Answer:
(A) The rate of change in the price of a bushel of corn in the current year is $7.
(B) The price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.
Step-by-step explanation:
The graph for the prices of different numbers of bushels of corn at a store in the current year is shown below.
Part A:
The rate of change in the price of a bushel of corn in the current year based upon the number of bushels is known as the slope of the line.
The formula to compute the slope is:
![\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Consider the ordered pairs: (4, 28) and (10, 70)
Compute the slope of the line as follows:
![\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![=\frac{70-28}{10-4}\\\\=\frac{42}{6}\\\\=7](https://tex.z-dn.net/?f=%3D%5Cfrac%7B70-28%7D%7B10-4%7D%5C%5C%5C%5C%3D%5Cfrac%7B42%7D%7B6%7D%5C%5C%5C%5C%3D7)
Thus, the rate of change in the price of a bushel of corn in the current year is $7.
Part B:
The data for the price of bushels in the previous year is as follows:
Number of Bushels Price
2 10
4 20
6 30
8 40
Compute the rate of change in the price of a bushel of corn in the previous year based upon the number of bushels as follows:
Consider the ordered pairs: (2, 10) and (6, 30)
![\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![=\frac{30-10}{6-2}\\\\=\frac{20}{4}\\\\=5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30-10%7D%7B6-2%7D%5C%5C%5C%5C%3D%5Cfrac%7B20%7D%7B4%7D%5C%5C%5C%5C%3D5)
The rate of change in the price of a bushel of corn in the previous year is $5.
Thus, the price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.
X is less than or equal to -3
explanation
first, i added 6x to both sides
next, i subtracted 25 from both sides
then i divided by 14 and got -3
You could multiply 19.45 by 0.2 to solve for it, but if you're not using a calculator, then 19.45/5 would be much more convenient and easier.
0.2 is 1/5 in fraction form, which is why we can do that.
19.45/5 = 3.89
Dino should leave $3.89 as a tip.
Answer:
x^2 +4x+4 = 4
Step-by-step explanation:
To complete the square take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 =4
Add it to both sides of the equation
x^2 +4x+4 = 4