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Kobotan [32]
3 years ago
10

Solve for x: 4(x + 4) = 6(x - 2) O A. x = 9 B. x = 14 O C. x = 8 D. x = 1

Mathematics
2 answers:
ad-work [718]3 years ago
5 0

Answer: 14 = x

Step-by-step explanation: Start by distributing through the parenthses

on each side of the equation to get 4x + 16 = 6x - 12.

Now move your x's to the right and numbers

to the left and you get 28 = 2x.

Divide both sides by 2 and 14 = x.

BigorU [14]3 years ago
4 0

Answer:

x = 14

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

4(x + 4) = 6(x - 2)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                   4x + 16 = 6x - 12
  2. Subtract 4x on both sides:         16 = 2x - 12
  3. Add 12 on both sides:                28 = 2x
  4. Divide 2 on both sides:              14 = x
  5. Rewrite:                                       x = 14

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    4(14 + 4) = 6(14 - 2)
  2. Add/Subtract:               4(18) = 6(12)
  3. Multiply:                        72 = 72

And we have our final answer!

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4 0
3 years ago
Suppose a parabola has vertex (6,5) and also passes through the point (7,7). Write the equation of the parabola in vertex form.
jek_recluse [69]

Answer:

Choice B: y = 2\, (x - 6)^{2} + 5.

Step-by-step explanation:

For a parabola with vertex (h,\, k), the vertex form equation of that parabola in would be:

\text{$y = a\, (x - h)^{2} + k$ for some constant $a$}.

In this question, the vertex is (6,\, 5), such that h = 6 and k = 5. There would exist a constant a such that the equation of this parabola would be:

y = a\, (x - 6)^{2} + 5.

The next step is to find the value of the constant a.

Given that this parabola includes the point (7,\, 7), x = 7 and y = 7 would need to satisfy the equation of this parabola, y = a\, (x - 6)^{2} + 5.

Substitute these two values into the equation for this parabola:

7 = (7 - 6)^{2}\, a + 5.

Solve this equation for a:

7 = a + 5.

a = 2.

Hence, the equation of this parabola would be:

y = 2\, (x - 6)^{2} + 5.

4 0
3 years ago
Why is this undefined
Burka [1]
Because you can’t divide something by zero!
Hope this helps!
7 0
3 years ago
Read 2 more answers
You have 6 liters of paint to share evenly among you and your 4 brothers.
Assoli18 [71]
6/4 = 1.5 liters of pain per brother
5 0
3 years ago
What is the ratio of x to y?
abruzzese [7]
\frac{3}{2} = \frac{2x}{2x+y}

From any proportion, we get another proportion by inverting the extremes (or the means):

\frac{2x+y}{2} = \frac{2x}{3} = k

so we have:

2x=3k
2x+y=2k therefore:
3k+y=2k
y= - k

x=\frac{3}{2} k

\frac{x}{y} = - \frac{3}{2}

The corect answer is A. -3/2

or:

\frac{3}{2} = \frac{2x}{2x+y}

From any proportion, we get another proportion by inverting the extremes and the means:

\frac{2x+y}{2x} = \frac{2}{3}

We use a property of proportions:

\frac{a}{b} = \frac{c}{d}  where a, d are extremes and b,c are means and the product of the extremes equals the product of the means (a*d=b*c),

so we have

\frac{a-b}{b} = \frac{c-d}{d}  or

\frac{a+b}{b} = \frac{c+d}{d}  (you can check this also by "the product of the extremes equals the product of the means")

\frac{2x+y}{2x} = \frac{2}{3}

\frac{(2x+y)-2x}{2x} = \frac{2-3}{3}

\frac{y}{2x} = \frac{-1}{3}

3y = - 2x

\frac{x}{y} = -\frac{3}{2}



4 0
3 years ago
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