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2 years ago

Which of the following is the correct factorization of the trinomial below? -7x^2-5x+18

Mathematics

2 answers:

ryzh [129]2 years ago

8 0

Answer: C. (-7x+9)(x-2)

Step-by-step explanation:

1. Factor out the negative sign.

−(7x^2+5x−18)

2. Split the second term in 7x2+5x−18 into two terms.

−(7x^2+14x−9x−18)

3, Factor out common terms in the first two terms, then in the last two terms.

−(7x(x+2)−9(x+2))

4. Factor out the common term x+2x+2x+2.

−(x+2)(7x−9) or (-7x+9)(x-2)

DaniilM [7]2 years ago

7 0

Answer:

-1 (7x - 9) (x + 2)

Step-by-step explanation:

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Answer:

amount is 1000 × $e^{0.08t}$

$40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500

Step-by-step explanation:

principal = $1000

rate = 8 % = 0.08

to find out

the future value, S(t)

principal when Donna's account will be 1 million dollars when she retires in 40 year

at what rate Donna's account will have a balance of 1 million dollars in 40 years

solution

we know compounded continuously formula i.e.

amount = principal × $e^{rt}$ ..................1

put the value principal and rate in equation 1 to find amount any time

amount = principal × $e^{rt}$

amount = 1000 × $e^{0.08t}$

in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1 to find principal

rt = 0.08 × 40 = 3.2

amount = principal × $e^{rt}$

1000000 = principal × $e^{3.2}$

principal = 1000000 / $e^{3.2}$

principal = 1000000 / 24.5325302

principal = 40762.20397

so $40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

in 3rd part we have amount 1 million and principal $2500 and time 40 year put all these in equation 1 to find rate

amount = principal × $e^{rt}$

1000000 = 2500 × $e^{40r}$

take ln both side

ln $e^{40r}$ = ln (1000000 / 2500 )

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r = 0.149787

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2 years ago

What are the explicit equation and domain for an arithmetic

max2010maxim [7]

Given:

First term of an arithmetic sequence = 5

Second term = 3

To find:

The explicit formula for the given arithmetic sequence.

Solution:

We have,

First term: $a_1=5$

Second term: $a_2=3$

Common difference is

$d=a_2-a_1$

$d=3-5$

$d=-2$

Now, the explicit formula for an arithmetic sequence is

$a_n=a+(n-1)d$

where, a is first term and d is common difference.

Putting a=5 and d=-2, we get

$a_n=5+(n-1)(-2)$

It can also be written as

$a_n=5-2n+2$

$a_n=7-2n$

Here, n is an integer greater than or equal to 1.

Domain is the set of input values.

Therefore, the explicit equation is $a_n=5+(n-1)(-2)$ or $a_n=7-2n$ and domain is all interest greater than or equal to 1.

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