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3 years ago

Find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).

1 answer:

4 0

Since M divides segment AB into a ratio of 5:2, we can say that M is 5/(5+2) of the length of AB. Therefore 5/7 × AB.
distance of AB = d
5/7×(x2 - x1) for the x and 5/7×(y2 - y1) for the y
5/7×(8 - 1) = 5/7 (7) = 5 for the x
and 5/7×(16 - 2) = 5/7 (14) = 10 for the y
But remember the line AB starts at A (1, 2),
so add 1 to the x: 5+1 = 6
and add 2 to the y: 10+2 = 12
Therefore the point M lies exactly at...
A) (6, 12)

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Quadratics need help making parabola

timama [110]

Answer:

The equation of the parabola is $y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4$ , whose real vertex is $(x,y) = (2, -5.333)$ , not $(x,y) = (2, -5)$ .

Step-by-step explanation:

A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:

$(x_{1}, y_{1}) = (-2, 0)$ , $(x_{2}, y_{2}) = (6, 0)$ , $(x_{3}, y_{3}) = (0, -4)$

From definition of second order polynomial and the three points described above, we have the following system of linear equations:

$4\cdot a -2\cdot b + c = 0$ (1)

$36\cdot a + 6\cdot b + c = 0$ (2)

$c = -4$ (3)

The solution of this system is: $a = \frac{1}{3}$ , $b = - \frac{4}{3}$ , $c = -4$ . Hence, the equation of the parabola is $y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4$ . Lastly, we must check if $(x,y) = (2, -5)$ belongs to the function. If we know that $x = 2$ , then the value of $y$ is:

$y = \frac{1}{3}\cdot (2)^{2}-\frac{4}{3}\cdot (2) - 4$

$y = -5.333$

$(x,y) = (2, -5)$ does not belong to the function, the real point is $(x,y) = (2, -5.333)$ .

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2 years ago

Hewo helppT-T pwease :3<br><br> 2/5+____= 11/15

ArbitrLikvidat [17]

Answer:

1/3 is the answer

Step-by-step explanation:

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stiks02 [169]

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3 years ago

What equation represents the parabola with focus (-1,4) and directrix y= -2

Llana [10]

Answer:

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y=(x+1)/12 +1

Step-by-step explanation:

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2 years ago

Choose all that correctly define the point on the directed line segment between the two given points that partitions the segment

Flura [38]

Answer:

A(1, 3) and B(5, 15). The coordinates (6, 2) divides the line segment directed from A to B in the ratio of 1:3. Line segment AB has endpoints A(0, 12) and B(8, 8). The coordinates (2, 11) divides the line segment directed from A to B in the ratio of 1:3.

Step-by-step explanation:

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3 years ago

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