The expression (x8 - 48) can be factored as (x2 - 42)2 (x2 + 42)2.
a. True
b. False

A.) x/2+1,000. Here is a picture to prove it

hopefully this helps you and gives you insight in how to solve the problems from now on (:

= $11.8 + (2012-1997)([$11.8-$7.4][1997-1990])

= $11.8 + 5 ($4.4/7)

= $11.8 4/5 + $22/7

= $59/5 + $22/7

= $413/35 + $110/35

= $523/35 or $14 33/35

answer : SALES IN 2012 WOULD BE $14 33/35 BILLION OR $14.9 3/7

Final answer:

A linear model representing retail sales at bookstores from 1990 through 1997 is s(T) = 0.63T + 7.4. The estimated sales at bookstores in 2012 would be approximately $21.46 billion.

Explanation:

To solve this problem, we need to create a linear model. A linear model is a mathematical representation expressed as y = mx + b, where m is the slope, and b is the y-intercept.

To determine the slope (m), we subtract the ending value of retail sales from the starting value and divide by the number of years. So, subtract $7.4 billion (sales in 1990) from $11.8 billion (sales in 1997) and divide by 7 (the number of years from 1990 to 1997): (11.8 - 7.4) / 7 = 0.63. So, m = 0.63.

The y-intercept (b) is the value of y when x = 0. In this model, this corresponds to the sales in 1990, because x is the number of years since 1990, and 'x = 0' therefore corresponds to the year 1990. So, b = $7.4 billion.

The final linear model for retail sales at bookstores from 1990 through 1997 is s(T) = 0.63T + 7.4.

To estimate the retail sales at bookstores in 2012, we plug T = 22 (because 2012 is 22 years after 1990) into our linear model: s(22) = 0.63*22 + 7.4 ≈ $21.46 billion. So, the estimated retail sales in bookstores in 2012 were about $21.46 billion.

Learn more about Linear Models here:

brainly.com/question/33713899

#SPJ2

Kevin has been working as an auto-mechanic. For maximizing weekly income Kevin should do 6 breaks replacement and 4 shock replacements. The time required for performing both the tasks has been equal. Since the time required has been the same, to increase the income, the task resulting in more income has been prioritized

Given :

• The charges for shock replacement = $450,
• The charge for breaks replacement = $200.

Since there have been more income with shock replacement, the brake replacement task has been prioritized.

The time Kevin works in a week has been 42 hours. Since each job takes 2 hours, the number of jobs he can perform has been 21 jobs.

The routine jobsof brake replacement performed by Kevin have been 6. Thus to increase his income, the rest jobs have been of shock replacement.

The number of shock replacement tasks performed by the Kevin =

= 21 - 6

= 15

The number of shock replacement jobs = 15.

Thus for increasing the income Kevin has to perform 6 brake replacement tasks and 15 shock replacement tasks.

For more information, refer to the link given below:

brainly.com/question/24406804

Answer:

Kevin should do 15 shock replacements and 6 brake replacements every week to maximize his weekly income.

Step-by-step explanation:

Both jobs take the same amount of time to complete (2 hours), therefore, in order to maximize his income, Kevin should prioritize the job that gives him the greatest income, which is replacing shocks.

If each job takes 2 hours and he works at most 42 hours per week, Kevin can complete 21 jobs per week. He should aim to do as little break replacements as possible and as many shock replacements as possible to maximize income.

If he completes at least 6 break replacements, the remaining jobs should all be shock replacements:

Kevin should do 15 shock replacements and 6 brake replacements every week to maximize his weekly income.

Answer:  Hello there! The correct answer is A.

If the bird flies 100 yards with an angle of elevation of x from the ground, then you could think this as a tringle rectangle, where the hypotenuse is 100 yards, the opposite cathetus is sin(x)*100 and this represents the height at which the bird dropped the fish, not really useful here.

The adjacent cathetus us 100*cos(x), in this case, you are calculating the displacement adjacent to them (because the angle is with respect to the ground) and knowing that the fish lands in a translated y yards horizontally we could write: y = cos(x)*100

now we want to isolate x:

y/100 = cos(x)

arcos(y/100) = arcos(cos(x)) = x

x = arcos(y/100) (or cos-1(y/100) like in the option A)

then, knowing the value of y, we could obtain the angle x with that equation.