I think the answer to the problem is eight
Answer:
An equation parallel to 4x + 5y = 19 would be y = -4/5x +12.
An equation perpendicular to 4x + 5y = 19 would be y = 5/4x + 10.
Step-by-step explanation:
The equation given represents a linear equation in Standard Form (Ax + By = C). Lines that are parallel to each other go the same direction and don't touch, so their slopes must be the same. However, lines that are perpendicular go in opposite directions and intersect, so their slopes must be the direct opposite of each other. In order to find the slope, you must first convert from the Standard Form given to Slope Intercept Form (y = mx +b). When you solve the given equation for 'y', you get: y = -4/5x + 19, where the slope = -4/5. To make a parallel equation, simply keep the same slope and choose a different y-intercept ('b'). To make a perpendicular equation, take the direct opposide of your slope 5/4 (positive) and choose a different y-intercept.
Hey :)
The answer is 100.
The overall area will be the length times the width:
200 times 300 = 60000.
If the plot of land doubles in size, then the resulting area will be 120000. To get to 120000, the question is saying that the same number was added to both 200 and 300, which were then multiplied together. The equation will look like this:
(x+200) times (x+300) = 120000
Now, you will multiply these together in a process called FOIL (which means you multiply the first numbers in each parentheses, then the outside numbers, then the inside numbers, then the last numbers):
x^2 (this means x squared, or x times itself) + 300x + 200x + 600 = 120000
Then, you will add together like terms:
x^2 + 500x + 600 = 120000
Next, you will subtract 120000 from both sides to get 0 on one side of the equation:
x^2 + 500x - 6000 = 0
Next, you will essentially perform the opposite of FOIL (now you're trying to get the right side of the equation into two parentheses):
(x + 600) times (x - 100) = 0 (you can check if this is correct by performing FOIL and making sure that product is the previous equation)
Now, set both of the parentheses equal to 0 and solve:
x + 600 = 0 ----> x = -600x - 100 = 0 ----> x = 100
Lastly, you will have to choose which value for x satisfies the initial question. Since the question is asking for a value within the real world, a negative answer will not work (you cannot give someone -600 meters of land). So, the answer is 100.
Hope this helps! :)
Answer:
the two numbers would be 28 and 17