Answer:
x = 5
Step-by-step explanation:
The area (A) o a rectangle is calculated as
A = lb ( l is length and b the breadth ), thus
x² + x - 12 × 
= 126 ← factor the quadratic
(x + 4)(x - 3) × = 126 ← cancel the common factor (x - 3)
(x + 4)(x + 9) = 126 ← expand factors using FOIL
x² + 13x + 36 = 126 ( subtract 126 from both sides )
x² + 13x - 90 = 0 ← in standard form
(x + 18)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 18 = 0 ⇒ x = - 18
x - 5 = 0 ⇒ x = 5
However x > 0 ⇒ x = 5
Answer: y = -x/3 + 5
Step-by-step explanation:
What we know:
- Our points are (-3, 6) and (0, 5)
First, we need to find the slope. The formula for finding slope is y2 - y1/x2 - x1.
Now, we need to plug in our values.
5 - 6/0 - (-3)
Solve.
-1/3
Our slope is -1/3.
But now we need to find the y-intercept. To do this, we will use the equation y = mx + b.
You can use either coordinate pair, but I will be using (-3, 6) first.
Plug in the values.
6 = -1/3(-3) + b
Simplify.
6 = 1 + b
Subtract 1 to both sides.
6 - 1 = 1 - 1 + b
5 = b
The y-intercept is 5. Now we can put everything together!
y = -1/3x + 5
y = -x/3 + 5
For the coordinate (0, 5), you do the same thing.
5 = -1/3(0) + b
5 = 0 + b
5 = b
y = -1/3x + 5
y = -x/3 + 5
