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puteri [66]
3 years ago
12

There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp

. Each year, 10 new crocodiles join the swamp.
Part B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years?
Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically.
Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0
A)

A=20(1.25^t)

C=25+10t

b)

A(4)=20(1.25^4)≈48.82≈49 alligators to nearest whole alligator

C(4)=25+10(4)=65 crocodiles.

c)

20(1.25^t)=25+10t

1.25^t=1.25+0.5t

t≈7
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The following equations are given:
jarptica [38.1K]

The solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3 and the solutions in part b hold for equation 4

<h3>Solving the variables using equations 1 and 2</h3>

There are three variables in the system

To solve the three variables, there must be at least three equations in the system of equations

Hence, the variables cannot be solved because the number of equations is not enough

<h3>Solving the variables using equations 1, 2 and 3</h3>

We have:

3x + z + y = 8

5y - x = -7

3z + 2x - 2y = 15

Make x the subject in (2)

x = 5y + 7

Substitute x = 5y + 7 in (1) and (3)

3(5y + 7) + z + y = 8

15y + 21 + z + y = 8

16y + z = -13

3z + 2(5y + 7) - 2y = 15

3z + 10y + 14 - 2y = 15

3z + 8y = 1

Multiply 16y + z = -13 by 3

48y + 3z = -39

Subtract 3z + 8y = 1 from 48y + 3z = -39

48y - 8y + 3z - 3z = -39 - 1

40y = -40

Divide by 40

y = -1

Substitute y = -1 in x = 5y + 7

x = 5(-1) + 7

x = 2

Make z the subject in 16y + z = -13

z = -13 - 16y

Substitute y = -1

z = -13 - 16(-1)

z = 3

Hence, the solution to the variables using equations 1, 2 and 3 is x = 2, y = -1 and z = 3

<h3>Can the solution work for equation 4?</h3>

We have:

4x + 5y - 2z = -3

Substitute x = 2, y = -1 and z = 3

4(2) + 5(-1) - 2(3) = -3

Evaluate

-3 = -3 --- this is true

Hence, the solutions in part b hold for equation 4

Read more about system of equations at:

brainly.com/question/12895249

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<u>Missing part of the question</u>

The following equations are given:

Equation #1: 3x + z + y = 8

Equation #2: 5y - x = -7

Equation #3: 3z + 2x - 2y = 15

Equation #4: 4x + 5y - 2z = -3

3 0
2 years ago
Robert usually earns $95 per week for
Ghella [55]

The amount of money Robert has this week after buying gas is $172.

<h3>Define arithmetic.</h3>

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction. The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. Addition, subtraction, multiplication, and division are the fundamental mathematical operations. The symbols shown above stand in for these procedures.

Given Data

Robert usually earns $95 per week for mowing lawns.

Amount = $95

This week, he doubled his normal earnings,

Amount = $95 × 2

Amount = 190

but, spent $18 on gas for his lawnmower.

Amount = $190 - $18

Amount = $172

The amount of money Robert has this week after buying gas is $172.

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4 0
1 year ago
Suppose that a car normally sells for $16,500 and now on sale ft $14,000. What is the percent of discount? If necessary round yo
krek1111 [17]
Percentage increase/decrease is given by (the difference ÷ original value) × 100

The decrease in value is 16500 - 14000 = 2500

The percentage decrease = (2500÷16500) × 100 = 15.2%
5 0
3 years ago
Hey pls help worth 30 points
GrogVix [38]

Step 1: Find the slope:

    m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{10-6}{6-5} = \dfrac{4}{1} = 4

Step 2: Set up your equation y-y_1=m(x-x_1) using one of the points.

    Using (5,6) we have y-6 = 4(x-5).

    Using (6,10) we have y-10 = 4(x-6)

Both of those equations would be correct.

5 0
3 years ago
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