The solution to the inequality |3x + 6| < 12 is -6 < x < 2, which corresponds to option C.
To solve the inequality |3x + 6| < 12, we can break it down into two separate inequalities:
3x + 6 < 12
-(3x + 6) < 12
Solving the first inequality:
3x + 6 < 12
Subtracting 6 from both sides:
3x < 6
Dividing both sides by 3 (since 3 is positive, we don't need to change the direction of the inequality):
x < 2
Solving the second inequality:
-(3x + 6) < 12
Distributing the negative sign:
-3x - 6 < 12
Adding 6 to both sides:
-3x < 18
Dividing both sides by -3 (since -3 is negative, we need to change the direction of the inequality):
x > -6
Combining the solutions from both inequalities, we have:
-6 < x < 2
Therefore, the correct option is C. -6 < x < 2.
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Answer:
Step-by-step explanation:
Left
When a square = a linear, always expand the squared expression.
x^2 - 2x + 1 = 3x - 5 Subtract 3x from both sides
x^2 - 2x - 3x + 1 = -5
x^2 - 5x +1 = - 5 Add 5 to both sides
x^2 - 5x + 1 + 5 = -5 + 5
x^2 - 5x + 6 = 0
This factors
(x - 2)(x - 3)
So one solution is x = 2 and the other is x = 3
Second from the Left
i = sqrt(-1)
i^2 = - 1
i^4 = (i^2)(i^2)
i^4 = - 1 * -1
i^4 = 1
16(i^4) - 8(i^2) + 4
16(1) - 8(-1) + 4
16 + 8 + 4
28
Second from the Right
This one is rather long. I'll get you the equations, you can solve for a and b. Maybe not as long as I think.
12 = 8a + b
17 = 12a + b Subtract
-5 = - 4a
a = - 5/-4 = 1.25
12 = 8*1.25 + b
12 = 10 + b
b = 12 - 10
b = 2
Now they want a + b
a + b = 1.25 + 2 = 3.25
Right
One of the ways to do this is to take out the common factor. You could also expand the square and remove the brackets of (2x - 2). Both will give you the same answer. I think expansion might be easier for you to understand, but the common factor method is shorter.
(2x - 2)^2 = 4x^2 - 8x + 4
4x^2 - 8x + 4 - 2x + 2
4x^2 - 10x + 6 The problem is factoring since neither of the first two equations work.
(2x - 2)(2x - 3) This is correct.
So the answer is D
O-16
o -2
O 8
0 10
Answer:
The last option, 10 is correct
Step-by-step explanation:
f(x) = 3x^2 - 4
f(2) = 3(2)^2 - 4
f(2) = 12 - 4
f(2) = 8
g(x) = 2x - 6
g(8) = 2(8) - 6
g(8) = 16 - 6
g(8) = 10
This means that g(f(2)) is equal to 10
Answer:
Its 10 or D
Step-by-step explanation:
Answer: x ≤ 5 or x > 7
Step-by-step explanation:
First, we will write an equation for the left side. It's a closed dot going to the left (less than) of 5.
x ≤ 5
Next, we will write the right side. It's an open dot going to the right (greater than) of 7.
x > 7
Lastly, we will combine these to create our compound inequality.
x ≤ 5 or x > 7
Answer:
-infinity less than or equal to 5 and 7 less than infinity
Step-by-step explanation:
20%
B.
80%
C.
110%
D.
125%
Answer:
Step-by-step explanation:
The straight, black, dashed line does not resemble the actual (green) line at all, and so it is pointless to compare slopes and y-intercepts here.
However, the pattern of black dots, which represent the measurements obtained through the experiment, do exhibit characteristics comparable to the solid green line. The green line has been drawn so that it is roughly in the middle of the dot pattern, which in turn indicates that the slope of this pattern is close to that of the green line. Because this pattern and the green line have similar positive slopes, we can say that the pattern and the line are positively linearly coordinated. The correlation coefficient is in the range 0.8 - 1.0, which is considered to be a "moderate positive correlation."
Answer:
Step-by-step explanation:
The straight, black, dashed line does not resemble the actual (green) line at all, and so it is pointless to compare slopes and y-intercepts here.
However, the pattern of black dots, which represent the measurements obtained through the experiment, do exhibit characteristics comparable to the solid green line. The green line has been drawn so that it is roughly in the middle of the dot pattern, which in turn indicates that the slope of this pattern is close to that of the green line. Because this pattern and the green line have similar positive slopes, we can say that the pattern and the line are positively linearly coordinated. The correlation coefficient is in the range 0.8 - 1.0, which is considered to be a "moderate positive correlation."