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3 years ago

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Solve: 4x - 2x + 6 = x + 12 A) x = 6 B) x = 2 C) no solution D) x = −6

2 answers:

Zanzabum3 years ago

8 0

Answer:

A) x = 6

Step-by-step explanation:

Step 1: Get all x terms to one side, and all constants to the other side

4x - 2x + 6 = x + 12

4x - 2x - x + 6 - 6 = x - x + 12 - 6 (subtract 'x' and '6' from both sides)

4x - 2x + x = 12 - 6 (simplify)

x = 6 (combine like terms, 4x - 2x + x is 'x', 12 - 6 is '6')

Kitty [74]3 years ago

7 0

Answer:

A) x = 6

Step-by-step explanation:

4x - 2x + 6 = x + 12

Combine like terms

2x +6 = x+12

Subtract 6 from each side

2x+6-6 = x+12-6

2x = x+6

subtract x

2x-x = x+6-x

x = 6

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

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Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

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

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

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