So think of |x+6| as a single object. Move the -6|x+6| to the left side and move the 8 to the right side to get 11|x+6| = 0. Then divide both sides by 11 to get |x+6| = 0 and in this instance the || can be dropped because +0 and -0 are the same. so x + 6 = 0 or x=-6
Answer:
B) False
Step-by-step explanation:
Counterexample
| 2x + 3 | = 7
2x + 3 = +7 , -7
The answer should be -116
Answer:
A polynomial function that meet the conditions is x³ - 8x² + 5x + 14 = 0
Step-by-step explanation:
Hi there!
Let´s start writting a generic factored function. In this case, the function has 3 zeros so that the factored form will have 3 terms:
(x + a)(x + b)(x + c) = 0
For this expression to be 0, either (x+a) = 0 or (x+b) = 0 or (x+c) = 0
Then:
x + a = 0 ⇒ x = -a
x + b = 0 ⇒ x = -b
x + c = 0 ⇒ x = -c
Then, the values "a", "b" and "c" are equal to the zeros of the function but with opposite sign. Then, in our case:
a = 1
b = -2
c = -7
Then, the polynomial fuction will be:
(x + 1)(x - 2)(x - 7) = 0
Apply distributive property:
(x² - 2x + x -2)(x -7) = 0
(x² - x - 2)(x - 7)
x³ - x² - 2x - 7x² + 7x + 14 = 0
x³ - 8x² + 5x + 14 = 0
Then, a polynomial function that meets the conditions is:
x³ - 8x² + 5x + 14 = 0
Have a nice day!
Answer:
The numbers are 18, 13, and 72.
Step-by-step explanation:
Let the three numbers be represented by <em>a, b</em>, and <em>c</em>.
The sum of the three is 103. Thus, we can write that:
The second number is five less than the first. So:
And the third number is four times the first. So:
Substitute:
Solve for <em>a</em>. Combine like terms:
Add five to both sides:
And divide both sides by six. Therefore:
So, the first number is 18.
Since the second number is five less than the first, the second number is 13.
And since the third number is four times the first, the third number is 72.
