In how many different, distinguishable orders can the letters of the word mathematics be arranged?
1 answer:
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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:
290ft
Step-by-step explanation:
First, add 40 and 50 together to get the side across giving you 90.
Next, take 60 and subtract 25 for the oposite side giving you 25.
Finally, add all sides together to get 290.
