<u>Solution-</u>
1- When rotating a figure 180 degrees around the origin (As it does not matter whether you move clockwise or counter-clockwise), we apply the rule (x, y) → (-x, -y).
Co-ordinates of the vertices,
P = (1, -1)
Q = (3, -2)
R = (3, -4)
And then calculating the co-ordinates of P', Q', R'
P' = (-1, 1)
Q' = (-3, 2)
R' = (-3, 4)
2- When reflecting a figure across X-axis, we apply the rule (x, y) → (x, -y).
Co-ordinates of the vertices,
P' = (-1, 1)
Q' = (-3, 2)
R' = (-3, 4)
And then calculating the co-ordinates of P'', Q'', R''
P'' = (-1, -1)
Q'' = (-3, -2)
R'' = (-3, -4)
Answer:
-20x+27
Step-by-step explanation:
-4 times 5x = -20x
-3 rimes -4 = 12
12+15=27
-20x+27
Do you notice anything strange about those points ?
(0, 1),
(1, 2),
(2, 4),
(3, 8).
The y-coordinate of each point is (2) raised to the power of the x-coordinate.
First point: x=0, y=2⁰ = 1
Second point: x=1, y=2¹ = 2
Third point: x=2, y=2² = 4
Fourth point: x=3, y=2³ = 8
The equation of the curve appears to be
y = 2 ^ x .
So, after 10 hours, x=10, and y = 2¹⁰ = 1,024 .
Answer:
≈0.819232 or
Step-by-step explanation:
times
Answer:
67 gallons.
Step-by-step explanation:
To determine how many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 60% antifreeze, the following calculation must be performed:
0.15 x 90 + 0.70 x 10 = 20.5 / 100 = 0.20
0.15 x 90 + 0.70 x 30 = 34.5 / 100 = 0.34
0.15 x 90 + 0.70 x 60 = 55.5 / 100 = 0.55
0.15 x 90 + 0.70 x 67 = 60.4 / 100 = 0.60
Thus, 67 gallons of 70% antifreeze solution will be needed to achieve a 60% mix of that solution.