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3 years ago

Simplify: (-x^2 - 7x + 10) - (8x^2 + 8x + 8).

Mathematics

1 answer:

JulijaS [17]3 years ago

8 0

Answer:

-(9 x^2 + 15 x - 2)

Step-by-step explanation:

Simplify the following:

-(8 x^2 + 8 x + 8) - x^2 - 7 x + 10

Factor 8 out of 8 x^2 + 8 x + 8:

-x^2 - 7 x + 10 - 8 (x^2 + x + 1)

-8 (x^2 + x + 1) = -8 x^2 - 8 x - 8:

-8 x^2 - 8 x - 8 - x^2 - 7 x + 10

Grouping like terms, -x^2 - 8 x^2 - 7 x - 8 x - 8 + 10 = (-x^2 - 8 x^2) + (-7 x - 8 x) + (10 - 8):

(-x^2 - 8 x^2) + (-7 x - 8 x) + (10 - 8)

-x^2 - 8 x^2 = -9 x^2:

-9 x^2 + (-7 x - 8 x) + (10 - 8)

-7 x - 8 x = -15 x:

-9 x^2 + -15 x + (10 - 8)

10 - 8 = 2:

-9 x^2 - 15 x + 2

Factor -1 out of -9 x^2 - 15 x + 2:

Answer: -(9 x^2 + 15 x - 2)

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Given: Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:

Number of years 1 2 3

Option 1 (amount in dollars) 1100 1200 1300

Option 2 (amount in dollars) 1100 1210 1331

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Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2?

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.

Part C: Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1?

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Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.

Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.

Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.

Part A:

In the case of option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This is because, in option one, the amount increases by a fixed amount every year.

In the case of option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. This is because, in option 2, the amount increase is higher than last year.

Part B:

For option 1, the function is

For option 2, the function is

Here, x is the increase in amount every consecutive year.

Part C:

After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference between 1900.

Therefore,

Part A: Linear and exponential functions can be used to describe the value of the investment after a fixed number of years using option 1 and option 2, respectively.

Part B: (n=n+100) and (n=n+100x) are the functions for each option to describe the value of the investment f(n), in dollars, after n years.

Part C: Yes, there will be a significant difference of 1900 in the value of Belinda's investment after 20 years if she uses option 2 over option 1.

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