4 parts, I'll multiply the size of one part by the number of parts for corn:94 acres/part × 4 parts = 376 acresTherefore, 376 acres were used for corn.

answer：First, calculate the total cost for each group on Monday:- **Children on Monday:** 7 children * 3/child = 21- **Adults on Monday:** 5 adults * 4/adult = 20- **Seniors on Monday:** 3 seniors * 3/senior = 9**Total for Monday:** 21 (children) + 20 (adults) + 9 (seniors) = 50Next, calculate the total cost for each group on Tuesday before the discount:- **Children on Tuesday:** 9 children * 4/child = 36- **Adults on Tuesday:** 6 adults * 5/adult = 30- **Seniors on Tuesday:** 2 seniors * 3/senior = 6**Total for Tuesday before discount:** 36 (children) + 30 (adults) + 6 (seniors) = 72Apply the 10% discount to the total for Tuesday:- **Discount amount:** 72 * 10% = 7.2**Total for Tuesday after discount:** 72 - 7.2 = 64.8Finally, add the totals for both days to find the total money made by the zoo:**Total for both days:** 50 (Monday) + 64.8 (Tuesday) = 114.8Therefore, the zoo made boxed{114.8} in total for both days.

answer：First, I'll define the variables:- Let ( L ) represent Leo's current weight.- Let ( K ) represent Kendra's current weight.From the problem, I know two key pieces of information:1. If Leo gains 12 pounds, his weight will be 70% more than Kendra's current weight.2. The combined current weight of Leo and Kendra is 210 pounds.Based on the first piece of information, I can set up the equation:[ L + 12 = 1.7K ]From the second piece of information, I have:[ L + K = 210 ]Now, I'll solve this system of equations. First, I'll express ( L ) in terms of ( K ) from the second equation:[ L = 210 - K ]Next, I'll substitute this expression for ( L ) into the first equation:[ (210 - K) + 12 = 1.7K ]Simplifying the equation:[ 222 - K = 1.7K ][ 222 = 2.7K ][ K = frac{222}{2.7} ][ K approx 82.22 ]Now that I have Kendra's weight, I'll find Leo's current weight:[ L = 210 - 82.22 ][ L approx 127.78 ]Therefore, Leo's current weight is approximately 127.78 pounds.

answer：To find the coordinates of the point corresponding to the complex number (frac{5 + 4i}{i}), I need to simplify the expression.First, I recognize that dividing by (i) can be simplified by multiplying both the numerator and the denominator by the complex conjugate of (i), which is (-i).Multiplying the numerator (5 + 4i) by (-i) gives:[(5 + 4i)(-i) = -5i - 4i^2]Since (i^2 = -1), this simplifies to:[-5i - 4(-1) = -5i + 4]Next, multiplying the denominator (i) by (-i) results in:[i(-i) = -i^2 = -(-1) = 1]Putting it all together, the simplified form of the complex number is:[frac{-5i + 4}{1} = 4 - 5i]In the standard form (a + bi), the real part (a) is 4 and the imaginary part (b) is (-5). Therefore, the coordinates of the point in the complex plane are ((4, -5)).

answer：First, I identify the number of fingers each person folded. Yoojung folded 2 fingers, and Yuna folded 5 fingers.Next, I add the number of fingers folded by Yoojung to the number of fingers folded by Yuna to find the total number of fingers folded by both people.Finally, I calculate the sum of 2 and 5, which equals 7.

answer：Okay, so I have this problem about folding a rectangular piece of paper. The paper measures 17 cm by 8 cm. When it's folded, a right angle is formed between two segments of the original bottom edge. I need to find the area of the new figure after folding.First, let me visualize the problem. The rectangle is 17 cm long and 8 cm wide. The bottom edge is 17 cm, and when it's folded, a right angle is formed somewhere along this edge. I'm assuming that folding creates a crease, and part of the paper overlaps another part.Since it's a rectangle, all angles are right angles, so folding it to create another right angle might mean that a corner is being folded over. Maybe the bottom right corner is being folded up to meet somewhere on the left side? Or perhaps the bottom left corner is being folded over to the right side?I think the key here is to figure out how the folding affects the dimensions of the new figure. The area of the original rectangle is 17 cm multiplied by 8 cm, which is 136 cm². But when we fold it, part of the area might overlap, so the area of the new figure could be less than 136 cm².Wait, but the problem says "the area of the new figure." So, does that mean the area of the visible part after folding? Or does it include the overlapped area? Hmm, I think it refers to the area of the figure after folding, which would be the same as the original area minus the overlapping part. But I'm not entirely sure.Let me think about how folding affects the area. If you fold a paper, the total area remains the same, but the visible area might change. However, the problem is asking for the area of the new figure, which might refer to the shape created after folding, not the visible part. So, maybe the area is still 136 cm²? But that doesn't make sense because the answer choices don't include 136.Wait, the answer choices are 104, 81, 72, 168, and 64. So, 136 isn't an option. That means the area must be different. So, perhaps when folding, part of the paper is hidden, and we need to subtract that hidden area from the original area.Let me try to sketch this mentally. The rectangle is 17 cm long and 8 cm wide. If I fold it so that a right angle is formed on the bottom edge, maybe the fold is such that a triangle is formed, and that triangle is overlapping another part of the rectangle.If I consider the bottom edge, which is 17 cm, and fold it to create a right angle, perhaps the fold is made at some point along the 17 cm edge, creating two segments that form a right angle. Let's say the fold is made at a distance 'x' from one corner, creating a right triangle with legs 'x' and 'y', and the hypotenuse would be the fold line.But since it's a rectangle, the height is 8 cm, so maybe the fold brings a part of the bottom edge up to meet the top edge? Or perhaps it's folding the bottom edge over to create a flap.Wait, maybe it's similar to folding a corner to create a right triangle. If I fold the bottom right corner up so that it touches the left side, forming a right angle at the fold. In that case, the overlapping area would be a right triangle.Let me try to model this. Suppose we have the rectangle with length 17 cm and width 8 cm. If I fold the bottom right corner up to meet the left side, the fold would create a right triangle. The legs of this triangle would be equal because the fold creates a right angle, so both legs would be 8 cm each.Wait, but the width is 8 cm, so if I fold the corner up, the vertical leg would be 8 cm, but the horizontal leg would be some portion of the 17 cm length. Hmm, maybe not. Let me think again.Alternatively, if I fold the bottom edge such that a right angle is formed, perhaps the fold is made at a point where the two segments of the bottom edge form a right angle. So, if the original bottom edge is 17 cm, and after folding, it's split into two segments that meet at a right angle.Let me denote the two segments as 'a' and 'b', such that a + b = 17 cm, and the angle between them is 90 degrees. Since it's a fold, the lengths 'a' and 'b' would correspond to the distances from the fold point to the two ends of the bottom edge.But how does this affect the area? The area of the new figure would be the area of the rectangle minus the area of the overlapping region, which is a right triangle with legs 'a' and 'b'.Wait, but if a + b = 17, and the angle between them is 90 degrees, then the area of the triangle would be (a*b)/2. But I don't know the values of 'a' and 'b' yet.Alternatively, maybe the fold creates a square or another rectangle. But since the original dimensions are 17 and 8, it's unlikely to form a square.Wait, perhaps the fold is such that the bottom edge is folded over to form a right angle, effectively creating a new figure that is a combination of the original rectangle and the folded part.But I'm getting confused. Maybe I should try to draw it out or use coordinate geometry.Let me place the rectangle on a coordinate system with the bottom-left corner at (0,0), so the rectangle extends to (17,0) at the bottom-right, (17,8) at the top-right, and (0,8) at the top-left.If I fold the bottom edge to form a right angle, perhaps the fold is made at some point (x,0), and the segment from (x,0) to (17,0) is folded upwards to meet somewhere on the left side.When folded, the point (17,0) would be mapped to a new point (x', y') on the left side, such that the fold creates a right angle at (x,0).Wait, this is getting complicated. Maybe I should use the Pythagorean theorem.If the fold creates a right angle between the two segments of the bottom edge, then the lengths of these segments must satisfy a^2 + b^2 = c^2, where c is the length of the fold.But since the paper is folded, the length of the fold would be the same as the distance between the two points where the fold intersects the bottom edge.Wait, I'm not sure. Maybe I need to find the point where the fold occurs such that the two segments form a right angle.Alternatively, perhaps the area of the new figure is the area of the rectangle minus the area of the overlapping triangle.If the overlapping area is a right triangle with legs of 8 cm each, then the area would be (8*8)/2 = 32 cm². So, the new area would be 136 - 32 = 104 cm², which is option A.But wait, why would the legs be 8 cm each? Because the width of the rectangle is 8 cm, so when folding, the height of the triangle would be 8 cm, but the base might be something else.Alternatively, maybe the fold creates a triangle with both legs equal to 8 cm, making the area 32 cm², so subtracting that from 136 gives 104.But I'm not entirely confident. Let me check.If the fold is such that the bottom edge is split into two segments forming a right angle, and each segment is 8 cm, then the area of the triangle would be 32 cm², and the new figure's area would be 136 - 32 = 104.Alternatively, maybe the fold doesn't remove 32 cm² but instead rearranges the area. But since folding doesn't change the total area, the area of the new figure should still be 136 cm². But since 136 isn't an option, I must be misunderstanding the problem.Wait, maybe the new figure refers to the visible part after folding, not the total area. So, if part of the paper is hidden under the fold, the visible area would be less than 136.If the overlapping area is a right triangle with legs 8 cm each, then the visible area would be 136 - 32 = 104 cm², which is option A.Alternatively, maybe the fold creates a smaller rectangle. If the fold is made such that the bottom edge is split into two segments of 8 cm each, forming a right angle, then the new figure would be a square of 8 cm by 8 cm, but that would only be 64 cm², which is option E. But that seems too small.Wait, no, because the original rectangle is 17 cm long, so if you fold 8 cm up, the remaining length would be 9 cm. So, the new figure might be a combination of a 9 cm by 8 cm rectangle and an 8 cm by 8 cm square, but that would make the area 72 + 64 = 136, which is the original area.Hmm, I'm getting confused again. Maybe I should think about the fold as creating a right triangle, and the area of the new figure is the area of the rectangle minus the area of the triangle.If the triangle has legs of 8 cm each, then area is 32, so 136 - 32 = 104.Alternatively, maybe the legs are different. Let me denote the two segments of the bottom edge as 'a' and 'b', with a + b = 17, and since they form a right angle, the area of the triangle is (a*b)/2.But without knowing 'a' and 'b', I can't compute the area. However, since the fold is such that the right angle is formed, and the paper is 8 cm wide, perhaps the height of the triangle is 8 cm, making the area (a*8)/2.But I still don't know 'a'.Wait, maybe the fold is such that the two segments of the bottom edge are equal, so a = b = 8.5 cm. But then the area of the triangle would be (8.5*8.5)/2, which is about 36.125, which isn't an integer, and 136 - 36.125 is about 99.875, which isn't an option.Alternatively, maybe the fold is made such that one segment is 8 cm and the other is 9 cm, since 8 + 9 = 17. Then the area of the triangle would be (8*9)/2 = 36, so the new area would be 136 - 36 = 100, which isn't an option either.Wait, maybe the fold isn't splitting the bottom edge into two segments, but rather creating a right angle by folding a corner up. So, if I fold the bottom right corner up to meet the left side, the fold would create a right triangle with legs equal to the width of the paper, which is 8 cm.So, the area of the triangle would be (8*8)/2 = 32, and the new figure's area would be 136 - 32 = 104 cm², which is option A.Yes, that makes sense. So, the answer should be 104 cm².