Manuel got a new job and was given a hiring bonus along with his monthly salary. His earnings after x months are modeled by the function f(x)=1,500x+300. How much did he receive as a hiring bonus?(1 point)
The hiring bonus is represented by the constant term in the function, which is $300. Therefore, Manuel received a hiring bonus of $\boxed{300}$.
Last year, Alayah ordered 4 cubic yards of soil and spent $220. This year, she orders 7 cubic yards of soil and spends $340. Write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost. Enter your answer in y=mx+b form.(1 point)
To write the equation of the linear function, we need to find the slope and the y-intercept.
The slope is equal to the change in y (total cost) divided by the change in x (number of cubic yards of soil ordered):
slope = (340 - 220) / (7 - 4) = 40
The y-intercept can be found by plugging in one set of values for x and y and solving for b. We'll use the second set of values:
340 = 40(7) + b
b = 50
Therefore, the equation of the linear function is:
y = 40x + 50
In y=mx+b form, this becomes:
$\boxed{y = 40x + 50}$
To find out how much Manuel received as a hiring bonus, we need to look at the given function: f(x) = 1,500x + 300.
The function represents Manuel's earnings after x months. The term "1,500x" represents his monthly salary, and the constant term "300" represents the hiring bonus.
In this case, the hiring bonus is the constant term, which is 300. Therefore, Manuel received a hiring bonus of $300.