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3 years ago

Find the roots of the equation x^3-3x^2+x+5

1 answer:

5 0

First observe that x=-1 is a root of the equation. Use long division to divide x^3-3x^2+x+5 by x+1, we find that (x^3-3x^2+x+5)/(x+1)=(x^2-4x+5). Now we need to find the roots of x^2-4x+5.
x^2-4x+5=0,
x^2-4x+4=-1,
(x-2)^2=i,
x-2=i or -1,
x=2+i or 2-i.
The three roots are 2+i, 2-i, -1.

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klemol [59]

Answer:

Step-by-step explanation:

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3 years ago

Solve for x and y:<br>x = <br>y =

ICE Princess25 [194]

Answer:

x = 15

y = 21

Step-by-step explanation:

*triangle sum theorem*

(6x - 11)° + (81)° + (x + 5)° = 180°

(7x - 6)° + (81)° = 180°

(7x)° + (75)° = 180°

(7x)° = (105)°

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*vertical angle theorem* *triangle sum theorem*

(6x - 11)° + (4y - 18)° + (y + 14)° = 180°

(79°) + (4y + y) + (14 - 18)°

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3 years ago

two trains leave stations 210 miles apart at the same time and travel tword each other. one train at 85 miles per hour while the

hodyreva [135]

recall your d = rt, distance = rate * time.

let's say we have two trains, A and B, A is going at 85 mph and B at 65 mph.

they are 210 miles apart and moving toward each other, at some point they will meet, when that happens, the faster train A has covered say d miles, and the slower B has covered then the slack from 210 and d, namely 210 - d.

When both trains meet, A has covered more miles than B because A is faster, however the time both have been moving, is the same, say t hours.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{Train A}&d&85&t\\ \textit{Train B}&210-d&65&t \end{array}\\\\ \dotfill\\\\ \begin{cases} \boxed{d}=85t\\ 210-d=65t\\[-0.5em] \hrulefill\\ 210-\boxed{85t}=65t \end{cases} \\\\\\ 210=150t\implies \cfrac{210}{150}=t\implies \cfrac{7}{5}=t\implies \stackrel{\textit{one hour and 24 minutes}}{1\frac{2}{5}=t}$

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3 years ago

I will give brainliest to the first one that does it correctly

Effectus [21]

Answer:

180-138

=42, is the answer

8 0

3 years ago

The perimeter of a rectangular toddler play area is 100 feet. The length is 10 feet more than 3 times the width. Find the length

Mekhanik [1.2K]

Answer:

length and width = 40 and 10 ft.

Step-by-step explanation:

The perimeter of a rectangular toddler play area is 100 feet.

Perimeter = 2(length + width)

Let the width = w

The length is 10 feet more than 3 times the width. Length = 10+(3w)

now put the values

100 = 2(10+3w + w)

100 = 2w + 20 + 6w

100 = (2w + 6w) + 20

100 = 8w + 20

8w = 100 - 20

w = $\frac{80}{8}$

w = 10 feet.

Now Length = 10+ (3w)

= 10+( 3 × 10)

= 10 + 30

= 40 feet

Therefore, length = 40 feet and width = 10 feet

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3 years ago