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inna [77]
3 years ago
11

what rational number lies in between -14/31 and -17/33? A. -989/3069 B. -123/276 C. -989/2046 D. -4/7

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
6 0
-14/31 and -17/33

-17/33 - (-14/31) = (-17/33*31/31) - (-14/31*33/33) = -527/1023 +  462/1023

= (-527+462)/1023 = -65/1023 

-65/1023 ÷ 2 = -65/1023 * 1/2 = -65/2046

-17/33 - (-65/2046) = (-17/33*62/62) - (-65/2046) = -1054/2046 + 65/2046
= -989/2046 Choice C.
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<h3>Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. </h3>

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Juan's equation is given as:

h = -0.001d^2 + 0.5d + 2.5

h =

Set d to multiples of 50 from 0 to 400.

So, the table of values of Juan's function is:

d (ft)                   h(ft)

0                          2.5

50                        25

100                      42.5

150                        55

200                      62.5

250                        65

300                      62.5

350                        65

400                      42.5

See attachment for the graph of Juan's function

<u>Mark</u>

A quadratic function is represented as:

h = ad^2 + bd + c

Using the values on the table of values, we have:

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h = ad^2 + bd + 3

Using the two other values on the table of values, we have:

23 = a(50)^2 + b(50) + 3

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Using a graphing tool, we have:

a = -0.001

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So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3

See attachment for Mark's graph.

<u>Barry</u>

From the graph, we have the table of values of Barry's function to be:

d (ft)                   h(ft)

0                          2.5

50                        21

100                      35

150                       44

200                      48

250                       46

300                      41

350                       30

400                      14

450                      0

Using a graphing tool, we have the quadratic function to be:

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<h3><u>The shortest and the greatest distance before hitting the ground</u></h3>

From the graphs, equations and tables, the distance travelled by the balls are:

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This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.

<h3>The height the balls hit a fence at 350 ft distance</h3>

To do this, we set d = 350

From the graphs, equations and tables, the height at 350 ft by the balls are:

Juan = 65 feet

Mark = 38 feet

Barry = 30 feet

The above represents the height the balls hit the fence

Read more about quadratic functions at:

brainly.com/question/12446886

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