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Julli [10]
2 years ago
13

What is the product of (2x-7) and (3x + 3)?

Mathematics
1 answer:
eduard2 years ago
3 0
<h3>✒️EVALUATION </h3>

==================================

\large\sf\underline{Problem:}

What is the product of (2x-7) and (3x + 3)?

  • A. 6x2 + 15x-21
  • B. 6x2 - 15x - 21
  • C. 6x2 + 15x + 21
  • D. 6x2 - 15x + 21

==================================

\large\sf\underline{Answer:}

\qquad \qquad \huge \rm Letter\:B.

*Please read and understand my solution. Don't just rely on my direct answer*

==================================

\large\sf\underline{Solution:}

Here we have the given choices:

  • A. 6x2 + 15x-21
  • B. 6x2 - 15x - 21
  • C. 6x2 + 15x + 21
  • D. 6x2 - 15x + 21

Solve this equation using the distributive property,where you multiply each term to get the number.

\begin{gathered} \rm2x - 7 = \boxed{ 6} \: \bigg| \small\boxed{\: 6 {x}^{2} } \\ \rm (7)(3) = \boxed{21} \bigg | \boxed{\: 21 x} \\ \\ \qquad \rm6x^{2}+(6x- 21x)-21 \\ \qquad \boxed{ \rm6 {x}^{2} + 15x - 21}\end{gathered}

Therefore, the correct option is letter B.

==================================

ヾ(^-^)ノ

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<u>Algebra I</u>

Slope Formula: \displaystyle m=\frac{y_2-y_1}{x_2-x_1}

Slope-Intercept Form: y = mx + b

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Step-by-step explanation:

We can draw any best line of fit, as long as it is <em>reasonable</em> around the points that are given.

We can just take 2 points and use slope formula and Slope-Intercept Form to find the equation for the best line of fit.

Using Linear Regression, we can determine the <em>true</em> best line of fit using graphing utilities.

<u>Finding the best line of fit</u>

<em>Define 2 points</em>

Point (21600, 205)

Point (27000, 290)

<em>Find slope m</em>

  1. Substitute in point [SF]:                    \displaystyle m=\frac{290-205}{27000-21600}
  2. [Fraction] Subtract:                           \displaystyle m=\frac{85}{5400}
  3. [Fraction] Simplify:                            \displaystyle m=\frac{17}{1080}

<em>Find equation</em>

  1. Define equation [SIF]:                        \displaystyle y = \frac{17}{1080}x + b
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  3. Multiply:                                             \displaystyle 290 = 425 + b
  4. Isolate y-intercept <em>b</em>:                         \displaystyle -135 = b
  5. Rewrite:                                             \displaystyle b = -135
  6. Redefine equation:                           \displaystyle y = \frac{17}{1080}x - 135

Slope-Intercept Form tells us that our slope <em>m</em> = \displaystyle \frac{17}{1080} and our y-intercept \displaystyle b = -135.

Setting this as function f(x), we can see from the graph that it is extremely accurate (Blue line).

<u>Using Linear Regression</u>

Depending on the graphing calc you have, the steps may be different.

Using a graphing calc, we can use statistics and determine the <em>best</em> best line of fit.

When we determine the values, we should see that our equation would be g(x) (Green Line).

<em>Credit to Lauren for collabing w/ me in graphing.</em>

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