These are
five questions and five answers:
<span>I attache a
pdf file with drawings for each question showing the answer and below the explanation for each drawing.
1. Suppose that a triangle and a rectangle lie in a plane. What is the greatest number of points at which they can intersect?Answer: 6.Because one line of the triangle can intersect maximum two lines of the rectangle, which makes two intersection points.
So, the maximum number of possible intersections is when you arrange the triangles so that its three lines intersect three different lines each.
See the attached picture.
2. Suppose that a circle and a square lie in a plane. What is the greatest number of points at which they can intersect?Answer: 8.The attached figure shows a circle and a square with 8 intersection points.
That is the maximum number of points at which a circle and a square in a plane can intersect: each line of the square intersect two different points of the circle.
3. Suppose two distinct triangles lie in a plane. What is the greatest number of points at which they can intersect?Answer: 6See the image attached.
Each line of a triangle intersect one different line of the other triangle in two different points.
4. Suppose that a circle and a triangle lie in a plane. What is the least number of points at which they can intersect?Answer: 0You can draw two figures that do not intersect each other. See the picture attached.
5. Suppose two distinct squares lie in a plane. What is the least number of points at which they can intersect?
Answer: 0As you can see the figure attached you can draw two different squares which to not intersect each other.
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Answer: Exact Form: a=3√6
Decimal Form: a=1.81712059....
Both angles added together equal 180 degrees.
B = 180 - 45 = 135 degrees.
Answer:
$165.38
Step-by-step explanation:
In the question, we are asked to work with percentages. We know that the person had bought three items of a total of 250 dollars (38 + 189 + 23). We are told that the items have a 30% discount, another 10% discount on that and a 5% tax increase on all of that.
First, let's work with the 30% discount. The official way of working out the problem you would use the unitary method. The unitary method is when we divide the total cost by 100. So 250/100, is 2.5. We multiply this by the remaining percent (100%- 30%=70%) so 2.5*70 is 175.
Then, we work with ten percent. The only difference is that instead of using the original price with are using the 30% discounted price. If we use the unitary method again we find that 175/100 is 1.75 and that multiplied by 90 (because we are only subtracting the 10% not 30%) is 157.50.
Finally, we do the same for the 5% percent only difference being we add it to 157.50. 157.50/100 is 1.575 and multiplied by 105 (because we are adding 5% onto 100% so it becomes 105%).
The final answer is 165.375 and when rounded to the nearest cent it becomes $165.38.