Definition: The points where a graph intersects the x-axis are called it’s _

How to complete the square with a leading coefficient?

Kamila [148]

Factor out the leading coefficient:

$ax^2+bx+c=a\left(x^2+\dfrac bax+\dfrac ca\right)$

Now complete the square:

$x^2+\dfrac bax+\dfrac ca=x^2+\dfrac bax+\dfrac{b^2}{4a^2}-\dfrac{b^2}{4a^2}+\dfrac ca=\left(x+\dfrac b{2a}\right)^2-\dfrac{b^2}{4a^2}+\dfrac{4ac}{4a^2}=\left(x+\dfrac b{2a}\right)^2-\dfrac{b^2-4ac}{4a^2}$

Now, redistributing the leading $a$ gives

$a\left(x+\dfrac b{2a}\right)^2-\dfrac{b^2-4ac}{4a}$

8 0

3 years ago

After graduating from college, Jane has two job offers to consider. Job A is compensated at $100,000 a year but

vaieri [72.5K]

Answer: (a) Job A , by approximately $69, 482

$\\$ (b) Job A , by approximately $6,867

$\\$ (c) Job B , by approximately $ 767,362

$\\$ (d) Job A

Step-by-step explanation:

JOB B

$\\$ The starting Salary is $ 10,000

Since there is an increment of 25% at the beginning of each new year. The breakdown of the increment is as follow:

$\\$ First year : 125% of $ 10,000 = $12,500

$\\$ Second year : 125% of $ 12,500 = $15,625

$\\$ Third year : 125% of $15,625= $19,531.25

$\\$ Fourth year: 125% of $19,531.25 = $24,414.06

$\\$ Fifth year : 125% of $24,414.06 = $30,517.58

$\\$ Sixth year: 125% of $30,517.58 = $38,147.00

$\\$ Seventh year: 125% of $38,147.00 = $47,683.75

$\\$ Eight year: 125% of $47,683.75 = $59,604.69

$\\$ Ninth year: 125% of $59,604.69 = $74,505.86

$\\$ Tenth year: 125% of $74,505.86 = $93,132.32

$\\$ Following the same procedure:

$\\$ Eleventh year = $116,415.40

$\\$ Twelfth year = $145,519.25

$\\$ Thirteenth year = $181,899.06

$\\$ Fourteenth year = $227,373.82

$\\$ Fifteenth year = $ 284,217.29

$\\$ Sixteenth year = $355,271.61

$\\$ Seventeenth year = $444,089.51

$\\$ Eighteenth year = $555,111.89

$\\$ Nineteenth year = $693,889.86

$\\$ Twentieth year = $867,362.32

$\\$ (a) Following the analysis above, at the beginning of the fifth year Job A will have a greater annual salary

$\\$ Difference: Salary of Job A at the beginning of fifth year remains $ 100,000 while that of Job B resulted into $ 30,517.58, the difference implies

$100,000 - $ 30,517.58 = $69,482

$\\$ (b) At the beginning of tenth year, Job A is still $100,000, Job B resulted into $93,132.32. Job A is still greater by approximately $6,867

$\\$ (c) At the beginning of the twentieth year, the annual salary of A is still $ 100,000 while the annual salary of B is $ 867,362.32. Job B annual salary is greater by approximately $ 767,362

$\\$ (d) If I were in Jane’s shoe I will take Job A and work for few years to gain more experience the look for a job that pays better. Waiting for many years in case of Job B is risky , market situation is uncertainty.