Answer: These are some points of the grahp:
(-2,4)
(0, 3)
(2, 2)
Explanation:
1) f(x) = -0.5x + 3, is the equation of the form y = mx + b
2) y = mx + b is slope-intercept equation of a line where the slope is m and the y-intercept is b, so, f(x) = - 0.5x + b has slope m = -0.5 and y-intercept b = 3.
3) To graph f(x) = -0.5x + 3, follow these steps:
- draw two perpedicular axis: vertical axis, labeled y, and horizontal axis, labeled x.
- draw marks on each axis, each mark equivalent to one unit.
- the intersection point of the vertical and horizontal axis is the origin, i.e. point (0,0).
- you can make a table with two or more points:
x f(x) = - 0.5x + 3
-2 4
0 3
2 2
4 1
6 0
4) You can see the graph in the figure attached, and select any of the points on the line either by using the table or by using the equation f(x) = -0.5x + 3.
Step-by-step explanation:
x=20
y=100
solution in image
Rectangle Area = length • width
5x • (x + 2) = area
(5x^2 + 10x) is the area, with no further ways to simplify.
Answer:
The possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares by purchasing land.
Step-by-step explanation:
Let the variable <em>X</em> represent the amount of land used for planting trees and <em>Y</em> represent the amount of land purchased.
The goal of the environmental initiative is to save at least 25 million hectares of rain forest.
That is:
<em>X</em> + <em>Y</em> = 25....(i)
Now it is provided that:
- The cost of planting trees is $ 400 per hectare.
- The cost of purchasing land is $ 260 per hectare.
- The initiative has a budget of $8,250 million.
Using the above data it can be said that:
400<em>X</em> + 260<em>Y</em> = 8250....(ii)
Solve equations (i) and (ii) simultaneously.
![\ \ \ \ x+y=25]\times 260\\400x+260y=8250\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\\Rightarrow\\\\260x+260y=6500\\400x+260y=8250\\(-)\_\_\_\_\_\ (-)\_\_\_\_(-)\_\_\_\\\\\Rightarrow\\\\-140x=-1750\\\\x=\frac{1750}{140}\\\\x=12.5](https://tex.z-dn.net/?f=%5C%20%5C%20%5C%20%5C%20x%2By%3D25%5D%5Ctimes%20260%5C%5C400x%2B260y%3D8250%5C%5C%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C_%5C%5C%5C%5C%5CRightarrow%5C%5C%5C%5C260x%2B260y%3D6500%5C%5C400x%2B260y%3D8250%5C%5C%28-%29%5C_%5C_%5C_%5C_%5C_%5C%20%28-%29%5C_%5C_%5C_%5C_%28-%29%5C_%5C_%5C_%5C%5C%5C%5C%5CRightarrow%5C%5C%5C%5C-140x%3D-1750%5C%5C%5C%5Cx%3D%5Cfrac%7B1750%7D%7B140%7D%5C%5C%5C%5Cx%3D12.5)
Then the value of <em>y</em> is:
Thus, the possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares for purchasing land.
Y=3.25x should be the most probable choice because 6.50 is the price of 2 pounds of candy and once it’s divided by 2 the equation will show how much the unit rate is or the price of each pound of candy.
