Question

Applying the definition of module and simplifications, fill in the gaps. |π‘₯| βˆ’ 2|π‘₯ βˆ’ 3| = { π‘₯ βˆ’ 6, 𝑠𝑒 π‘₯ < 0 ___________, 𝑠𝑒 0 ≀ π‘₯ < ______ ______, 𝑠𝑒_________________

56

likes
279 views

Answer to a math question Applying the definition of module and simplifications, fill in the gaps. |π‘₯| βˆ’ 2|π‘₯ βˆ’ 3| = { π‘₯ βˆ’ 6, 𝑠𝑒 π‘₯ < 0 ___________, 𝑠𝑒 0 ≀ π‘₯ < ______ ______, 𝑠𝑒_________________

Expert avatar
Rasheed
4.7
110 Answers
|x| - 2|x - 3| = \begin{cases} x - 6, & \text{if } x < 0 \\3x - 6, & \text{if } 0 \leq x < 3 \\-x + 6, & \text{if } x \geq 3 \end{cases}

1. For \(x < 0\):
|x| = -x \quad \text{and} \quad |x - 3| = -x + 3
-x - 2(-x + 3) = x - 6

2. For \(0 \leq x < 3\):
|x| = x \quad \text{and} \quad |x - 3| = -x + 3
x - 2(-x + 3) = 3x - 6

3. For \(x \geq 3\):
|x| = x \quad \text{and} \quad |x - 3| = x - 3
x - 2(x - 3) = -x + 6

Frequently asked questions (FAQs)
What is the value of sin 45Β°?
+
Math Question: Convert the number 5,000,000,000,000,000 into scientific notation.
+
What is the average selling price of 50 cars, given that the maximum price is $100,000 and the minimum price is $5,000?
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
Find 2 numbers that the sum of 1/3 of the first plus 1/5 of the second will be equal to 13 and that if you multiply the first by 5 and the second by 7 you get 247 as the sum of the two products with replacement solution
𝑦 = ( π‘₯2 βˆ’ 3) (π‘₯3 + 2 π‘₯ + 1)
5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight
Evaluate limxβ†’βˆžtanβˆ’1(x) using that y=tanβˆ’1(x) exactly when x=tan(y) . (Hint: Both tan and tanβˆ’1 are continuous!)
The sum of two numbers is 6, and the sum of their squares is 28. Find these numbers exactly
A soft drink machine outputs a mean of 23 ounces per cup. The machines output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 26 and 28 ounces round your answer to four decimal places
To make brine, JosΓ© buys 1 kg of salt and pays 12 pesos. If he buys 4 kg, they charge him 48 pesos, but for 100 pesos they sell him 9 kg. What is the constant of proportionality?
"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?" The answer is the number of response units.
determine the polynomial F of degree 2 that interpolates. f at points (0;1) (2;5) (4;6). calculate F(0.8). Note: Using the polynomial expression with difference operator.
The question is using rule 72 determine Kari wants to save 10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current 5,000 savings based on 6%, 12% and 18% interest rate .
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
15.A newly married couple purchased a home with a $123710 down payment. They financed the remaining balance of the home with a mortgage. Their payments were $15395 at the end of every six months for 23 years and the interest rate was 10.6%, compounded semi-annually. How much did they purchase their home for. Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0
The blood types of individuals in society are as follows: A: 30%, B: 25%, AB: 20%, 0: 25%. It is known that the rates of contracting a certain disease according to blood groups are as follows: A: 7%, B: 6%, AB: 7%, 0: 4%. Accordingly, if a person selected by chance is known to have this disease, what is the probability of having blood group O?
Gender and communication : Answer the question ( 1 paragraph is ok) . Please can you write about women? Compared to your other identities, how much of a role does gender play in your life? And has your own sex/gender offered you privileges or disadvantages? How so?
Find I (Intrest) using simple interest formula of 17700 @ 15% for 4 years
Solve for z: 2z-6=10z+2
64-6x^2>0
Find the number of liters of water needed to reduce 9 liters of lotion. shave containing 50% alcohol to a lotion containing 30% alcohol.