Answer:
Step-by-step explanation:
4x+2=5x-6
4x-5x=-6-2
-x=-8
therefore, x=8
If B is the midpoint of AC, that means that the distances from A to B and B to C are the same. The distance from A to B is 8x + 4, and the distance from B to C is 10x - 6, so we can set these two equivalent:
8x + 4 = 10x - 6
Solving for x:
4 = 2x - 6 (subtract 8x from both sides)
10 = 2x (add 6 to both sides)
5 = x (divide both sides by 2)
So, x = 5, which is the second option given.
Answer:
(x, g(x)) = {(-2, -2), (0, 0), (2, 2), (4, -3), (6, -3)}
Step-by-step explanation:
The first three values of x in the table are all less than or equal to 2, so the first part of the function definition applies. The y-value is equal to the x-value. The ordered pairs are ...
(-2, -2), (0, 0), (2, 2)
The last two values of x in the table are more than 2, so the last part of the function definition applies. For those values of x, the y-value is -3. The ordered pairs are ...
(4, -3), (6, -3)
The answer is actually choice A
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If we add up the equations straight down we will have 0a+2b = 6
Note how adding the 'a' terms gives us 3a + (-3a) = 3a-3a = 0a. The 0a term is really 0 since 0 times anything is 0. So the 'a' terms will go away
The equation 0a+2b = 6 turns into 0+2b = 6 and that simplifies to 2b = 6
To isolate b, we divide both sides by 2
2b = 6
2b/2 = 6/2
b = 3
We can stop here since only one answer choice has b = 3, which is choice A. However, let's keep going to find the value of 'a'
Plug b = 3 into any equation with 'a' and 'b', then solve for 'a'
3a+4b = 9
3a+4*3 = 9
3a+12 = 9
3a+12-12 = 9-12
3a = -3
3a/3 = -3/3
a = -1
So a = -1 and b = 3 pair up to form (a,b) = (-1,3)
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To check, plug this ordered pair back into both equations
Equation 1:
3a+4b = 9
3*(-1)+4*3 = 9
-3+12 = 9
9 = 9
Equation 1 has been checked out
Equation 2:
-3a-2b = -3
-3(-1)-2(3) = -3
3 - 6 = -3
-3 = -3
this is true as well
So this confirms that the final answer is choice A
Answer:
(f-g)(x)=-7x-3
Step-by-step explanation:
