The simplified rational expression is (y - 3)/(y + 3). Where y ≠ -3.
<h3>How to simplify a rational expression?</h3>
A rational expression is in the p/q form. Where p and q are polynomial functions.
To simplify this rational equation,
- Factorize the polynomials in both numerator and denomiantor.
- Cancel out common factors if any.
- If the denominator and the numerator have no common factors except 1, then that is said to be the simplest form of the given rational expression.
<h3>Calculation:</h3>
The given rational equation is
Factorizing the expression in the numerator:
y² - 12y + 27 = y² - 9y - 3y + 27
⇒ y(y - 9) - 3(y - 9)
⇒ (y - 3)(y - 9)
Factorizing the expression in the denominator:
y² - 6y - 27 = y² - 9y + 3y - 27
⇒ y(y - 9) + 3(y - 9)
⇒ (y + 3)(y - 9)
Since they have (y - 9) as the common factor, we can simplify,
⇒ (y - 3)/(y + 3) where y ≠ -3(denomiantor)
Here there are no more common factors except 1; this is the simplest form of the given rational expression.
Learn more about simplifying rational expressions here:
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Answer:
It was an exponential increase
In 3 months, the bill will be $285.61
Step-by-step explanation:
First, this scenario is exponential, because the price of food is increasing with a percentage, based on the price that it was the previous amount.
Next, to find what the bill will be in 3 months, an equation needs to be made representing the situation.
Use the standard exponential equation: y = ab^x, where a is the initial amount, b is the growth rate, and x is the amount of time.
Plug in the values we know:
y = 130(1.3)^3
Solve for y
y = 285.61
So, 3 months later, the bill will be $285.61
Answer:
Sandra need to score at least <u>56%</u> in her fifth test so that her average is 80%.
Step-by-step explanation:
Given:
First 4 test scores = 87%, 92%, 76%,89%
Average targeted = 80%
We need to find the minimum score she needs to make on fifth test to achieve average of at least 80%.
Solution:
Let the minimum score she needs to make in fifth test be 'x'.
Total number of test = 5
Now we know that;
Average is equal to sum of all the scores in the test divided by number of test.
framing in equation form we get;
Multiplying both side by 5 we get;
Subtracting both side by 344 we get;
Hence Sandra need to score at least <u>56%</u> in her fifth test so that her average is 80%.
Answer:
x= 1
Step-by-step explanation:
Solve
Let's solve your equation step-by-step.
4x−2=2x
Step 1: Subtract 2x from both sides.
4x−2−2x=2x−2x
2x−2=0
Step 2: Add 2 to both sides.
2x−2+2=0+2
2x=2
Step 3: Divide both sides by 2.
2x
2
=
2
2
x=1
Answer:
k = - 6.6667
Step-by-step explanation:
this is quite very simple to begin. I would encourage you take other practice questions similar to help with understanding it.
let us begin.
Given that ;
dT/dt = k ( Tm - T) where Tm is the temp of the medium
dT/dt = 5 degrees Celsius per minute when T = 70
so we have that, 5 = k ( 25 - 70)
remember to convert 5 degree celsius per minute to seconds
we have that;
5*60(sec) = k ( 25 - 70)
k = 5*60 / ( 25 - 70)
k = - 6.6667
note K is negative because we consider it for cooling process (temp decreasing).
cheers i hope this helps!!!
