Answer:
Only one solution
Step-by-step explanation:
Given that there is a coordinate plane (say xy)
Two lines are given.
One line crosses the y axis at 3 and has a slope of negative 1.
hence equation of I line is y = -x+3
The other line crosses the y axis at 3 and has a slope of two thirds.
So equation is y = 2x/3 +3
Since the two lines lie in the same plane and are having different slopes, they intersect at one point.
Eliminate y to get
-x+3=2x/3+3
Or x=0
y=3
Hence solutionis (0,3) for the system.
Answer:
x = 0 and y = 3
Step-by-step explanation:
Using elimination method, we can solve for x and y in the simultaneous equation
y = 2x + 3 .................................eqn 1
y = -3x + 3 .................................eqn 2
multiply equation 1 by 3 and equation 2 by 2, then we will have
(y = 2x + 3) × 3
(y = -3x + 3) × 2
3y = 6x + 9 ...............................eqn 3
2y = -6x + 6 ................................eqn 4
Add eqn 3 and 4 together and we will eliminate x and have
5y = 15
Divide both sides by 5, and we will have
y = 3
To solve for x, substitute 3 for y in eqn 1
y = 2x + 3
3 = 2x + 3
collect like terms
3 - 3 = 2x
0 = 2x
Therefore x = 0
Sheila is incorrect! I think what she did is think the 38 was actually a 35, which WOULD of made her statement true, but since it's 38, she's very incorrect. Sheila should be using the quotient for the size of each piece. 38 divided by 5 is 7.6. The correct answer is 7.6 inches.
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On the slope a transverse line between 4, (-4)
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Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h
