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MatroZZZ [7]
3 years ago
7

Long Division: (3x^4-8x^3-x^2+9x+5) / (x-2) pleaseee answer this

Mathematics
1 answer:
Drupady [299]3 years ago
7 0

3<em>x</em>⁴ = 3<em>x</em>³ • <em>x</em>, and

3<em>x</em>³ (<em>x</em> - 2) = 3<em>x</em>⁴ - 6<em>x</em>³

Subtract this from the numerator to get a remainder of

(3<em>x</em>⁴ - 8<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) - (3<em>x</em>⁴ - 6<em>x</em>³) = -2<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5

-2<em>x</em>³ = -2<em>x</em>² • <em>x</em>, and

-2<em>x</em>² (<em>x</em> - 2) = -2<em>x</em>³ + 4<em>x</em>²

Subtract this from the previous remainder to get a new remainder of

(-2<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) - (-2<em>x</em>³ + 4<em>x</em>²) = -5<em>x</em>² + 9<em>x</em> + 5

-5<em>x</em>² = -5<em>x</em> • <em>x</em>, and

-5<em>x</em> (<em>x</em> - 2) = -5<em>x</em>² + 10<em>x</em>

Subtract this from the last remainder to get a new one of

(-5<em>x</em>² + 9<em>x</em> + 5) - (-5<em>x</em>² + 10<em>x</em>) = -<em>x</em> + 5

-<em>x</em> = -1 • <em>x</em>, and

-1 (<em>x</em> - 2) = -<em>x</em> + 2

This gives a new remainder of

(-<em>x</em> + 5) - (-<em>x</em> + 2) = 3

3 does not divide <em>x</em>, so we're done.

So, we have

(3<em>x</em>⁴ - 8<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) / (<em>x</em> - 2) = 3<em>x</em>³ - 2<em>x</em>² - 5<em>x</em> - 1 + 3/(<em>x</em> - 2)

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maksim [4K]

Answer:

B. 21.2

Step-by-step explanation:

Perimeter of ∆ABC = AB + BC + AC

A(-4, 1)

B(-2, 3)

C(3, -4)

✔️Distance between A(-4, 1) and B(-2, 3):

AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

AB = \sqrt{(-2 - (-4))^2 + (3 - 1)^2} = \sqrt{(2)^2 + (2)^2)}

AB = \sqrt{4 + 4}

AB = \sqrt{16}

AB = 4 units

✔️Distance between B(-2, 3) and C(3, -4):

BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

BC = \sqrt{(3 - (-2))^2 + (-4 - 3)^2} = \sqrt{(5)^2 + (-7)^2)}

BC = \sqrt{25 + 49}

BC = \sqrt{74}

BC = 8.6 units (nearest tenth)

✔️Distance between A(-4, 1) and C(3, -4):

AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

AC = \sqrt{(3 - (-4))^2 + (-4 - 1)^2} = \sqrt{(7)^2 + (-5)^2)}

AC = \sqrt{47 + 25}

AC = \sqrt{74}

AC = 8.6 units (nearest tenth)

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8 0
3 years ago
Please help <br> !!!!!!!!!!!!!!!!
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Answer:

6 in 2.

Step-by-step explanation:

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3 years ago
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A company manufactures cell phones. In August, a random sample of 125 cell phones was inspected, and 3 phones were found to be d
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Answer:

192

Step-by-step explanation:

To find how many phones are expected to be defective, we need to represent the values in a fraction.

\dfrac{x}{8000}=\dfrac{3}{125}

x = number of defective phones

Now we can solve this using algebra.

To get the value of x we need to multiply both sides by 8000 to leave x alone.

x=\dfrac{3}{125}(8000)

x=0.024(8000)

x=192

So around 192 cell phones are expected to be defective out of 8000 phones.

6 0
3 years ago
Evaluate (212)base3-(121)base3+(222)base3​
NemiM [27]

Answer:

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3 years ago
What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (
aalyn [17]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx

in this problem we have

the point (5,12) is on the line of direct variation

so

Find the constant of proportionality k

y/x=k-------> substitute ------> k=12/5

the equation is

y=\frac{12}{5}x

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

<u>case A)</u> point (0,0)

x=0\ y=0

Substitute the value of x and y in the direct variation equation

0=\frac{12}{5}*0

0=0 -------> is true

therefore

the point (0,0) is on the line of direct variation

<u>case B)</u> point (2.5,6)

x=2.5\ y=6

Substitute the value of x and y in the direct variation equation

6=\frac{12}{5}*2.5

6=6 -------> is true

therefore

the point (2.5,6) is on the line of direct variation

<u>case C)</u> point (3,10)

x=3\ y=10

Substitute the value of x and y in the direct variation equation

10=\frac{12}{5}*3

10=7.2 -------> is not  true

therefore

the point (3,10) is not on the line of direct variation

<u>case D)</u> point (7.5,18)

x=7.5\ y=18

Substitute the value of x and y in the direct variation equation

18=\frac{12}{5}*7.5

18=18 -------> is true

therefore

the point (7.5,18) is on the line of direct variation

<u>case E)</u> point (12.5,24)

x=12.5\ y=24

Substitute the value of x and y in the direct variation equation

24=\frac{12}{5}*12.5

18=30 -------> is not true

therefore

the point  (12.5,24) is not on the line of direct variation

<u>case F)</u> point (15,36)

x=15\ y=36

Substitute the value of x and y in the direct variation equation

36=\frac{12}{5}*15

36=36 -------> is true

therefore

the point (15,36) is on the line of direct variation

therefore

<u>the answer is</u>

(0,0)

(2.5,6)

(7.5,18)

(15,36)


5 0
3 years ago
Read 2 more answers
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