Answer:
3 =n
Step-by-step explanation:
-3 +3(n+8)= 2(1 + 6n) - 8
Distribute
-3 +3n +24 = 2 +12n -8
Combine like terms
21+3n = 12n -6
Subtract 3n from each side
21+3n-3n = 12n-3n -6
21 = 9n -6
Add 6 to each side
21+6 = 9n-6+6
27 = 9n
Divide each side by 9
27/9 = 9n/9
27/9 =n
Divide the top and bottom by 3
3 =n
Answer:
16/15
Step-by-step explanation:
The two minus signs cancel, so the result is positive.
Answer: (32/2)*3=48
Step-by-step explanation:
In order to find the answer, we must find one third of last year's trip. To do this, we can simply divide the cost of this years trip by two, 32/2=16.
Now if we multiply this this number by 3, 16*3=48, we can see that the total cost of last year's trip was $48.
If we'd like to turn this into one equation, it looks like this: (32/2)*3=48
The solutions for the given quadratic equation are x = -1 and x = 3. So, option B is correct.
<h3>What are the solutions to an equation?</h3>
- The solutions to an equation are the one that satisfies the equation and makes it true.
- There are different methods to solve an equation and find its solutions.
- These solutions are also called zeros or roots of the equation.
<h3>Calculation:</h3>
The given equation is 4x² - 8x - 12 = 0
Since it is a quadratic equation, it has 2 roots or solutions.
On factorizing the given equation,
4x² - 8x - 12 = 0
⇒ 4x² - 12x + 4x -12 = 0
⇒ 4x(x - 3) + 4(x - 3) = 0
⇒ (4x + 4)(x - 3) = 0
According to the zero-product rule,
4x + 4 = 0 or x - 3 = 0
So, x = -4/4 = -1 or x = 3
Therefore, the solutions of the given equation are -1 and 3.
So, option B) x = -1 and x = 3 is correct.
Learn more about solving an equation here:
brainly.com/question/25678139
#SPJ4
<h2>
Answer: y = ⁵/₂ x - 13 OR y + 8 =
⁵/₂ x - 5 </h2>
<h3>
Step-by-step explanation:</h3>
<u>Find the slope of the perpendicular line</u>
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are <em>negative-reciprocal</em>s of each other.
⇒ if the slope of this line = - ²/₅
then the slope of the perpendicular line (m) = ⁵/₂
<u>Determine the equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-8) = ⁵/₂ (x - 2)
∴ y + 8 = ⁵/₂ (x - 2)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y + 8 = ⁵/₂ (x - 2)
y = ⁵/₂ x - 13
