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Mariulka [41]
3 years ago
12

Divide (x^3-20x+16)/(x-4)

Mathematics
2 answers:
Lorico [155]3 years ago
8 0
\frac{( x^{3}-20x+16) }{(x-4)}

Use the rational root theorem:
a_{o}=16, a_{n}=1

The dividers of a_{o}: 1,2,4,8,16 
The dividers of a_{n}: 1

Therefore, check the following rational numbers: +-\frac{1,2,4,8,16}{1}

\frac{4}{1} is a root of the expression, so factor out x-4

Compute \frac{ x^{3}-20x+16 }{x-4} to get the rest of the equation.

\frac{(x-4)( x^{2} +4x-4)}{x-4}

Cancel the common factor:
x^{2}+4x-4 is the final answer
tankabanditka [31]3 years ago
5 0

Answer 1 d 2b 3b 4 a

Step-by-step explanation:

Dividing polynomials quick check goodluck 2019

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A 450-gallon tank full of water is draining at a rate of 20 gallons per minute.
Stels [109]

Answer:

The answer is below

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. The independent variable (input) does not depend on other variables while the dependent variable (output) depend on other variables.

In this question, amount of water in tank is dependent variable and the time taken is the independent variable. Let y represent amount of water in tank and x represent the time it has been draining. Therefore:

a) This can be represented by the equation:

y = 450 -  20x

At 7 minutes (x = 7)

y = 450 - 20(7)

y = 310 gallons

b) For 200 gallons (y = 200), the time taken is:

200 = 450 - 20x

200 - 450 = -20x

-20x = -250

x = -250/-20

x = 12.5 minutes

c) y = 450 - 20x

d) The graph was plotted using geogebra onling graphing calculator.

e) When the tank is empty, y = 0, hence

0 = 450 - 20x

20x = 450

x = 450 / 20

x = 22.5 minutes

6 0
3 years ago
Assume that X is Normal with mean $ 240 and standard deviation $60 . the probability that , in a randomly selected week , Dan wi
enyata [817]

Answer:

The probability of Dan making less than $255 is 0.5987 or 59.87%

Step-by-step explanation:

Given that:

Mean = μ = $240

SD = σ = $60

We have to find the probability that Dan will make less than $255

First of all, we have to find the z-score of 255

z-score is denoted by z and is given by the formula

z = \frac{x-mean}{SD}

Here,

x = 255

Putting the values

z = \frac{255-240}{60}\\z = \frac{15}{60}\\z = 0.25

Now we have to look at the z-score table to find the probability of 0.25

P(x<255) = 0.5987

Converting into percentage

59.87%

Hence,

The probability of Dan making less than $255 is 0.5987 or 59.87%

3 0
3 years ago
Find the sum of all multiples of 4 between 25 and 100​
Mademuasel [1]

Answer:

Sum of all multiples of 4 between 25 and 100 is 1116.

Step-by-step explanation:

Multiples of 4 between 25 and 100 = 28,32,36,40..............,96

let's check the series whether it is an arithmetic progression

a1 = 28 , a2 = 32 , a3 = 36 , a4 = 40

Common difference (d)=a2-a1=32-28 = 4

=a3-a2=36-32 = 4

=a4-a3=40-36 = 4

Common difference exists then the series of numbers is an Arithmetic progression.

To find number of terms :

a(a1) = 28 , d = 4 , l( last term ) = 96

l = a + (n-1)d

96 = 28 + (n-1)4

96 - 28 = (n-1)4

68 = (n-1)4

68/4 = (n-1)

17 = n - 1

17 + 1 = n

18 = n

Sum of all terms:

a = 28 , d = 4 , n = 18 , l = 96

Sn = n/2 ( a + l )

S18 = 18 / 2 (28 + 96)

S18 = 9 (124)

S18 = 1116

Therefore,Sum of all multiples of 4 between 25 and 100 is 1116.

<em>NOTE:</em>

<em>Here </em><em>100 </em><em>is </em><em>also</em><em> </em><em>a </em><em>multiple </em><em>of </em><em>4</em><em> </em><em>but </em><em>question</em><em> </em><em>is </em><em>asked </em><em>between</em><em> </em><em>2</em><em>5</em><em> </em><em>and </em><em>100 </em><em>so </em><em>100 </em><em>is </em><em>not </em><em>considered </em><em>in </em><em>multiples.</em>

7 0
3 years ago
Solve for x, simplify as much as possible<br><br> 3x/2=5
Andrej [43]
<span>3x/2=5
3x = 10
x = 10/3
hope it helps</span>
4 0
4 years ago
Read 2 more answers
PLEASE HELP I HAVE 8 min left
sweet-ann [11.9K]

Answer:

I would help but I can't see the picture... sorry good luck

Step-by-step explanation:

4 0
3 years ago
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