Answer:
<u>The number of intersections = ∞</u>
Step-by-step explanation:
Given the system of equations:
0.5 x + 5y = 6
3x + 30y = 36
By multiplying the first equation by 6
∴ 6 (0.5 x + 5y) = 6 * 6
∴ 3x + 30y = 36
So, Those equations are "Dependent", because they are really the same equation, just multiplied the first equation by 6.
So, the two equations are identical
Therefore: <u>They have infinity number of solutions.</u>
<u>See the attached figure.</u>
0.5 x + 5y = 6 ⇒ in black color
3x + 30y = 36 ⇒ in red color
Answer:
= 0.05P - 150
Step-by-step explanation:
Let P(t) be the balance of the loan at time t years,
Let P(t) will satisfy 
where r = annual interest rate
R = per year payment rate
R = $150/year
r = 
= 0.05
Now we have the following picture,
Interest Balance Payment
5% ⇒ P(t) ⇒ $150/year
(0.05)
Therefore, a linear ODE satisfied by P(t) is given by
= 0.05P - 150
Answer: Option #4: the 0.2 could be changed to 2.
Explanation:
The table is designed to make the concept of percentages more understandable. The table first allocates the total amount of 70 in terms of its "fifths," or 20% parts. Then it expresses these parts in the last row of the table, showing that 20% of 70 is 14 and all the five parts sum up to 70 again.
Now, Mikel is supposed to express 40% of the amount. So she writes (incorrectly): 0.2 * 14. This statement needs to be changed to 2 * 14 (two times 14 = 28), to correspond to 2 times 20%, or 40% of 70.
This is reflected in the last (fourth) option "The 0.2 in the expression could be changed to 2."
Option #3 is incorrect because changing 14 to 70, will result in an incorrect number (2.8).
Options 1 and 2 are similarly incorrect (as can be easily verified)
Y*20=30
y=20/30
y=2/3
Hope this helps :)
The characteristic of these geometric figures that create the different requirements would be how these the undefined terms are situated. For the case of parallel lines, these are lines that would not intersect now matter how long the line is extended or whether it goes infinitely thus the lines lie on the same plane. For perpendicular lines, these lines would intersect at one point and would form angles which measure 90 degrees on that point. Thus, these lines can be situated at any plane as long as they intersect with a 90 degrees angle.
