Answer:
gg
Step-by-step explanation:
<h2>
Question:</h2>
Find k if (x+1) is a factor of 2x³ + kx² + 1
<h2>
Answer:</h2>
k = 1
<h2>
Step-by-step explanation:</h2>
The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.
<em>This is because;</em>
i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.
ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e
=> (-3)² - 9
=> (9) - 9 = 0
Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.
<em><u>From the question</u></em>
Given polynomial: 2x³ + kx² + 1
Given factor: x + 1.
Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e
2(-1)³ + k(-1)² + 1 = 0
2(-1) + k(1) + 1 = 0
-2 + k + 1 = 0
k - 1 = 0
k = 1
Therefore the value of k is 1.
Answer:
The population will reach 34,200 in February of 2146.
Step-by-step explanation:
Population in t years after 2012 is given by:
In what month and year will the population reach 34,200?
We have to find t for which P(t) = 34200. So
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots 
such that 
, given by the following formulas:
In this question:
So 
Then
We only take the positive value.
134 years after 2012.
.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.
So the population will reach 34,200 in February of 2146.
Answer:
$9600 saving / year
Step-by-step explanation:
1/5 of $21000 = 21000 / 5 = $4200 / month on rent
3/7 of $21000 = (21000 / 7) x 3 = $9000 / month on food (shocking right :) food is expensive)
1/3 of $21000 = 21000 / 3 = $7000 on other expenses / month
total savings/month = salary/month - rent/month - food/month - other expenses/month
total savings/month = 21000 - 4200 - 9000 - 7000
total savings/month = $800
<u><em>BUT</em></u> the question asks for savings per year. therefore, we must multiply the savings per month by total months per year (12)
800 x 12 = $9600
the person's total savings per year, with a salary of $21000 per month, is equal to $9600 per year
