1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
densk [106]
3 years ago
5

Use the real zeros to factor f x^4 plus 10^3 minus 20x^2 minus 90x plus 99

Mathematics
1 answer:
Furkat [3]3 years ago
7 0

Answer:

f(x) = (x + 11) (x + 3) (x − 1) (x − 3)

Step-by-step explanation:

f(x) = x⁴ + 10x³ − 20x² − 90x + 99

f(x) is a fourth order polynomial, so it has 4 roots.  Use rational root theorem to find possible rational roots.

±99, ±11, ±9, ±3, ±1

By trial and error, the zeros are -11, -3, 1, and 3.

f(x) = (x + 11) (x + 3) (x − 1) (x − 3)

You might be interested in
I need help. See attachment for detail.
lesantik [10]

Answer:

4.5

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
Please help me !! ASAP!
Anettt [7]

Answer:

3√265

Step-by-step explanation:

The distance between the given points is √265. If all the side are the same length on an equilateral triangle, then the perimeter is 3 times as long.

3 0
3 years ago
Answer the question below
lys-0071 [83]

Answer:

A) -1

Step-by-step explanation:

\frac{3 + 2\sqrt{5} }{2\sqrt{5}-3 } \\

We can rewrite 2√5 - 3 as -(3 + 2√5)

Therefore,

\frac{3+ 2\sqrt{5} }{-(3 + 2\sqrt{5} )} \\

We can cancel out 3 + 2√5 both in the numerator and the denominator. So we get

= 1/-1

= -1

Answer : A) -1

Thank you.

6 0
3 years ago
Lim (n/3n-1)^(n-1)<br> n<br> →<br> ∞
n200080 [17]

Looks like the given limit is

\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}

With some simple algebra, we can rewrite

\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)

then distribute the limit over the product,

\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, <em>e</em> :

\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n

To make our limit resemble this one more closely, make a substitution; replace 9/(<em>n</em> - 9) with 1/<em>m</em>, so that

\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1

From the relation 9<em>m</em> = <em>n</em> - 9, we see that <em>m</em> also approaches infinity as <em>n</em> approaches infinity. So, the second limit is rewritten as

\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}

Now we apply some more properties of multiplication and limits:

\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9

So, the overall limit is indeed 0:

\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}

7 0
3 years ago
Trains Two trains, Train A and Train B. weigh a total of 196 tons. Train A is heavier than Train B. The
aleksklad [387]

Answer:

Train A = 128

Train B = 68

Step-by-step explanation:

We can set up a system of equations for this problem

Let A = # of tons of Train A

Let B = # of tons of Train B

A + B = 196

A = B + 60

Now, we plug in A for the first equation, using substitution

(B+60) + B = 196

2B + 60 = 196

Subtract 60 from both sides

2B = 136

Divide both sides by 2

B = 68

Plug in 68 for B in the 2nd equation

A = 68 + 60

A = 128

Checking work: 128 + 68 = 196 :D hope this helped

5 0
2 years ago
Other questions:
  • Rick has 7 cats. Carrie has 14 cats. How many fewer cats does Rick have
    12·1 answer
  • Find the sum in simplest form. 10 3/5 + 2 3/5
    10·1 answer
  • Find the value of x in each case:
    13·1 answer
  • When a customer places an order at Ying Ying's bakery, there is an 8\%8%8, percent probability that the customer will report a f
    12·1 answer
  • A home improvement store buys snow shovels from a supplier for $8.50. The day before a snowstorm the store manager marks up the
    9·2 answers
  • Name a survey that you would like to do and what method of survey are you using?
    6·2 answers
  • Factor the expression using the GCF.<br><br> 26x - 13
    10·2 answers
  • On school days, Kiran walks to school. Here are the lengths of time, in minutes, for Kiran’s walks on 5 school days.
    10·1 answer
  • Find the volume of the prism.​
    11·1 answer
  • 10-2 (2x+1) = 4 (x-2)
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!