-3v -7 less equal sign 2v + 8

Question

GPT-4o mini · Accepted Answer

To solve the inequality $-3v - 7 \leq 2v + 8$, follow these steps: 1. **Combine like terms**: Start by isolating the variable term on one side. We can do this by adding $3v$ to both sides: $$ -3v + 3v - 7 \leq 2v + 3v + 8 $$ This simplifies to: $$ -7 \leq 5v + 8 $$ 2. **Isolate the variable**: Next, we subtract $8$ from both sides: $$ -7 - 8 \leq 5v $$ Simplifying that gives: $$ -15 \leq 5v $$ 3. **Divide by 5**: Now, divide both sides by $5$: $$ \frac{-15}{5} \leq v $$ This simplifies to: $$ -3 \leq v $$ or equivalently: $$ v \geq -3 $$ So, the solution to the inequality is: $$ v \geq -3 $$

BTS ARMY · Answer

y = 2x + 3 x y -2 -1 0 1

GPT-4o mini · Answer

To find the corresponding $ y $ values for each $ x $ value using the equation $ y = 2x + 3 $, we can substitute the given $ x $ values into the equation: 1. For $ x = -2 $: $$ y = 2(-2) + 3 = -4 + 3 = -1 $$ 2. For $ x = -1 $: $$ y = 2(-1) + 3 = -2 + 3 = 1 $$ 3. For $ x = 0 $: $$ y = 2(0) + 3 = 0 + 3 = 3 $$ 4. For $ x = 1 $: $$ y = 2(1) + 3 = 2 + 3 = 5 $$ Now, we can summarize the results in a table: $$ \begin{array}{|c|c|} \hline x & y \ \hline -2 & -1 \ -1 & 1 \ 0 & 3 \ 1 & 5 \ \hline \end{array} $$ So the corresponding $ y $ values for the given $ x $ values are: - For $ x = -2 $, $ y = -1 $ - For $ x = -1 $, $ y = 1 $ - For $ x = 0 $, $ y = 3 $ - For $ x = 1 $, $ y = 5 $

BTS ARMY · Answer

is the graph linear or nonlinear x y 1 -1 5 3 9 7 13 3

GPT-4o mini · Answer

To determine if the relationship between $ x $ and $ y $ is linear or nonlinear, we can check if the change in $ y $ is consistent with the change in $ x $.

Given the points:

$ (1, -1) $
$ (5, 3) $
$ (9, 7) $
$ (13, 3) $

Step 1: Calculate the slopes between each pair of points

Between (1, -1) and (5, 3): \[ \text{slope} = \frac{3 - (-1)}{5 - 1} = \frac{3 + 1}{4} = \frac{4}{4} = 1 \]
Between (5, 3) and (9, 7): \[ \text{slope} = \frac{7 - 3}{9 - 5} = \frac{4}{4} = 1 \]
Between (9, 7) and (13, 3): \[ \text{slope} = \frac{3 - 7}{13 - 9} = \frac{-4}{4} = -1 \]

Step 2: Analyze the slopes

The slope between the first two points is $1$, and the slope between the second and third points is also $1$, indicating that these segments are linear. However, the slope between the last two points is $-1$, which indicates a change in direction.

Conclusion

Since the slopes between the points are not consistent (they change between the third and fourth points), the relationship between $ x $ and $ y $ is nonlinear. The graph formed by these points will not be a straight line, as the direction of change in $ y $ does not remain constant.

BTS ARMY · Answer

is the graph linear or nonlinear x y -2 4 -1 9 0 14 1 19

GPT-4o mini · Answer

To determine whether the relationship between $ x $ and $ y $ is linear or nonlinear, we'll check the slopes between each pair of points.

Given the points:

$ (-2, 4) $
$ (-1, 9) $
$ (0, 14) $
$ (1, 19) $

Step 1: Calculate the slopes between each pair of consecutive points

Between (-2, 4) and (-1, 9): \[ \text{slope} = \frac{9 - 4}{-1 - (-2)} = \frac{5}{1} = 5 \]
Between (-1, 9) and (0, 14): \[ \text{slope} = \frac{14 - 9}{0 - (-1)} = \frac{5}{1} = 5 \]
Between (0, 14) and (1, 19): \[ \text{slope} = \frac{19 - 14}{1 - 0} = \frac{5}{1} = 5 \]

Step 2: Analyze the slopes

The slopes between each pair of consecutive points are all equal to $ 5 $. This indicates that the relationship between $ x $ and $ y $ is consistent throughout the entire set of points.

Conclusion

Since the slopes between all pairs of points are the same, the relationship between $ x $ and $ y $ is linear. The graph formed by these points will be a straight line.

BTS ARMY · Answer

rewrite the equation in Ax + By = C form use integers for ABC y - 2 = 3 (x + 3)

GPT-4o mini · Answer

To rewrite the equation $ y - 2 = 3(x + 3) $ in the form $ Ax + By = C $ using integers for $ A $, $ B $, and $ C $, we can follow these steps: 1. **Distribute** the $ 3 $ on the right side: $$ y - 2 = 3x + 9 $$ 2. **Add $ 2 $** to both sides to isolate $ y $: $$ y = 3x + 9 + 2 $$ $$ y = 3x + 11 $$ 3. **Rearrange** the equation to the form $ Ax + By = C $ by moving all terms to one side: $$ -3x + y = 11 $$ 4. To express it in standard form, we prefer $ A $ to be positive, so we can multiply the entire equation by $-1$: $$ 3x - y = -11 $$ Now, in the form $ Ax + By = C $, we have: $$ 3x - y = -11 $$ ### Summary In standard form $ Ax + By = C $, the integers are: - $ A = 3 $ - $ B = -1 $ - $ C = -11 $ Thus, the equation $ y - 2 = 3(x + 3) $ can be rewritten as $ 3x - y = -11 $.

BTS ARMY · Answer

find the slope and y-intercept of the line y = 4x - 5

GPT-4o mini · Answer

The given equation of the line is: $$ y = 4x - 5 $$ This equation is already in the slope-intercept form, which has the general form: $$ y = mx + b $$ where: - $ m $ is the slope - $ b $ is the y-intercept ### Identifying the Slope and Y-Intercept: 1. **Slope ($ m $)**: From the equation $ y = 4x - 5 $, we can see that the slope is $ 4 $. 2. **Y-Intercept ($ b $)**: The y-intercept is the value of $ y $ when $ x = 0 $. In this equation, the y-intercept is $ -5 $. ### Summary: - **Slope**: $ 4 $ - **Y-Intercept**: $ -5 $ Thus, the slope of the line is $ 4 $ and the y-intercept is $ -5 $.