Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?
Answers
Answer:
Step-by-step explanation:
Ginny determines that the population is decreasing at an average rate of 3% per year.
So, this is an exponential decay case
Formula :
where a is the amount after n years
a is the initial amount
r is the rate of depreciate
n is the number of years
Now we are given that When she began her study, the frog population was estimated at 1,200.
So, a=1200
r = 3% = 0.03
n =x
Substitute the values in the formula:
Hence function represents the frog population after x years is
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David wants to hang a mirror in his room. The mirror and frame must have an area of 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?2x2 + 14x − 2 = 0 3x2 + 10x − 8 = 0 4x2 + 10x − 2 = 0 x2 + 7x − 8 = 0
f(x)
-1
0
2
Answers
Answer:
Step-by-step explanation:
Given the equation of a line expressed as y = 3x-1, we are to find y = f(x) for the following values of x in the table.
If y = 3x-1, then f(x) = 3
When x = -1
f(-1) = 3(-1)-1
f(-1) = -3-1
f(-1) = -4
Hence when x = -1, f(x) = -4
When x = 0
f(0) = 3(0)-1
f(0) = 0-1
f(0) = -1
Hence when x = 0, f(x) = -1
When x = 2
f(2) = 3(2)-1
f(2) = 6-1
f(2) = 5
Hence when x = 2, f(x) = 5
Final answer:
To complete the table for the equation of the line, substitute the given x-values into the equation and solve for y.
Explanation:
To complete the table for the equation of the line y = 3x - 1, we substitute the given x-values into the equation and solve for y. For x = -1, y = 3(-1) - 1 = -4. For x = 0, y = 3(0) - 1 = -1. And for x = 2, y = 3(2) - 1 = 5. Therefore, the completed table is:
x
f(x)
-1
-4
0
-1
2
5
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Answers
the equation is y-3=-12(x-5)==>y=-12x+63
==================================
x2 + 10x + 25
x2 − 25
x2 + 25
Answers
All I did was divide both and I got the answer.
Answer: x^2 - 25
Explanation:
Here is a tip/ shortcut to multiplying binomials in the (a + b)(a - b) format.
The only things you have to look for is the factor of a * a and the factor of b * b.
The reason being, a * -b and b * a cancel each other out no matter what.
For example
1. (x + 5)(x - 5) Multiply by
x * x =
2. (x + 5)(x - 5) Multiply by -5 in the second binomial
x * -5 = -5x
3. (x + 5)(x - 5) Multiply 5 in the first binomial to
5 * x = 5x
4. (x + 5)(x - 5) Multiply 5 in the first binomial to -5 in the second binomial
5 * -5 = -25
5. Now that you have all of your answers, write your equation, in order, to look like this.
- 5x + 5x - 25
6. -5x and 5x cancel each other out when combining like terms so you're left with.
- 25
In the end, steps 2, 3, 5, and 6. can be taken out by doing this.
Just multiply by
to get
Then just multiply 5 in the first binomial to -5 in the second binomial to get -25
Then write your answer.
- 25
This works because there is no need for steps 2,3,5, and 6 since they lead to the same outcome from doing steps 1 and 4.
Answers
(1 foot)³ = (12 inches)³
12³ = 1,728 in³
To change 10 cubic feet into cubic inches
10 ft³ * 1728 in³/ft³ = 17,280 in³ Choice C. Multiply by 1,728
45%
as a fraction in simplest form.
Answers
Answers
The expression which represents the amount of money he makes is 10m + 96
How to be write mathematical expression?
- Amount earned per hour for lawns = $10
- Amount earned per hour to rake leaves = $8
- Number of hours mowed = m
- Number of hours raked = 12 hours
Total amount of money earned = (10 × m) + (8 × 12)
= 10m + 96
Therefore, the expression which represents the amount of money he makes is 10m + 96
Learn more about mathematical expression:
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10m+8(12)
Harrison mowes lawns for 11 hours, so m=11. How Much money does he make in September? He makes 206 $.