Brandon purchased a new guitar in 2012. The value of his guitar, t years after he bought it, can be modeled by the function A(t)

To formulate the system, it's necessary to consider the slope of each line along with at least one point from each line. The two lines will connect each plane's location to their destination airport. It's important to note that the airport's coordinates represent the intersection of these two lines, corresponding to the solution of the system. First, the slope of the line from airplane one to the airport is: m = 2; this can be observed by plotting the two points. From airplane 1's location, the rise is 8 units while the run is 4 units to reach the airport, making the slope 8 divided by 4 = 2. We then insert the slope and point (2,4) into the point-slope form: y - 4 = 2(x - 4), which can be rearranged to standard form 2x - y = 0. For airplane two, the slope to the airport is obtained by observing the vertical decrease of 3 and a horizontal increase of 9 as we move from the airport to airplane 2. We then substitute the slope and the point (15,9) into the point-slope form: y - 9 = -1/3(x - 15), which can be rearranged to the standard form: x + 3y = 42. Consequently, the system of equations is: 2x - y = 0 and x + 3y = 42. Multiplying the first equation by 3 produces a system of: 6x - 3y = 0 and x + 3y = 42. Adding these equations results in the equation 7x = 42. Thus, x = 6, and by substituting this value back into 2x - y = 0, we determine y = 12. Thus, we demonstrate that the airport's coordinates do indeed comprise the solution to our system.

Let X denote <span>the baby’s weight.
Let y represent </span>the doctor’s weight.
Let z stand for the nurse’s weight.

From the equations: x + y = 78 implies y = 78 - x
and x + z = 69 gives z = 69 - x
then we have x + y + z = 142

Substituting y = 78 - x and z = 69 - x into the equation x + y + z = 142

x + y + z = 142
x + 78 - x + 69 - x = 142
-x + 147 = 142
-x = -5
x = 5

Conclusion

<span>the baby’s weight was 5 kg</span>

Answer:   a)     b)

Step-by-step explanation:

a) To achieve an even total, there are 3 possible combinations:

1) Even, Even, Even, Even    

2) Even, Even, Odd, Odd  

3) Odd, Odd, Odd, Odd  

Order is irrelevant

Summing these yields your final result:

b) If one die shows a 2 and another a 3, while the remaining two can show any digits, there’s only one way to get a 2, one way for a 3, and six potential numbers for each of the other two dice.

A) The independent variable in this scenario is the quantity of books purchased. C) The overall cost for the year hinges on the number of books obtained. E) The output of this function is the total yearly cost.

Utilize the details to create inequalities that reflect each limitation or requirement.

2) Label the variables. 

c: count of color copies
b: count of black-and-white copies

3) Define each constraint:

i) <span>Printing a color copy requires 3 minutes while a black-and-white copy takes 1 minute.
</span><span>
</span><span>3c + b
</span><span>
</span><span>
</span><span>ii) He must print a minimum of 6 copies ⇒ c + b ≥ 6
</span><span>
</span><span>
</span><span>iv) Moreover, he must finish the prints within 12 minutes at most ⇒</span>

3c + b ≤ 12
<span />

4) Additional limits include c ≥ 0, and b ≥ 0 (meaning only non-negative counts are valid for each type of copy)

5) Here’s how to illustrate that:

i) For 3c + b ≤ 12: draw the line representing 3c + b = 12 and shade the area above and to the right of this line.

ii) For c + b ≥ 6: draw the line c + b = 6 and shade the area below and to the left of this line.

iii) Given that c ≥ 0 and b ≥ 0, the relevant region is located in the first quadrant.

iv) The concluding area is the overlap of the previously mentioned shaded regions.

v) The graph can be viewed in the attached figure.