Answer:
B
Step-by-step explanation:
When you add 2pi to the angle, the amount is still the same. Therefore, you can make -17pi/4 positive by adding 6pi to it.
6pi + (-17pi/4)
= 24pi/4 - 17pi/4
= 7pi/4
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:
72 kg
Step-by-step explanation:
For concreatting a tower cement, sand, stones are in the ratio 1:2:4 For 144kg sand.. What amount of cement is required?
We are given the ratio
cement: sand:stones
= 1:2:4
The sum of proportion =
1 + 2 + 4 = 7
We are given the kg of sand = 144kg
Step 1
We find the total kg of cement, sand and stones = x
Using the proportion of sand,
2/7 of x = 144kg
2/7 × x = 144kg
2x/7 = 144kg
Cross Multiply
2x = 7 × 144kg
x = 7 × 144kg/2
x = 504kg
Therefore the total kg of cement, sand and stone = 504kg
Step 2
The amount of cement required is calculated as:
1/7 × 504 kg = 72 kg
Therefore, 72kg of cement is required.
Answer:
x ≈ 18
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Trigonometry</u>
Law of Cosines: a^2 = b^2 + c^2 - 2(b)(c)cosA
- a is a side length
- b is a side length
- c is a side length
- A is an angle corresponding with side a
Step-by-step explanation:
<u>Step 1: Define</u>
a = x
A = 30°
b = 16
c = 30
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute: x² = 16² + 30² - 2(16)(30)cos30°
- Exponents: x² = 256 + 900 -2(16)(30)cos30°
- Evaluate: x² = 256 + 900 -2(16)(30)(√3/2)
- Multiply: x² = 256 + 900 - 480√3
- Add: x² = 1156 - 480√3
- Subtract: x² = 324.616
- Isolate <em>x</em>: x = √324.616
- Evaluate: x = 18.0171
- Round: x ≈ 18
