Hello there!
For these, you can only add the numbers with the same index. For example, you can add x² and 2x², but not x³ and x².
So here, you can just look based on their indexes:
There are two with an index of 4:
4

and

.
You can add those, and you get 5

.
There's one with an index of 3: x³. So there's an +x³ in the final equation.
For those with an index of 2, there are two: x² and -x². Those two cancel out just to equal 0.
For just x, there's x, and -x. Those two cancel out as well.
There's the final -1.
So you're looking for:
5

+ x³ - 1, or C.
The x-intercept of the function
is -2
<h3>How to determine the x-intercept?</h3>
The equation of the function is given as:
![h(x) = 8 * \sqrt[3]{x - 6} + 16](https://tex.z-dn.net/?f=h%28x%29%20%3D%208%20%2A%20%5Csqrt%5B3%5D%7Bx%20-%206%7D%20%2B%2016)
The x intercept is the x value when h(x) = 0
So, we have:
![8 * \sqrt[3]{x - 6} + 16 = 0](https://tex.z-dn.net/?f=8%20%2A%20%5Csqrt%5B3%5D%7Bx%20-%206%7D%20%2B%2016%20%3D%200)
Subtract 16 from both sides
![8 * \sqrt[3]{x - 6} = -16](https://tex.z-dn.net/?f=8%20%2A%20%5Csqrt%5B3%5D%7Bx%20-%206%7D%20%3D%20-16)
Divide both sides by 8
![\sqrt[3]{x - 6} = -2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%20-%206%7D%20%3D%20-2)
Take the cube of both sides
x - 6 = -8
Add 6 to both sides
x = -2
Hence, the x-intercept of the function
is -2
Read more about x-intercept at:
brainly.com/question/3951754
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Answer:
22.2%
Step-by-step explanation:
Probability is the chance of an event happening, it can be found by using the following formula,

Where the word (desired) represents the outcomes one wants, and (total) represents the total number of outcomes.
In this case, one is asked to find the probability of the sum of two numbers the results from rolling two dice, not being a multiple of (3) or (2). In this case, it is easier to list out the number of numbers between (1) and (12) that are not a multiple of three or two. Please note, the largest sum of number one can get when rolling two dice is (12), since the largest value on a dice is (6), and (6+6) equals (12).
Not multiples of (3) or (2):
1, 5, 7, 11
There are (4) numbers that are not multiples of (2) or (3). This means that there are (8) multiples of (2) or (3) between the numbers of (1) and (12), since (12 - 4 = 8)
The total number of outcomes is the following:

This is because there are (6) sides on a die, the number of outcomes is equal to (6) times (6), thus (
) or (
).
Now set up the probability equation:

Substituted,

Write as a decimal:
0.222
As a percent:
22.2%
The distance from his home to his work place is 118.125 miles
<h3>How to find the distance from his home to his work place?</h3>
He drove from home to work at an average speed of 45 mph. Therefore,
speed = 45 mph
let
time = x
speed = distance / time
distance = 45x
His return trip home took 45 minutes longer because he could only drive at 35 mph. Therefore,
45 minutes = 0.75 hours
distance = 35(x + 0.75)
distance = 35x + 26.25
Therefore,
45x = 35x + 26.25
45x - 35x = 26.25
10x = 26.25
x = 26.25 / 10
x = 2.625
Therefore,
distance = 45(2.625) = 118.125 miles
learn more on distance here: brainly.com/question/21329221
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