Borrowing money is a way to purchase something now and pay for it over time. But, you usually pay “interest” when you borrow money. The longer you take to pay back the money you borrowed, the more you will pay in interest. It pays to shop around to get the best deal on a loan.
Answer:
∠B = 17°
Step-by-step explanation:
Vertical angles are congruent, thus
5x + 7 = x + 15 ( subtract x from both sides )
4x + 7 = 15 ( subtract 7 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
Hence
∠B = 5x + 7 = (5 × 2) + 7 = 10 + 2 = 17°
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).
See the attached picture.
Answer:
90
Step-by-step explanation:
90/10= 9
90/5= 18
No number larger than 90 would work.
