I need help with these problems:
11. The 2 captains of the school football team meet with the 3 captains of another team for the coin toss. If each captain shakes hands with each captain from the opposing team, how many different handshakes occur?
14. Find the maximum area of a rectangle with a perimeter of 144 inches.
35. Determine if the conjecture is true or false based on the given information-- Given: Point P is in the interior of <KJQ
Conjecture: m<KJP is congruent to m<PJQ
False?
40. If two points lie in a plane, the line containing them ______.
a. intersects the plane once
b. lies in the same plane
c. is skew
d. does not intersect the plane
A?
41. A plane and a point not on the plane are ____ coplanar.
a. always
b. sometimes
c. never
d. not enough information to tell
C?
Thanks
-MC
I will not answer 11. You can figure it out by drawing lines between captains on a piece of paper.
14. You could guess a square but to prove it:
2 x + 2 y = 144
so
y = 72-x
A = x y = x(72-x)
x^2 - 72 x = -A
x^2- 72 x + 1296 = -(A-1296)
(x-36)^2 = -(A-1296)
vertex at x = 36, Area = 1296,
36 * 4 = 144 so square 36 on a side with area = 1296
I will not answer 35. Again draw it on a piece of paper.
40 are two points on your desk top in the same plane??? If you draw the line between them is it on the desk top?
41. Is a point not on your desk top on your desk top or not?
Sure, I am here to help you with your problems. Let's go through each problem and find the solutions together.
11. The 2 captains of the school football team meet with the 3 captains of another team for the coin toss. If each captain shakes hands with each captain from the opposing team, how many different handshakes occur?
To find the number of different handshakes, we can use the concept of combinations. Each captain from one team can shake hands with each captain from the other team only once. So, for each captain from the first team, there are 3 possible handshakes with the captains from the other team. Since there are 2 captains in the first team, the total number of handshakes would be 2 captains multiplied by 3 possible handshakes each, which is 6 handshakes.
Answer: There are 6 different handshakes that occur.
14. Find the maximum area of a rectangle with a perimeter of 144 inches.
To find the maximum area of a rectangle, we need to consider that a square has the maximum area for a given perimeter. In a square, all sides are equal, so the perimeter of a square would be 4 times the length of one side.
In this case, the perimeter is given as 144 inches. Dividing 144 by 4 gives us the length of one side of the square. So, the length of one side is 36 inches.
Now, to find the area of the square, we square the length of one side. The area of the square is 36 inches multiplied by 36 inches, which is 1296 square inches.
Answer: The maximum area of a rectangle with a perimeter of 144 inches is 1296 square inches.
35. Determine if the conjecture is true or false based on the given information-- Given: Point P is in the interior of <KJQ Conjecture: m<KJP is congruent to m<PJQ False?
To determine if the conjecture is true or false, we need to understand what the conjecture states. The conjecture states that "m<KJP is congruent to m<PJQ". Here, "m<ABC" represents the measure of the angle ABC.
Based on the given information that point P is inside the angle KJQ, we cannot determine if the conjecture is true or false. The conjecture compares two angles, m<KJP and m<PJQ, but we don't know the specific measures of these angles or any relationship between them. Without further information, we cannot determine the truth or falsity of the conjecture.
Answer: We cannot determine if the conjecture is true or false based on the given information.
40. If two points lie in a plane, the line containing them ______.
a. intersects the plane once
b. lies in the same plane
c. is skew
d. does not intersect the plane
To determine what happens when two points lie in a plane, we need to understand the relationships between points, lines, and planes. If two points lie in a plane, any line passing through those points will also lie in the same plane. This is because a plane contains an infinite number of lines, and any line connecting two points in the plane will also lie in that plane.
Answer: The line containing the two points lies in the same plane.
41. A plane and a point not on the plane are ____ coplanar.
a. always
b. sometimes
c. never
d. not enough information to tell
To determine the coplanarity of a point and a plane, we need to consider if the point lies within the plane or not. Coplanar refers to objects that lie in the same plane.
In this case, a plane and a point not on the plane are never coplanar. This is because the point is not located within the plane, so it is not part of the same plane as the other points.
Answer: A plane and a point not on the plane are never coplanar.
I hope this helps! Let me know if you have any more questions.