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aleksley [76]
2 years ago
14

(5x^3-8x^2+9x+12)/(x-3) please answer with sentences on how to do it step by step. thanks!

Mathematics
1 answer:
umka21 [38]2 years ago
5 0

Answer:

5x^2 + 7x + 30 + 102/x-3

Step-by-step explanation:

     _________________

x-3| 5x^3 - 8x^2 + 9x + 12      

   

First you would want to set it up as either long polynomial division or using synthetic division. Whichever one is easier for you. However, I am going to use long polynomial division since you might not be familiar with synthetic division just yet.

    _<u>5x^2</u>_____________

x-3|  5x^3 - 8x^2 + 9x + 12        Because 5x^3 divided by x gives you 5x^2

     <u>- (5x^3 - 15x^2)</u>______       and -3 times 5x^2 gives you -15x^2

              0 + 7x^2 +9x               But since the negative is outside the   parentheses then you distribute it turning he -15x^2 it into +15x then adding it to the -8x^2 above it thus giving you 7x^2. Afterwards bring down the 9x.

A negative times a negative is a positive (just as a reminder)

Next,

    _<u>5x^2+7x</u>_________

x-3| 5x^3 - 8x^2 + 9x + 12

   <u>- (5x^3 - 15x^2)</u>______                    7x^2 divided by x gives you 7x

            0 + 7x^2 + 9x

               <u>- (7x^2 - 21x)</u>___                  and 7x times -3 gives you -21x

                       0 + 30x +12                  you distribute the negative in the parentheses again.  

 

Then,

     _<u>5x^2   +7x  +30</u>____

x-3| 5x^3 - 8x^2 + 9x + 12

   <u>- (5x^3 - 15x^2</u>)______

            0 + 7x^2 + 9x

              <u> - (7x^2 - 21x)</u>___

                       0 + 30x + 12                30x divided by x gives you 30.

                          <u>- (30x - 90)</u>                Distribute the negative again.

                                0  + 102                102 is the remainder.  

When writing remainders in long polynomial equations, it is expressed by writing the remainder over the divisor. Which is 102/x-3.

So the answer is 5x^2 + 7x + 30 + 102/x-3.      

                   

               

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Given: ∆ABC, m∠C = 90° CB = 8, m∠B = 38º Find the area of a circumscribed circle. Find the area of the inscribed circle.
vitfil [10]

Answer:

Circumscribed circle: Around 80.95

Inscribed circle: Around 3.298

Step-by-step explanation:

Since C is a right angle, when the circle is circumscribed it will be an inscribed angle with a corresponding arc length of 2*90=180 degrees. This means that AB is the diameter of the circle. Since the cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse:

\cos 38= \dfrac{8}{AB} \\\\\\AB=\dfrac{8}{\cos 38}\approx 10.152

To find the area of the circumscribed circle:

r=\dfrac{AB}{2}\approx 5.076 \\\\\\A=\pi r^2\approx 80.95

To find the area of the inscribed circle, you need the length of AC, which you can find with the Pythagorean Theorem:

AC=\sqrt{10.152^2-8^2}\approx 6.25

The area of the triangle is:

A=\dfrac{bh}{2}=\dfrac{8\cdot 6.25}{2}=25

The semiperimeter of the triangle is:

\dfrac{10.152+6.25+8}{2}\approx 24.4

The radius of the circle is therefore \dfrac{25}{24.4}\approx 1.025

The area of the inscribed circle then is \pi\cdot (1.025)^2\approx 3.298.

Hope this helps!

6 0
3 years ago
64, –48, 36, –27, ...
frozen [14]
The only formula that can be used to describe the sequence is definitely the third one f(x + 1) = -3/4 f(x). So count like that64* -\frac{3}{4}  = -48&#10;48* -\frac{3}{4} = 36 and so on. You can check others by yourself to check if I'm right or not.
4 0
3 years ago
Multiply 4 and 7. Then, divide by q.
Makovka662 [10]

Answer:

28/q

Step-by-step explanation:

4 times 7 equals 28 and then divide 28 by q

5 0
3 years ago
For his long distance phone service, Ahmad pays a $3 monthly fee plus 11 cents per minute. Last month, Ahmad's long distance bil
Alenkinab [10]

Answer:

198 minutes (3 hours and 18 minutes)

Step-by-step explanation:

24.78 - 3 = 21.78

21.78 ÷ 0.11 = 198

Hope this helped!

Stay safe! <3

3 0
2 years ago
(I is confusion)What fraction of an hour is 35 minutes?give your answer in simplest form
lesya [120]
Answer
1 hour=60 minutes
Fraction= 35/60= 7/12
So your answer would be 7/12 :)
​
5 0
2 years ago
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