Answer:
ABCD is a rectangle
Step-by-step explanation:
∵ A = (-5 , 0) , B = (2 , -6) , C = (8 , 1) , D = (1 , 7)
∵ The x-coordinate of the mid-point of AC = (-5 + 8)/2 =3/2
∵ The y-coordinate of the mid-point of AC = (0 + 1)/2 = 1/2
∴ The mid-point of AC = (3/2 , 1/2)
∵ The x-coordinate of the mid-point of BD = (2 + 1)/2 =3/2
∵ The y-coordinate of the mid-point of BD = (-6 + 7)/2 = 1/2
∴ The mid-point of BD = (3/2 , 1/2)
∴ The mid-point of AC = The mid-point of BD ⇒ (1)
∵ AC = √[(8 - -5)²+(1 - 0)² = √170
∵ BD = √[(1 - 2)²+(7 - -6)² = √170
∴ AC = BD ⇒ (2)
From (1) and (2)
AC and BD equal each other and bisects each other
∴ ABCD is a rectangle
Answer: (:
-0.3
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For 3 different values of x
Here, we want to get the values of x for which
√(48/x) is a whole number
We have to consider that the values of x that will make the expression a whole number must be less than or equal to 48
Also, we have to consider that, the division we have to make must yield a perfect square so as to have a whole number square root
The factors of 48 that can yield a whole number are;
1,2,3,4,6,8,12,16,24 and 48
However, the divisions that can yield a perfect square are
3 (yield 16)
12 ( yield 4)
48 ( yield 1)
So the numbers of the value of x that can yield a whole number is 3
9514 1404 393
d. -9 ≤ y ≤ 5
The range is the vertical extent of the graph. This graph goes from a low of -9 to a high of +5. Then the range is ...
-9 ≤ y ≤ 5
1. 3; 2. 12; 3. 5; 4. 13; 5. 10; 6. 10
We can use the distance formula to calculate the lengths of the line segments.
1. A (1,5), B (4,5) (red)
2. A (2,-5), B (2,7) (blue)
3. A (3,1), B (-1,4 ) (green)
4. A (-2,-5), B (3,7) (orange)
5. A (5,4), B (-3,-2) (purple)
6. A (1,-8), B (-5,0) (black)