Answer:
5 no = 1 .................m
Answer:
x=2, y=1
Step-by-step explanation:
The left and right sides are equal
7x-2 = 5x+2
Subtract 5x from each side
7x -5x-2 = 5x-5x+2
2x-2 = 2
Add 2 to each side
2x -2+2 = 2+2
2x = 4
Divide by 2
2x/2 = 4/2
x =2
The top and the bottom are the same length
6x+y = 7x-1
6(2) +y = 7(2)-1
12 +y = 14-1
Subtract 12 from each side
12 +y-12 = 13-12
y = 1
Some schools do this differently, but since I don’t have any of the answer choices I’ll show you how to
Factor: -6|x+5|-2
Factor out the two
2(-3|x+5|-1)
And if you are looking for a graph here:
Answer:
B
Step-by-step explanation:
The rulers tell you the length of the sides
The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
