Answer:
1) (3,5)
2) (4,-7)
3) (6,4)
4) (-4,-3)
Step-by-step explanation:
1)
Subtract y from both sides of the equation.
x = 8 − y
x − y = −2
Replace all occurrences of x in x − y = −2 with 8 − y.
x = 8 − y
(8 − y) − y = −2
Subtract y from −y.
x = 8 − y
8 − 2y = −2
Solve for y in the second equation.
x = 8 − y
y = 5
Replace all occurrences of y in x = 8 − y with 5.
x = 8 −(5)
y = 5
Simplify 8 −(5).
x = 3
y = 5
Slope = (3,5)
2)
Multiply each term by 2 and simplify.
2x+y=12
y+6=−x−4
Move all terms containing variables to the left side of the equation.
2x+y=1x+2
y+6=−4
Move all terms not containing a variable to the right side of the equation.
2x+y=1x+2
y=−10
Multiply each equation by the value that makes the coefficients of x opposite.
2x+y=1(−2)⋅
(x+2y)=(−2)(−10)
Simplify.
2x+y=1−2x−4
y=20
Add the two equations together to eliminate x from the system.
2x+y=1+−2x−4
y=20−3
y=21
Divide each term by −3 and simplify.
y = −7
Substitute the value found for y into one of the original equations, then solve for x.
x = 4
slope (4,-7)
3)
Subtract y from both sides of the equation.
2x−y=8x−y=2
Multiply each equation by the value that makes the coefficients of y opposite
2x−y=8(−1)⋅
(x−y)=(−1)(2)
Simplify. 2x−y=8
−x+y=−2
Add the two equations together to eliminate y from the system.
2x−y=8 + −x+y=−2x=6
Substitute the value found for x into one of the original equations, then solve for y.
y=4
slope (6,4)
4)
Simplify 2(x+1).
y−3=2x+2
y=−3(x+5)
Simplify −3(x+5)
y−3=2x+2
y=−3x−15
Move all terms containing variables to the left side of the equation.
−2x+y−3=2
y=−3x−15
Add 3x to both sides of the equation.
−2x+y−3=2
y+3x=−15
Move all terms not containing a variable to the right side of the equation.
−2x+y=5
y+3x=−15
Reorder the polynomial.
−2x+y=5
3x + y=−15
Multiply each equation by the value that makes the coefficients of y opposite.
−2x+y=5(−1)⋅
(3x+y)=(−1)(−15)
Simplify.
−2x+y=5
−3x−y=15
Add the two equations together to eliminate y from the system.
−2x+y=5 + −3x−y=15−5x=20
Divide each term by −5 and simplify.
x=−4
Substitute the value found for x into one of the original equations, then solve for y.
y=−3
slope (-4,-3)
Answer:
The correct answer is option C: (8, 14).
Step-by-step explanation:
The car's displacement in vector form can be found by subtracting the initial points from the final points.
Initial: (x₁, y₁) = (-3, -5)
Final: (x₂, y₂) = (5, 9)
For the x-coordinate, we have:
And for the y-coordinate, we have:
The car's displacement in vector form is:
Therefore, the correct answer is option C: (8, 14).
I hope it helps you!
we can turn any decimal number to a fraction by <u>using as many zeros at the bottom as there are decimals and losing the dot atop</u>, so let's see, we have 3 decimals in this case, so we'll use 3 zeros at the bottom.
recall that to turn an improper fraction to mixed, we divide numerator by denominator, and the quotient is the number alone and the numerator is the remainder of the division.
Answer:
5 km/h
Step-by-step explanation:
In this problem, Lashonda swam 4 km against the current. So the distance covered in this case is
Calling the velocity of Lahonda without the current, and
the velocity of the current, in this situation Lahonda's velocity is
So we can write:
where is the time taken to cover the distance.
When Lashonda swims with the current, her velocity is
So we can write
where
is the distance covered in this case, and
the time taken.
The velocity of the current is
Since Lashonad takes the same time to cover the two distances,
So we can write
And solving for v, we find Lashonda's velocity without the current: