Pls help I need to pass this

What are the quotient and remainder of (x^5-x^3+-5) divided by (x-2)

pishuonlain [190]

Answer:

x⁴+2x³ +3x²+6x +12 r. $\dfrac{19}{x-2}$

Step-by-step explanation:

You can do this through synthetic division. It is a shorthand way of dividing polynomials.

First you need to make your divisor equal to zero so you can solve for what goes into the division box:

x - 2 = 0 → x = 2

The next step is to arrange your polynomials in descending powers. All missing terms, you will put in a zero.

x⁵ - x³ + (-5) → x⁵ + 0x⁴- x³ + 0x² + 0x + (-5)

Now you can proceed to synthetic division. Make an upside down division box with the divisor outside and the coefficients of the dividend listed, along with their sign. Leave a space below the divident

+2 | +1 0 -1 0 0 -5

|

Next you bring down the first coefficient:

+2 | +1 0 -1 0 0 -5

|

+1

Then you multiply it by the divisor and write the product under the next coefficient:

+2 | +1 0 -1 0 0 -5

| +2

+1

Next add the column and put the sum below it:

+2 | +1 0 -1 0 0 -5

| +2

+1 +2

Then multiply again and repeat until you reach the last coefficient:

+2 | +1 0 -1 0 0 -5

| +2 +4 +6 +12 +24

+1 +2 +3 +6 +12 +19

Now that you have your results, add in the x and their powers. The powers will start with the highest power but 1 less than the dividend. Since the dividend's highest power is 5, then the quotient's highest power will be 4. Then write it in descending order :

+1x⁴ +2x³ +3x² +6x +12 +19

Now the last coefficient is your remainder. So your results will be:

x⁴+2x³ +3x²+6x +12 r. $\dfrac{19}{x-2}$

7 0

3 years ago

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The midpoint of UV is point W. What are the coordinates of point V?

madreJ [45]

Since you don't provide the coordinates of the point W, I will help you in a general form anyway. In the Figure below is represented the segment that matches this problem. We have two endpoints U and V. So, by using the midpoint formula we may solve this problem:

$Midpoint=W=W(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})=W(x_{3}, y_{3}) \\ \\ where:\\ \ U=U(x_{1}, y_{1}) \ and \ V=V(x_{2}, y_{2}) \\ \\ and: \\ x_{3}=\frac{x_{1}+x_{2}}{2} \\ y_{3}=\frac{y_{1}+y_{2}}{2}$

Therefore:

$x_{2}=2x_{3}-x_{1} \\ y_{2}=2y_{3}-y_{1}$

So we know $x_{3} \ and \ y_{3}$ but we also must know $x_{1} \ and \ y_{1}$

Finally, knowing the points U and W we can find the endpoint V.

7 0

3 years ago

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A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. Two hours later, a cyclist sta

yanalaym [24]

If the runner moves at 6 miles per hour for 2 hours before the cyclist starts, the runner has a 12 mile lead at the beginning. If the cyclist is going at 16 miles per hour, he is overtaking the runner at 10 miles per hour, because 16-6=10. Then, the amount of time it takes the cyclist to go 2 miles in 10 miles per hour is the answer. this is 1/5 of an hour, or 12 minutes.

5 0

3 years ago

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Can I please please get help with this?

Hatshy [7]

Answer:

the answer is 42

84÷2

42

4 0

3 years ago

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drag each expression to the correct location on the graph and equation. not all expressions will be used. complete the given dia

Svetllana [295]

What we have here in the picture is a graph of a segment. The goal is to find the segment's length, which we can do by using the distance formula:

$d^2=(x_2-x_1)^2-(y_2-y_1)^2$

Note that the distance between two points is equal to the length of the line segment that joins them.

So now we already have answers for two of the boxes.

The difference in the x-coordinates gives us the horizontal distance between the two points, while the difference in the y-coordinates gives us the vertical distance between the points.

So, the other two boxes should contain:

5 0

1 year ago