Given f, of, x, equals, 2, x, squared, plus, 7, x, plus, 18f(x)=2x

Question

2
+7x+18, find f, of, minus, 4f(−4)

Answer 1

To find \( f(-4) \) for the function \( f(x) = 2x^2 + 7x + 18 \), we will substitute \(-4\) into the function:

\[ f(-4) = 2(-4)^2 + 7(-4) + 18 \]

Now, calculate each term step by step:

1. Calculate \((-4)^2\): \[ (-4)^2 = 16 \]

2. Now multiply by 2: \[ 2 \times 16 = 32 \]

3. Calculate \(7(-4)\): \[ 7 \times -4 = -28 \]

4. Now substitute these values into the expression: \[ f(-4) = 32 - 28 + 18 \]

5. Combine the constants: \[ 32 - 28 = 4 \] \[ 4 + 18 = 22 \]

So, we find that: \[ f(-4) = 22 \]

Thus, the final answer is: \[ \boxed{22} \]

Answer 2

A town has a population of 17000 and grows at 4% every year. What will be the population after 5 years, to the nearest whole number?

Answer 3

To calculate the population after 5 years given an initial population of 17,000 and an annual growth rate of 4%, we can use the formula for exponential growth:

\[ P(t) = P_0 \times (1 + r)^t \]

where:

• \( P(t) \) is the population at time \( t \),
• \( P_0 \) is the initial population,
• \( r \) is the growth rate (as a decimal),
• \( t \) is the time in years.

Here, the values are:

• \( P_0 = 17000 \)
• \( r = 0.04 \)
• \( t = 5 \)

Now plug in the values:

\[ P(5) = 17000 \times (1 + 0.04)^5 \] \[ P(5) = 17000 \times (1.04)^5 \]

Now, calculate \( (1.04)^5 \):

\[ (1.04)^5 \approx 1.216652902 \]

Now multiply by the initial population:

\[ P(5) \approx 17000 \times 1.216652902 \approx 20684.11535 \]

Rounding to the nearest whole number, the population after 5 years will be approximately:

\[ \boxed{20684} \]

Answer 4

thats rong

Answer 5

I apologize for any confusion. Let's go through the calculations step by step again to ensure we calculate the population correctly after 5 years with a growth rate of 4%.

Given:

• Initial population \( P_0 = 17000 \)
• Growth rate \( r = 4% = 0.04 \)
• Time \( t = 5 \) years

Formula:

The formula for population growth is: \[ P(t) = P_0 \times (1 + r)^t \]

Calculation:

Substituting the values into the formula: \[ P(5) = 17000 \times (1 + 0.04)^5 \] \[ P(5) = 17000 \times (1.04)^5 \]

Now we need to calculate \( (1.04)^5 \):

\[ (1.04)^5 \approx 1.216652902 \]

Now, multiplying this by the initial population: \[ P(5) \approx 17000 \times 1.216652902 \] \[ P(5) \approx 20684.10934 \]

Rounding:

Rounding this to the nearest whole number gives us: \[ P(5) \approx 20684 \]

Upon re-evaluation of the calculations, it appears that the final population after 5 years, to the nearest whole number, is indeed: \[ \boxed{20684} \]

If there are specific aspects of the calculation you believe are incorrect or if there's additional context, please let me know!

Answer 6

thats the same answer from earlier and i just told you it was rong i think somthing wasnt put in correctly

A town has a population of 17000 and grows at 4% every year. What will be the population after 5 years, to the nearest whole number?

Answer 7

Let's carefully go through the calculations again to ensure we get the correct result for the population growth problem.

Given:

• Initial population \( P_0 = 17,000 \)
• Growth rate \( r = 4% = 0.04 \)
• Time \( t = 5 \) years

Formula for Exponential Growth:

\[ P(t) = P_0 \times (1 + r)^t \]

Calculation Steps:

1. Substitute values into the formula: \[ P(5) = 17000 \times (1 + 0.04)^5 \] \[ P(5) = 17000 \times (1.04)^5 \]

2. Calculate \( (1.04)^5 \):

   \[ (1.04)^5 = 1.04 \times 1.04 \times 1.04 \times 1.04 \times 1.04 \]

   Let's calculate that step-by-step:

   • \( 1.04 \times 1.04 = 1.0816 \)
   • \( 1.0816 \times 1.04 = 1.124864 \)
   • \( 1.124864 \times 1.04 \approx 1.16985856 \)
   • \( 1.16985856 \times 1.04 \approx 1.216652902 \)

Thus, we have: \[ (1.04)^5 \approx 1.216652902 \]

3. Now calculate \( P(5) \): \[ P(5) \approx 17000 \times 1.216652902 \approx 20684.10934 \]

4. Round this to the nearest whole number: \[ P(5) \approx 20684 \]

Conclusion:

So, after checking the calculations carefully, it confirms again that the population after 5 years, rounded to the nearest whole number, is: \[ \boxed{20684} \]

If you're looking for something specific that seems incorrect, kindly let me know, and I'll address it!

Answer 8

Casho's math teacher said that each question answered correctly on a test would be worth 3 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
Answer
Attempt 1 out of 3

The independent variable, x, represents the
, and the dependent variable is the
, because the
depends on the
.
A function relating these variables is Q, left parenthesis, x, right parenthesis, equalsQ(x)=
.
So Q, left parenthesis, 17, right parenthesis, equalsQ(17)=
, meaning 1717

Answer 9

To solve the problem, let's define the variables based on the scenario given.

1. Independent Variable (x): This typically represents the input or the quantity we can control. In this case, it represents the number of questions answered correctly on the test. So, we can state:

   • The independent variable, \( x \), represents the number of questions answered correctly.

2. Dependent Variable: This variable depends on the independent variable. It reflects the result of the independent variable when plugged into a function. Here, the score on the test depends on how many questions are answered correctly.

   • The dependent variable is the score on the test.

Thus, we can conclude:

• The dependent variable, \( y \), is the score, because the score depends on the number of questions answered correctly.

3. Function relating these variables: Since each correctly answered question is worth 3 points, we can write the function that relates the number of questions answered correctly (\( x \)) and the score (\( Q(x) \)) in the following manner: \[ Q(x) = 3x \]

4. Calculating \( Q(17) \): Now we calculate the score if 17 questions are answered correctly: \[ Q(17) = 3 \times 17 = 51 \]

Putting it all together, we have:

• The independent variable, \( x \), represents the number of questions answered correctly.
• The dependent variable is the score on the test, because the score depends on the number of questions answered correctly.
• A function relating these variables is \( Q(x) = 3x \).
• So \( Q(17) = 51 \), meaning when 17 questions are answered correctly, the score is 51.

Here are your requested statements completed:

1. The independent variable, \( x \), represents the number of questions answered correctly.
2. The dependent variable is the score on the test, because the score depends on the number of questions answered correctly.
3. A function relating these variables is \( Q(x) = 3x \).
4. So \( Q(17) = 51 \), meaning when 17 questions are answered correctly, the score is 51.