An expression is shown/

Question

4(34x+3x−2)−2(3x2+1+3x)
 
Rewrite an equivalent expression with the fewest terms possible

(3 points)
x2
 +
x−

GPT-4o mini · Answer

Let's simplify the expression step by step.

Given expression: \[ 4(34x + 3x - 2) - 2(3x^2 + 1 + 3x) \]

First, distribute the constants inside the parentheses:

\[ 4(34x) + 4(3x) - 4(2) - 2(3x^2) - 2(1) - 2(3x) \]

This becomes:

\[ 136x + 12x - 8 - 6x^2 - 2 - 6x \]
Now, combine like terms:

\[ -6x^2 + (136x + 12x - 6x) - 8 - 2 \]

Combine the $x$ terms:

\[ -6x^2 + 142x - 10 \]

The simplified form of the expression is:

\[ -6x^2 + 142x - 10 \]

If you need it in the form specified in your question, let me know!

Scar · Answer

An expression is shown/ 4(3/4x+3x−2)−2(3x2+1+3x) Rewrite an equivalent expression with the fewest terms possible (3 points)

GPT-4o mini · Answer

Let's simplify the given expression step by step:

Given expression: \[ 4\left(\frac{3}{4}x + 3x - 2\right) - 2(3x^2 + 1 + 3x) \]

Distribute the constants inside the parentheses:
- For the first term: \[ 4\left(\frac{3}{4}x\right) = 3x \] \[ 4(3x) = 12x \] \[ 4(-2) = -8 \] So, the first term becomes: \[ 3x + 12x - 8 = 15x - 8 \]
- For the second term: \[ -2(3x^2) = -6x^2 \] \[ -2(1) = -2 \] \[ -2(3x) = -6x \] So, the second term becomes: \[ -6x^2 - 6x - 2 \]
Combine the two results: The entire expression now looks like this: \[ (15x - 8) + (-6x^2 - 6x - 2) \]
Combine like terms: \[ -6x^2 + (15x - 6x) + (-8 - 2) \] Which simplifies to: \[ -6x^2 + 9x - 10 \]

Thus, the equivalent expression with the fewest terms possible is: \[ -6x^2 + 9x - 10 \]

Scar · Answer

An equation is shown. y−5 = −3(x+6) (2 points) The equation rewritten in slope-intercept form is . The point is on the graph of the line.

GPT-4o mini · Answer

To rewrite the equation $ y - 5 = -3(x + 6) $ in slope-intercept form (which is $ y = mx + b $), we'll follow these steps: 1. **Distribute the $-3$ on the right side:** $$ y - 5 = -3x - 18 $$ 2. **Add $5$ to both sides to isolate $y$:** $$ y = -3x - 18 + 5 $$ $$ y = -3x - 13 $$ Now, the equation in slope-intercept form is: $$ y = -3x - 13 $$ ### Identifying a Point on the Graph: To find a point on the graph of the line, we can choose any value for $x$ and solve for $y$. Let's choose $x = 0$: 1. Plug $x = 0$ into the equation: $$ y = -3(0) - 13 = -13 $$ Thus, the point $(0, -13)$ is on the graph of the line. ### Final Answers: - The equation in slope-intercept form is: $$ y = -3x - 13 $$ - The point that is on the graph of the line is: $$ (0, -13) $$

Scar · Answer

y-5=-3(x+6) slope intercept the point

GPT-4o mini · Answer

To rewrite the equation $ y - 5 = -3(x + 6) $ in slope-intercept form and find a point on the graph, follow these steps: ### Step 1: Rewrite in Slope-Intercept Form Start with the given equation: $$ y - 5 = -3(x + 6) $$ 1. **Distribute the $-3$:** $$ y - 5 = -3x - 18 $$ 2. **Add $5$ to both sides:** $$ y = -3x - 18 + 5 $$ $$ y = -3x - 13 $$ ### Slope-Intercept Form The equation in slope-intercept form is: $$ y = -3x - 13 $$ - **Slope (m):** $-3$ - **Y-intercept (b):** $-13$ ### Step 2: Find a Point on the Graph We can find a point by substituting a value for $x$ into the equation. **Let's choose $x = 0$:** $$ y = -3(0) - 13 = -13 $$ Thus, one point on the graph is: $$ (0, -13) $$ ### Summary - **Slope-Intercept Form:** $y = -3x - 13$ - **Point on the Graph:** $(0, -13)$

Scar · Answer

there is no 0,-13

GPT-4o mini · Answer

I apologize for the oversight! Let's reassess the equation and calculate a suitable point accurately.

Given the equation:

\[ y - 5 = -3(x + 6) \]

Step 1: Rewrite in Slope-Intercept Form

Distribute the $-3$:

\[ y - 5 = -3x - 18 \]

Add $5$ to both sides:

\[ y = -3x - 18 + 5 \]

\[ y = -3x - 13 \]

Slope-Intercept Form

The equation in slope-intercept form is: \[ y = -3x - 13 \]

Slope (m): $-3$
Y-intercept (b): $-13$

Step 2: Find a Point on the Graph

Let's find a point by choosing a different value for $x$.

Let's choose $x = -6$ (a convenient choice because it simplifies our original equation): \[ y = -3(-6) - 13 \]

Calculating it: \[ y = 18 - 13 = 5 \]

Thus, we have the point: \[ (-6, 5) \]

Summary

Slope-Intercept Form: $y = -3x - 13$
Point on the Graph: $(-6, 5)$

Thank you for your patience! If you have further questions, feel free to ask!

Scar · Answer

Complete the statements.

The slope of the line is Response area
The y-intercept is Response area Write this as an ordered pair
An equation of the line in slope-intercept form is Response area
A point on the graph that is NOT the y-intercept is Response area
An equation of the line in point-slope form is Response area

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GPT-4o mini · Answer

Let's complete the statements based on the equation we derived earlier, which is:

\[ y = -3x - 13 \]

Completing the Statements

The slope of the line is:
Response area: $-3$
The y-intercept is:
Response area: $-13$
(This can also be written as the ordered pair (0, -13).)
Write this as an ordered pair:
Response area: $(0, -13)$
A point on the graph that is NOT the y-intercept is:
Response area: $(-6, 5)$
(This is the point we found in the previous response.)
An equation of the line in point-slope form is:
The point-slope form is given by the formula:
\[ y - y_1 = m(x - x_1) \]
Using the point $(-6, 5)$ and the slope $-3$:
Response area:
\[ y - 5 = -3(x + 6) \]
(This is equivalent to the form we started with.)

Summary of Responses

The slope of the line is: -3
The y-intercept is: -13
Write this as an ordered pair: (0, -13)
A point on the graph that is NOT the y-intercept is: (-6, 5)
An equation of the line in point-slope form is: y - 5 = -3(x + 6)

Feel free to ask any further questions!