Answer:
1. (10, -⁸/₃)
2. (2, ⁸/₃)
3. (12, -4)
Step-by-step explanation:
I will do the first 3 as examples.
1. Y is ⅔ of the distance from X to Z.
Y − X = ⅔ (Z − X)
The x-coordinate of Y is:
x − -6 = ⅔ (18 − -6)
x + 6 = ⅔ (24)
x + 6 = 16
x = 10
The y-coordinate of Y is:
y − 8 = ⅔ (-8 − 8)
y − 8 = ⅔ (-16)
y − 8 = -³²/₃
y = -⁸/₃
Y is at (10, -⁸/₃).
2. The ratio of XY to YZ is 1:2.
(Y − X) / (Z − Y) = 1 / 2
Cross multiply.
2 (Y − X) = Z − Y
The x-coordinate of Y is:
2 (x − -6) = 18 − x
2x + 12 = 18 − x
3x = 6
x = 2
The y-coordinate of Y is:
2 (y − 8) = -8 − y
2y − 16 = -8 − y
3y = 8
y = ⁸/₃
Y is at (2, ⁸/₃).
3. Y is ¼ of the distance from Z to X.
Y − Z = ¼ (X − Z)
The x-coordinate of Y is:
x − 18 = ¼ (-6 − 18)
x − 18 = ¼ (-24)
x − 18 = -6
x = 12
The y-coordinate of Y is:
y − -8 = ¼ (8 − -8)
y + 8 = ¼ (16)
y + 8 = 4
y = -4
Y is at (12, -4).
The coordinates of the point where the passenger was dropped of is the point (-2, 2).
(1, -2) + (3, -1) = ((1 + 3), (-2 - 1)) = (4, -3)
(4, -3) + (-6, 5) = ((4 - 6), (-3 + 5)) = (-2, 2)
Answer:
x<-2
Step-by-step explanation:
That is the answer derived from the given graph, where you can see that there is no inclusion of the number -2,
If you begin with 1.5 yd^3 of topsoil and want the topsoil to be only 4 inches deep, then the area of the garden can be found as follows:
Convert 4 in to yards: 4 in 1 yd
------- * ----------- = (1/9) yd
1 36 in
The dimensions of the garden are x (width) by 2x (length) by (1/9) yd (depth). The volume of topsoil would be 2x^2/9 = 1.5 yd^3.
Solving for x: (2/9)x^2 = 1.5 yd^3, or x^2 = (1.5 yd^3) (9/2)
Then: x = sqrt(6.75 yd^3) = 2.6 yd and 2x = 5.2 yd
Check: Does (2.6 yd)(5.2 yd)(1/9) = 1.5 cu yd? YES
Thus, the max size of the garden would be 2.6 yd wide, 5.2 yd long, and 4 inches (or 1/9 foot) deep.
The answer is -6. Use the slope formula y2-y1/x2-x1