Excuse me but his answer is incorrect. To find the proper rate of change you might have to solve it like you would for slope.
First you would find the points for x = 3 and x = 15 would be (3, 0.08) and (15, 327.68). Then using the slope formula you can find 327.60/ 12. That gives 27.3. So in that case the correct answer is C.
Hi there!
The question here asks us to find all the roots, or solutions, of the quartic equation x⁴ - 4x³ + x² + 12x - 12 = 0. We can start off by using the Rational Root Theorem, which calls for the constant over the leading coefficient, which for us would be 12 over 1. Since we need to list all the factors of 12, they all become + or -.
<u>+</u>12 / <u>+</u> 1
=> <u>+</u>1, <u>+</u>2, <u>+</u>3, <u>+</u>4, <u>+</u>6, <u>+</u>12 / <u>+</u>1
Now, just simplify each one. We get the possible roots 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12. The next part is the most tedious. Plug in each possible factor for x and see if the resulting value is 0. We get that only root 2 makes the whole equation equal to zero. However, we are not done yet. The question asks for the ALL the roots of the equation, not just real, but also imaginary. Let's use synthetic division to find the other roots.
We can set the divisor to 2, as (x - 2) = 0 is equal to x = 2.
2| 1 -4 1 12 -12
2 -4 -6 12
1 -2 -3 6 0
We can now factor the whole original equation to (x - 2)(x³ - 2x² -3x + 6) = 0. Now, we have to factor the expression x³ - 2x² -3x + 6, and grouping seems like the most appropriate way.
x³ - 2x² -3x + 6 = 0
(x³ - 2x²) + (-3x + 6) = 0
x²(x - 2) - 3(x - 2) = 0
(x² - 3)(x - 2) = 0
Next, use the Zero Product Property to get the values of x.
x² - 3 = 0
x² = 3
x = √3
x ≈ <u>+</u> 1.73
x - 2 = 0
x = 2
Therefore, the roots of the equation x⁴ - 4x³ + x² + 12x - 12 = 0 are x = 2,x = 2 (repeated solution), x = 1.73, x = -1.73. Hope this helped and have a great day!
Answer:
a. 1 hour and 32 minutes b. 8:07
Step-by-step explanation:
a.8:34-7:02
b. 9 minutes +1 hour and 32 minutes+12 minutes=1.53 hours before 10=8:07
Answer:
Step-by-step explanation:
<u>Multiply the number of containers by the amount in each to find the total amount of sugar:</u>
- 2 4/5 * 2 3/7 =
- 14/5 * 17/7 =
- 2*17/5 =
- 34/5 =
- 6 4/5
