No, because (2,0) is a coordinate. x=2 and y=0. So just plug in the numbers where there's x or y with the appropriate number, (2 or 0). So in the first equation, x-2y=0, when you pug in the numbers, 2-2(0)=0, you know it's wrong because 2-0=0 isn't correct. So no. the point (2,0) is not a solution to the first equation. Now plug in the numbers for the second coordinate. You get 2(2)-3(0)=1. So 4-0=1. This is once again false no no. (2,0) satisfies neither equations.
If you're solving for x, you'd move all the terms containing x to the left side of the equation:
d^2y/dx^2+4y/x-12y-cos^2(x)+sin^2(x)=0
If you're solving for y, you'd simplify both sides of the equation, then isolating the variable:
y=xcos(2x)
Answer:
1) 12
2) 72
Step-by-step explanation:
1) The GCF of 36 and 24 is 12. So, each child would get 3 prizes and 2 balloons.
2) The LCM of 18 and 24 is 72. When the first radio station is playing the song for the fourth time, the second radio station will play the song for the third time. This will happen 72 minutes after they both play it for the first time.
Answer:
17 rows
Step-by-step explanation:
We know that f(x) = 2x² - 10x models the total number of spaces and x models the number of rows.
Since we are given the total number of spaces of 408. We let f(x) = 408
2x² - 10x = 408
Now we solve as a quadratic, subtract 408 to both sides
2x² - 10x - 408 = 0
Divide 2 on both sides
x² - 5x - 204 = 0
We look for terms that multiply to -204 and add to -5.
Those terms are -17 and 12
x² - 17x + 12x - 204 = 0
x(x-17) + 12(x-17)
(x+12)(x-17)
x = -12 x = 17
We can not have -12 rows but we can have 17 rows.
17 rows is the answer.
