21)
PT = TQ
Given PT = 4x - 6 and TQ = 3x + 4
so
4x - 6 = 3x + 4
Subtract 3x from both sides
4x - 6 - 3x = 3x + 4 - 3x
Simplifying
x - 6 = 4
Add 6 to both sides
x - 6 + 6 = 4 + 6
Simplifying
x = 10
PT = 4(10) - 6 = 40 - 6
PT = 34
Answer
PT = 34
A segment is bounded by two endpoints.
The two segments can have up to two common points
Assume the line segments are AB and CD where the length of AB is greater than the length of CD.
<u>The possibilities are:</u>
- <em>A point of segment CD lies on segment AB</em>
- <em>Both points of segment CD lie on segment AB.</em>
<em />
See attachment for both possibilities.
Hence, it is possible for the two segments to have two common points.
Read more about line segments at:
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Answer:
Perimeter of ABCD - Perimeter of PQRS = 4x + 2
Step-by-step explanation:
i. For rectangle ABCD;
length, l = 2x -3
width, w = 4x + 5
Perimeter of a rectangle = 2(l + w)
Perimeter of ABCD = 2((2x -3) + (4x + 5))
= 2(2x -3 + 4x + 5)
= 2(6x + 2)
Perimeter of ABCD = 12x + 4
ii. For rectangle PQRS;
length, l = x - 1
width, w = 3x + 2
Perimeter of a rectangle = 2(l + w)
Perimeter of PQRS = 2((x - 1) + (3x + 2))
= 2(x - 1 + 3x + 2)
= 2(4x + 1)
Perimeter of PQRS = 8x + 2
So that,
Perimeter of ABCD - Perimeter of PQRS = (12x + 4) - (8x + 2)
= 12x + 4 - 8x - 2
= 4x + 2
Perimeter of ABCD - Perimeter of PQRS = 4x + 2
Answer:
Step-by-step explanation:
10. We know the area of a rectangle is
A=L*W
They gave us the area so we can plug it in
30 = L*W
Since we know two points, we know one side of the rectangle is the distance between the two points. So one side is 7-2 = 5. We can plug that into the formula.
30 = 5W
W = 6 (divide both sides by 5)
So now we know the width of the rectangle is 6. That means the other coordinates are (6,2) and (6,7).
11. To find the perimeter of a rectangle, we would need to find the length and the width of the triangle. So we would need to subtract one x value from another x value and multiply that by 2. Then subtract one y value from the other y value and multiply that by 2. Add both of those values to get the perimeter.
Equation:
P = 2 * (Change in X) + 2 * (Change in Y)