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777dan777 [17]
3 years ago
14

AD= 36 cm. Points C, B∈AD, such that AB:BC:CD=2:3:4. Find the distance of midpoints of the segments AB and CD.

Mathematics
1 answer:
brilliants [131]3 years ago
4 0

Answer:

The distance of the midpoints of AB and CD is 24 cm

Step-by-step explanation:

The given information are;

The length of AD = 36 cm.

C and B are points on AD

The ratio of AB:BC:CD 2:3:4

The distance of the midpoints of segments AB and CD required

Therefore, we have the following proportion of the total length, 36

Segment AB = 2/(2 + 3 + 4) = 2/9×36 = 8 cm

Segment BC = 3/(2 + 3 + 4) = 3/9×36 = 12 cm

Segment CD = 4/(2 + 3 + 4) = 4/9×36 = 16 cm

The x-coordinate of the midpoint of segment AB = 4 cm

The x-coordinate of the midpoint of segment CD = 8 + 12 + 16/2 = 28 cm

Which gives;

The distance of midpoint of segment AB from A = 4 cm

The distance of midpoint of segment CD  from A = 28 cm

And the distance of the midpoints of AB and CD = 24 - 4 = 24 cm.

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Graph the data in the table. Which kind of function best models the data? Write an equation to model the data. quadratic; y = 2.
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Answer:

Option (1)

Step-by-step explanation:

x               -2              -1                 0                    1                   2

y               10            2.5                0                  2.5                3.0

Ist difference,

d_1=y_2-y_1

    =2.5-10=-7.5

d_2=y_3-y_2

    =0-2.5

    = -2.5

d_3=y_4-y_3

    =2.5-0

    = 2.5

d_4=y_5-y_4

    =10.0-2.5

    = 7.5

2nd difference,

x_1=d_2-d_1

    =-2.5+7.5

    = 5

x_2=d_3-d_2

    =2.5+2.5

    = 5

x_3=d_4-d_3

    =7.5-2.5

    = 5

Since 2nd difference is common, given table represents a quadratic equation.

Let the equation is,

y = ax²+ bx + c

For a point (0, 0) passing through the quadratic equation,

0 = c

Therefore, quadratic equation is y = ax² + bx

Since ordered pair (-1, 2.5) passes through the graph of the function,

2.5 = a(-1)² + b(-1)

a - b = 2.5 ------(1)

For another point (1, 2.5)

2.5 = a(1)² + b(1)

a + b = 2.5 ------(2)

By adding equations (1) and (2),

2a = 5

a = 2.5

and from equation (2)→ y = 0

Therefore, equation of the quadratic function given in the table is y = 2.5x²

Option (1) is the answer.

8 0
3 years ago
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