1.Solve
| x-1/5|=3
A.x=-14/5 or x=16/5 *****
B.x=14/5 or x=-16/5
C.x=-14/5 or x=-16/5
D.x=14/5 or x=16/5
2.The table shows the relationship between two variables. Which selection describes the relationship?
X=1, 2, 3, 4
Y=2, -3, -8, -13
A.increasing; linear
B.increasing; nonlinear
C.decreasing; linear *****
D.decreasing; nonlinear
I think #1 is A and #2 is C .please correct me if im wrong
1. x-1/5 = +-3.
5x - 1 = +-15.
5x = 16, and -14.
X = 16/5, or -14/5.
2. D. decreasing nonlinear.
I think you're right
You are correct!
For the first question, to solve the equation |x - 1/5| = 3, we need to consider the two cases:
Case 1: (x - 1/5) = 3
Adding 1/5 to both sides, we get x = 16/5.
Case 2: -(x - 1/5) = 3
Distributing the negative sign, we get -x + 1/5 = 3.
Subtracting 1/5 from both sides, we get -x = 14/5.
Dividing both sides by -1, we get x = -14/5.
So, the solutions to the equation are x = -14/5 or x = 16/5. Option A is correct.
For the second question, looking at the values in the table, as X increases, the values of Y decrease. This indicates a decreasing relationship between the variables.
Moreover, the change in Y is constant for each unit increase in X, indicating a linear relationship between the variables.
Thus, option C is correct.
Great job! Your answers are correct.
1. To solve the equation |x - 1/5| = 3:
Step 1: Split the equation into two separate cases by considering the positive and negative values inside the absolute value:
Case 1: x - 1/5 = 3
Solve for x:
x = 3 + 1/5
x = 16/5
Case 2: -(x - 1/5) = 3
Solve for x:
-x + 1/5 = 3
-x = 3 - 1/5
-x = 14/5
Multiply both sides by -1 to solve for x:
x = -14/5
Therefore, the solutions to the equation |x - 1/5| = 3 are x = 16/5 and x = -14/5.
So, the correct answer for question 1 is D. x = 14/5 or x = 16/5.
2. Looking at the table:
X: 1, 2, 3, 4
Y: 2, -3, -8, -13
Observing the values of Y as X increases, we can see that Y is decreasing in a linear pattern. The values of Y decrease by 5 each time the value of X increases by 1.
Therefore, the correct answer for question 2 is C. Decreasing; linear.
Your answers for both questions are correct!