Answer:
y = -3/2x + 3
General Formulas and Concepts:
<u>Algebra I</u>
Equality Properties
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
Step-by-step explanation:
<u>Step 1: Define</u>
Standard Form: 3x + 2y = 6
<u>Step 2: Find slope-intercept form</u>
- Subtract 3x on both sides: 2y = 6 - 3x
- Divide both sides by 2: y = 3 - 3/2x
- Rewrite: y = -3/2x + 3
And we have our final answer!
Answer:
Option (3)
Step-by-step explanation:
If binomial (x - 6) and trinomial (-2x² + x + 9) are the factors of a polynomial then their multiplication will be equal to the polynomial.
(x - 6)(-2x² + x + 9) = x(-2x² + x + 9) - 6(-2x² + x + 9)
= -2x³ + x² + 9x + 12x² - 6x - 54
= -2x³ + 13x² + 3x - 54
Therefore, Option (3) will be the correct option.
Answer:
Step-by-step explanation:
Geometric sequence
Each term in a geometric sequence can be computed as the previous term by a constant number called the common ratio. The formula to get the term n is
where 
is the first term of the sequence
The problem describes Georgie took 275 mg of the medicine for her cold in the first hour and that in each subsequent hour, the amount of medicine in her body is 91% (0.91) of the amount from the previous hour. It can be written as
amount in hour n = amount in hour n-1 * 0.91
a)
This information provides the necessary data to write the general term as
b)
In the 8th hour (n=8), the remaining medicine present is Georgie's body is
Answer:
VY
Step-by-step explanation:
Coz they all look the same on the sides
Answer:
(x + 1)² = 7
Step-by-step explanation:
Given:
-2x = x² - 6
We'll start by rearranging it to solve for zero:
x² + 2x - 6 = 0
The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.
Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:
x² + 2x + 1 - 1 - 6 = 0
Now can group our perfect square on the left and our constants on the right:
x² + 2x + 1 - 7= 0
x² + 2x + 1 = 7
(x + 1)² = 7
To check our answer, we can solve for x:
x + 1 = ± √7
x = -1 ± √7
x ≈ 1.65, -3.65
Let's try one of those in the original equation:
-2x = x² - 6
-2(1.65) = 1.65² - 6
- 3.3 = 2.72 - 6
-3.3 = -3.28
Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.
