For a system of linear equations, the solution for the system is____.
Answer: The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4,7) is the solution to the system of linear equations.
Picture:
C. y - 3 = 2/3(x-3)
Nothing much to do here except examine each equation and plug in the numbers to see if it's true.
a. y + 3 = 3/2(x+3)
Try 3,3
3 + 3 = 3/2(3+3)
6 = 3/2(6). And no need to go further, it's obviously not equal.
b. y - 3 = 3/2(x-3)
Try 3,3
3 - 3 = 3/2(3-3)
0 = 3/2(0). OK. Let's try 6,5
5 - 3 = 3/2(6-3)
2 = 3/2(3)
2 = 9/2 And it's not true, so check the next one.
c. y - 3 = 2/3(x-3)
Try 3,3
3 - 3 = 2/3(3-3)
0 = 0. Check 6,5
5 - 3 = 2/3(6-3)
2 = 2/3(3)
2 = 2. Good. Both sample points work. This is the correct answer.
Just to be sure, let's check the next option
d. y + 3 = 2/3(x+3)
Try 3,3
3 + 3 = 2/3(3+3)
6 = 2/3(6). And doesn't match.
Answer:
x=8.5
Step-by-step explanation:
To solve this equation, we want to find out what x is. To do this, we need to get x by itself.
Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.
4(x-5)=14
4 is being multiplied by x-5. The opposite of multiplication is division. Divide both sides by 4.
4(x-5)/4=14/4
x-5=14/4
x-5=3.5
5 is being subtracted from x. The opposite of subtraction is addition. Add 5 to both sides.
x-5+5=3.5+5
x=3.5+5
x=8.5
Let's check our solution. Plug 8.5 in for x in the original equation.
4(x-5)=14
4(8.5-5)=14
4(3.5)=14
14=14
Both sides of the equation are the same, so we know our solution, <u>x=8.5 </u>is correct.
Answer: The velocity of the ball is 108.8 ft/s downwards.
Step-by-step explanation:
When the ball is dropped, the only force acting on the ball will be the gravitational force. Then the acceleration of the ball will be the gravitational acceleration, that is something like:
g = 32 ft/s^2
To get the velocity equation we need to integrate over time, to get:
v(t) = (32ft/s^2)*t + v0
where v0 is the initial velocity of the ball. (t = 0s is when the ball is dropped)
Because it is dropped, the initial velocity is equal to zero, then we get:
v(t) = (32ft/s^2)*t
Which is the same equation that we can see in the hint.
Now we want to find the velocity 3.4 seconds after the ball is dropped, then we just replace t by 3.4s, then we get:
v(3.4s) = (32ft/s^2)*3.4s = 108.8 ft/s
The velocity of the ball is 108.8 ft/s downwards.
Step-by-step explanation:
6*8+10*4+5*4=48+40+20=108
