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ioda
3 years ago
7

PLEASE HELP meeeeeeee

Mathematics
1 answer:
BigorU [14]3 years ago
6 0
<h3>Answer: Distance between x intercepts is 1 unit.</h3>

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

Explanation:

Let's find the x intercept of f(x). Replace f(x) with 0 and solve for x

f(x) = -2x+2

0 = -2x+2

2x = 2

x = 2/2

x = 1

Plugging x = 1 into f(x) leads to f(x) = 0. The x intercept of f(x) is 1.

-----------------------

Now onto g(x). If we were given a row that had y = 0, then we'd immediately find the x intercept. However, that isn't given, so we'll have to do a bit of work to find the equation for g(x).

First we need the slope. Pick any two rows to find the slope. I'll pick the middle two rows.

m = (y2-y1)/(x2-x1)

m = (3-6)/(1-0)

m = -3/1

m = -3 is the slope

The y intercept is b = 6 as the table shows this pairs with x = 0. The y intercept always happens when x = 0.

So with m = -3 and b = 6, we see that g(x) = -3x+6.

-------------------------

Plug in g(x) = 0 and solve for x. We'll use similar ideas done in the first section at the very top

g(x) = -3x+6

0 = -3x+6

3x = 6

x = 6/3

x = 2 is the x intercept of g(x)

--------------------------

In summary, we found...

  • x = 1 is the y intercept of f(x)
  • x = 2 is the y intercept of g(x)

Subtract the x intercept values to get 2-1 = 1, which is the distance between the x intercepts. The distance is never negative.

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Answer:

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Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

<u>When factoring trinomials of the form ax² + bx + c</u>:

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1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

  1. 4x + 7 = 0
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<u><em>Case 1:</em></u>

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = \bold{-\dfrac{7}{4}}

<u><em>Case 2:</em></u>

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = \bold{\dfrac{1}{2}}

Solutions:

\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

brainly.com/question/27638369

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