Answer:
Counterclockwise rotation 90° or clockwise rotation 270°
Step-by-step explanation:
The total amount is 156.86. By multiplying .15 to the 136.40, the tip would be 20.46. So 136.40 plus the 20.46 dollar tip would equal 156.86
Answer:
6/5
Step-by-step explanation:
Using the given points (0, 3) and (-2.5, 0) you can substitute it into the slope formula which is y2-y1/x2-x1
In this case, 3 in the first parenthesis is the y2, while 0 in the second parenthesis set is 0.
so,
= substitute in the numbers for the slope formula: 3-0/0-(-2.5)
= reduce the fraction and you get: 1.2
= convert to simplified fraction to get: 6/5
Hope this helps, I did this on a quiz and got the answer right.
Answer:
2
Step-by-step explanation:
If the value of the discriminant is positive, there are two real solutions for x, meaning the graph of the solution has two distinct x-intercepts
Here 25 is positive discriminant, hence the function will have 2 x - intercepts
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).
