Answer:
It's a function that associates a real number x with a positive real number using the flowing definition: If the number is not negative (so either positive or 0) the absolute value is x. If x is negative, the absolute value is -x.
This means that to find the absolute value of x you must first determine if x is negative or not, and if it is, multiply it by -1. If it isn't, leave it as it is.
Since the absolute value is a function (of a given number), you can't just plot that number in the number line but the function (so in this case absolute value must be taken first.
The absolute value of x is never negative, so given the absolute value of x we can't determinate if x was positive or negative (if x =/ 0) before the absolute value was taken.
Answer:
53.54m
Step-by-step explanation:
Using the formulas
A=πr2
d=2r
Solving for d
d=2A
π=2·2251
π≈53.53562m
Answer:
Richard will have $60,000 in his account in 20 years.
Step-by-step explanation:
(1) Multiply $250 x 12
(2) Multiply the answer of $250 x 12 which is 3000 by 20
(3) Final answer would be $60,000
Question 3. The true statements are:
4g2 – g = g2(4 – g) ⇒ should be: 4g² - g = g(4g - 1)
9g3 + 12 = 3(3g3 + 4) ⇒ should be: 9g³ + 12 = 3(3g³ + 4) TRUE
24g4 + 18g2 = 6g2(4g2 + 3g) ⇒ should be: 24g⁴ + 18g² = 6g²(4g² + 3)
<span>35g5 – 25g2 = 5g2(7g3 – 5) </span>⇒ should be: 35g⁵ - 25g² = 5g²(7g³ - 5) TRUE
Question 4. Completely factored.
16y⁵ + 12y³ = 4y³(4y² + 3) FACTORED COMPLETELY
18y³ - 6y = 6y(3y² - 1)
20y⁷ + 10y² = 10y²(2y⁵ + 1)
32y¹⁰ - 24 = 8(4y¹⁰ - 3) FACTORED COMPLETELY
As the question states, let r be the number of hours worked at the restaurant, and y be the number of hours of yard work.
We know that she can only work a maximum of 15 hours per work total, and that at she must work at least 5 hours in the restaurant.
Therefore:
r + y ≤ 15
r ≥ 5
We also know that she wants to earn at least 120 dollars, earning $8/hr in the restaurant and $12/hr in the yard:
8r + 12y ≥ 120
What is the maximum of hours Lia can work in the restaurant and still make at leas 120 hours?
Lia's parents won't let her work more than 15 hours, so we know that the answer won't be higher than 15.
If she worked all 15 hours in the restaurant, she would make 8*15 = 120.
The maximum number of hours she can work in the restaurant is therefore 15 hours
What is the maximum amount of money Lia can earn in a week?
Lia has to work a minimum of 5 hours in the restaurant. She makes more money doing yard work, so she should devote the rest of her available work hours to yard work.
That means that, given her 15 hour work limit, she will maximize her income by working 5 hours in the restaurant and 10 hours in the yard.
5*8 + 10*12 = 40 + 120 = 160
The most she can make is 160 dollars, working 5 hours in the restaurant and 10 hours in the yard
