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balandron [24]
3 years ago
13

UV has the endpoints U(0, 3) and V(–4, –5). Which shows the correct calculation for finding the x-coordinate of the point that p

artitions the line segment into a 4:3 ratio? x = (–4) x = (–4) x = (–5 – 3) + 3 x = (–5 – 3) – 5

Mathematics
2 answers:
Pavlova-9 [17]3 years ago
6 0

Solution:

The end points of line segment UV is U(0, 3) and V(–4, –5).

The line segment is Partitioned by a point in the ratio of 4:3.Let that point be (x,y).

Formula for internal division

A line segment having end points (x_{1},y_{1}) and (x_{2},y_{2}) divided by a point (x,y) in the ratio of m:n.  

x=\frac{m x_{2}+nx_{1}}{m+n}, y=\frac{m y_{2}+ny_{1}}{m+n}

x=\frac{3\times 0+4 \times -(4)}{4+3}=\frac{-16}{7}



sleet_krkn [62]3 years ago
4 0

Answer: A:   X=(4/7)(-4)

Step-by-step explanation: question was on E2020


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a) is A b) is D c) is D d) is 2 e) is At lunch time, Benjamin often borrows money from his friends to buy snacks in the school cafeteria. Benjamin borrowed $0.75 from his friend Clyde four days last week to buy ice cream bars. How much does he owe Clyde.

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p is the point on the line 2x+y-10=0 such that the length of OP, the line segment from the origin o to p is a minimum. find the
REY [17]
Coolio

alright, so the disatnce formula is
D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

solve for y in the equation given on top
2x+y-10=0
y=10-2x
ok
so (x1,y1)=(0,0), the first point
(x2,y2)=(x,10-2x)
so subsitute to get

D=\sqrt{(x-0)^2+(10-2x-0)^2}
D=\sqrt{(x)^2+(10-2x)^2}
D=\sqrt{x^2+4x^2-40x+100}
D=\sqrt{5x^2-40x+100}
find the miniumum
we only need to minimize what is under the square root so
take the derivitive of 5x²-40x+100
that is 10x-40
it is 0 at x=4
when x<4, the derivitive is negative
when x>4, the derivitive is positve
goes from negative to positive
so it is a minimum

at x=4
find y
y=10-2x
y=10-2(4)
y=10-8
y=2

(4,2)
find min distance

D=\sqrt{(x-0)^2+(y-0)^2}
D=\sqrt{(4-0)^2+(2-0)^2}
D=\sqrt{(4)^2+(2)^2}
D=\sqrt{16+4}
D=\sqrt{20}
D=2\sqrt{5}



the point, P, is (4,2) and the minimum distance is 2√5
5 0
4 years ago
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