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MakcuM [25]
2 years ago
13

A penguin population increases by 60%, representing an increase of 3840 penguins. How many penguins were there before the increa

se?
Mathematics
1 answer:
8090 [49]2 years ago
8 0

Answer:

2304

Step-by-step explanation:

The equation for this is 3840*0.6 which equals 2304. And to check, we can divide 2304 by 0.6, and that gives us 3840. I hope this helps! :)

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The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the h
Mama L [17]

The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively

<h3>Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. </h3>

<u>Juan</u>

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:

c = 3 -- the constant value

So, the equation becomes

h = ad^2 + bd + 3

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

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

38 = a(100)^2 + b(100) + 3

Using a graphing tool, we have:

a = -0.001

b = 0.45

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:

y = -0.001x^2 +0.4x +2.5

<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:

Juan = 505 feet

Mark = 457 feet

Barry = 450 feet

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

#SPJ1

4 0
1 year ago
3(x-4) = 2(-2x + 1)<br>this is confusing me​
nata0808 [166]

Answer:

x = 2

Step-by-step explanation:

<em>Distribute</em>

3 (−4) = 2 (−2+1)

3 − 12 = 2 (-2x +1)

<em>Distrubute again</em>

3x - 12 = -4x + 2

<em>Add twelve to both sides of the equation</em>

<em>Simpfly</em>

3x = -4x + 14

<em>Add 4x to both sides of the equation</em>

<em>simpfly</em>

7x = 14

<em>Divide both sides of the equation by the same term</em>

<em>Simpfly</em>

x = 2

5 0
2 years ago
The radius of a circle with area A can be approximated using the formula r = the square root of A/3 . Estimate the radius of a w
Arturiano [62]

Answer: 12

Step-by-step explanation:

Given:

A = 452

r = √A/3

Step 1: Substitute 452sqf for A

r = √452/3

Step 2: Solve

452 ÷ 3 = 150.66∞

√150.66∞ = 12.27∞

12.27∞ rounded to the nearest integer equal 12

3 0
2 years ago
The average of eight numbers is 56. When one of the numbers was left out, the mean decreased to 54. What number was left out?
Alexandra [31]

The number that was left out is 70.

<h3>What is the number that was left out?</h3>

Average is the sum of a set of numbers divided by the total numbers in the data set.

Average = sum of numbers / total numbers

  • Sum of numbers when there are 8 numbers = 56 x 8 = 448
  • Sum of numbers when there are 7 numbers = 54 x 7 = 378
  • Difference = 448 - 378 = 70

To learn more about average, please check: brainly.com/question/25842202

#SPJ1

4 0
1 year ago
Convert 4 5/7 to an improper fraction
Musya8 [376]

Answer:

33/7

Step-by-step explanation:

8 0
3 years ago
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